FEA in Practice â€“ Instructor Manual - Sustainability Workshop

Finite Element Analysis in Practice

Instructor Manual

Based on: Autodesk® Algor® Simulation Professional 2011

II FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010

FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010 III

© 2010 Autodesk, Inc. All rights reserved.

Finite Element Analysis in Practice – Instructor Manual Based on: Autodesk® Algor® Simulation Professional 2011

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Disclaimer

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Published by: Autodesk, Inc. 111 Mclnnis Parkway San Rafael, CA 94903, USA

IV FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010

FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010 V

COURSE INTRODUCTION: Overview .....................................................................................................VII Software Installation, Services, and Support ..............................................VII

Installing and Running Autodesk® Algor® Simulation ........................................VII System Requirements ....................................................................................VIII Autodesk Algor Simulation Help ...................................................................... IX Subscription Center ......................................................................................... X Web Links ........................................................................................................ X Tutorials .......................................................................................................... XI Webcasts and Web Courses ........................................................................... XI How to Receive Technical Support ................................................................. XI Updates ..........................................................................................................XII

Navigating the User Interface .....................................................................XII Toolbars........................................................................................................ XIV Using the Keyboard and Mouse ..................................................................... XV Introduction to the ViewCube ........................................................................ XVI Additional View Controls .............................................................................. XVII Legacy View Controls in Autodesk Algor Simulation ................................... XVIII

Notes Concerning the “Steps for Exercises” Section .............................. XVIII

PRESENTATION SLIDESHOW: Introduction ................................................................................................... 3 FEA Overview and Examples using Autodesk® Algor® Simulation ................. 8

Introductory Example .................................................................................. 12 FEA Concepts ............................................................................................. 16

Exercise A - FEA Example by Hand .............................................................. 25

Analysis Options ......................................................................................... 30 Element Options ......................................................................................... 36 Meshing and Modeling ................................................................................ 37 Loads and Constraints ................................................................................ 41 Truss Elements ........................................................................................... 49

Exercise B - Truss Frame Model.................................................................... 50

Beam Elements .......................................................................................... 51 Exercise C - Support Beam Under Gravity ..................................................... 53

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2-D Elements .............................................................................................. 54 Exercise D - Axisymmetric Thick-walled Cylinder ........................................... 56

Plate/Shell Elements ................................................................................... 56 Exercise E - Plate Under Uniform Pressure ................................................... 59

Brick Elements ............................................................................................ 59 Exercise F - Cantilever Beam Model .............................................................. 60

Comparing Element Types ......................................................................... 61 Exercise G - Comparing Element Types ........................................................ 61

Mesh Convergence ..................................................................................... 62 Exercise H - Mesh Convergence.................................................................... 64

Meshing CAD Solid Models ........................................................................ 65 Exercise I - Bracket Model ............................................................................. 67

Exercise J - Hanger Assembly Model ............................................................ 69

Combining Element Types .......................................................................... 69 Contact ....................................................................................................... 71

Exercise K - Linear Contact Model ................................................................. 72

Solving Options ........................................................................................... 73 Results Evaluation ...................................................................................... 74 Presentation of Results ............................................................................... 77 Other Analysis Types .................................................................................. 80

Thermal Analysis ................................................................................... 81 Exercise L - Thermal Model ..................................................................... 85

Electrostatic Analysis ............................................................................. 86 Fluid Flow Analysis ................................................................................ 89 Mechanical Event Simulation (MES) ..................................................... 92

Exercise M - Nonlinear Material Model .................................................. 101

Combining Analysis Types (Multiphysics) ................................................. 103 Material Models ........................................................................................ 105

Exercise N - Mechanical Event Simulation, Geneva Mechanism ................ 107

STEPS FOR EXERCISES .......................................................... SE.1

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Course Introduction Overview

This course will introduce the students to the analysis products available within Autodesk® Algor® Simulation Professional and the proper usage of these tools. The program capabilities include static stress with linear and nonlinear material models, mechanical event simulation, heat transfer, fluid flow, linear dynamics, natural frequency (modal) analysis with nonlinear materials, transient mass transfer, and electrostatics analyses. The course will utilize hand-built models and those originating from CAD solid modeling programs. The students will learn basic Finite Element Analysis (FEA) theory, the various meshing options, available load and constraint options, and how to create results presentations (including images, animations, and HTML reports). The Finite Element Analysis in Action course curriculum is organized into three main sections, as follows.

• This Course Introduction section contains necessary prerequisite information concerning

software installation and configuration, how to obtain updates and technical support, and basics concerning the user interface. The program emulates the view orientations and mouse actions of many popular CAD packages. However, the procedures detailed within this course are all based on the default Algor Simulation settings for the views and mouse functions. Please ensure that all student workstations are set up accordingly so that the software behavior will be consistent with the text.

• The Presentation Slideshow is provided in two forms. Within the second section of this Instructor Manual, the slides are presented in handout fashion, two per page. In addition, a separate Microsoft® PowerPoint® presentation is included for classroom projection.

• The Steps for Exercises section includes descriptions of all of the exercises included within the slideshow presentation along with keystroke-specific procedures for correctly completing the exercises.

Software Installation, Services, and Support

Installing and Running Autodesk® Algor® Simulation

The simulation software is distributed on DVDs with the exception of software for the Linux platform, which is distributed on CDs. In addition, the software may be downloaded from the Autodesk website. When you place the software DVD into a DVD-ROM drive, a launch dialog having four options will appear. If you want to set up the software on a client workstation, whether you will be using a license locked to a single computer or a network license, press the "Install Products" button. If using a network license, you must already have the license server software installed to a computer on the network. If you wish to create pre-configured deployments for installing the product on multiple client workstations, choose the "Create Deployments" command. If you want to set up the computer as a license server to control the number of concurrent users through a network, or, if you wish to install optional reporting tools, press the "Install Tools and Utilities" command. Finally, a fourth command on the launch screen, "Read the Documentation," leads to a screen from which you can access a ReadMe file and other installation and licensing guides.

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During the product installation process, you will need to specify your name, the name of your organization. You will also need to enter the product serial number and the product key. Otherwise, you will be limited to a 30-day trial period. To customize the installation location on your computer, the components to be installed, and/or to specify a network license server, you will have to press the "Configuration" button that appears on one of the screens during the installation process. Then, follow the prompts, provide the required information, and click the "Configuration Complete" button to continue the installation process. Any time after the installation, you will be able to start the software by using the available shortcut found in the "Start" menu folder, "All Programs: Autodesk: Autodesk Algor Simulation." The version number is included in the start menu folder name and shortcut. The name of the shortcut will depend upon which package has been purchased ("Simulation," "…Simulation MES," "…Simulation CFD," or "…Simulation Professional"). In the dialog that appears when the program is launched, you will be able to open an existing model or begin a new model. The simulation software will be used to create, analyze, and review the results of an analysis within a single user interface, regardless of the analysis type.

System Requirements

We recommend the following system specifications for a Microsoft Windows® platform running Autodesk Algor Simulation. These specifications will allow you to achieve the best performance for large models and advanced analysis types.

32-Bit

• Dual Core or Dual Processor Intel® 64 or AMD 64, 3 GHz or higher

64-Bit *

• 2 GB RAM or higher (3 GB for MES and CFD applications)

• 30 GB of free disk space or higher

• 256 MB or higher OpenGL accelerated graphics card

• DVD-ROM drive

• Dual Core or Dual Processor Intel 64 or AMD 64, 3 GHz or higher

• 8 GB RAM or higher

• 100 GB of free disk space or higher

• 512 MB or higher OpenGL accelerated graphics card

• DVD-ROM drive

Supported Operating Systems:

• Microsoft Windows 7 (32-bit and 64-bit editions) • Microsoft Vista™ (32-bit and 64-bit editions) • Microsoft Windows Server 2003 and Windows Server 2008 • Microsoft Windows XP (32-bit and 64-bit editions) • Linux **

Other Requirements (All Platforms):

• Mouse or pointing device • Sound card and speakers *** • Internet connection *** • Web browser with Adobe Flash Player 10 (or higher) plug-in ***

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Notes Concerning System Requirements:

* We recommend usage of a 64-bit version of the operating system to run large models of any analysis type and for Mechanical Event Simulation, CFD, and Multiphysics analyses. While a 32-bit machine can be configured for larger system memory sizes, architectural issues of the operating system limit the benefit of the additional memory.

** Linux may be used as a platform for running the solution phase of the analysis only. It

may be used for a distributed processing (or clustering) platform. However, pre- and post-processing is done in the graphical user interface, which must be installed and run on a Microsoft Windows platform.

*** These requirements are due to the use of multimedia in our product line and the

availability of distance learning webcasts, software demos, and related media. Minimum system requirements and additional recommendations for Linux platforms may be found on the Autodesk website. To navigate to the Autodesk Algor Simulation web page, access the HELP pull-down menu within the user interface, select the "Web Links" pull-out menu, and choose the "Autodesk Algor Simulation" link. Autodesk Algor Simulation Help, often referred to as the Help files or user’s guide, contains the following information:

Autodesk Algor Simulation Help

• Documentation for all of the model creation options within the user interface • Documentation for all of the Autodesk Algor Simulation analysis types • Documentation for all of the result options available within the user interface • Step-by-step examples that illustrate many modeling and analysis options

How to Access the Help Files

• From the user interface, access the HELP pull-down menu and select the "Contents" command. The Autodesk Algor Simulation Help title page of will appear.

• You can navigate through the user's guide via the table of contents to the left or by using the "Search" or "Index" tabs.

Features of the Help Files

• Autodesk Algor Simulation Help is a set of compiled help files that are installed with the software but are also accessible from the Autodesk website.

• Hyperlinks and a table of contents make it easy to move quickly from topic to topic. • The Help window contains a standard Internet browser toolbar, so you can move forward

and backward and print with ease.

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Figure 1: Autodesk Algor Simulation User’s Guide

Search the Help Files using Keywords

• All of the pages in the Help files can be searched based on keywords. • The keywords are entered at the top of the "Search" tab on the left side of the User’s

Guide screen. Topics that match the search criteria are listed below. • Keywords are used to search the Help files. You may use single or multiple keywords. • Boolean operators (AND, OR, NEAR, and NOT) are available to enhance the search utility.

Also, phrases may be enclosed in quotes to search only for a specific series of words.

Subscription Center

Along with your Autodesk Algor Simulation software purchase, you have the option of purchasing various levels of Subscription Center access and support. The Subscription Center is accessible via the "key" icon near the right end of the program title bar and also via the "Help: Web Links" menu. Through the Subscription Center, you can download software updates, service packs, and add-on applications. You can access training media, such as topical webcasts. Finally, you can also submit technical support requests via the Subscription Center.

Web Links

Within the HELP pull-down menu of the Autodesk Algor Simulation user interface, there is a "Web Links" pull-out menu. The following content can be accessed via the web links within this menu:

• Autodesk Algor Simulation product page • Subscription Center • Services and Support information • Discussion Group

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• Training course information • Autodesk Labs – where you may obtain free tools and explore developing technologies • Manufacturing Community

Tutorials

Tutorials are available that demonstrate many of the capabilities of the Autodesk Algor Simulation software. Each analysis is presented through step-by-step instructions with illustrations to assist the user. The tutorials are accessed from the "Help: Tutorials" command and the associated model files are in the "\Tutorials\Models" subdirectory within the program installation folder. The tutorials will appear next to the user interface. You will be able to follow the steps using the software without switching between the two windows.

Webcasts and Web Courses

Webcasts focus on the capabilities and features of the software, on new functionality, on accuracy verification examples, and on interoperability with various CAD solid modeling packages. These streaming media presentations are available for on-demand viewing from the Subscription Center via your web browser. Similarly, web courses are also available for on-demand viewing. Web courses are typically longer in duration than webcasts and focus on more in-depth training regarding the effective usage of your simulation software. The topics cover a wide variety of application scenarios. For a list of available webcasts and web courses, follow the "Training" link from the home page of the Subscription Center. Choose the "Autodesk Algor Simulation" product in the "Browse the Catalog" list. This leads to the Autodesk Algor Simulation e-Learning page, in which the available webcasts and web courses are listed according to topic.

How to Receive Technical Support

Technical support is reachable through several contact methods. The means you can use may depend upon the level of support that was purchased. For example, customers with "Silver" support must obtain their technical support from the reseller that sold them the software. "Gold" subscription customers may obtain support directly from Autodesk. Five ways to contact Technical Support:

• Reseller: Obtain phone, fax, and/or e-mail information from your reseller. • Subscription Center: Access the Subscription Center from the link provided in the program

interface. Click the Tech Support link on the left side of the page and then click on the "Request Support" link.

• Autodesk Phone: (412) 967-2700 [or in USA/Canada: (800) 482-5467] • Autodesk Fax: (412) 967-2781 • Autodesk E-mail: [email protected]

When contacting Technical Support:

• Have your contract number ready before contacting Technical Support. • Know the current version number of your software. • Have specific questions ready. • Remember, Technical Support personnel cannot perform, comment on, or make

judgments regarding the validity of engineering work.

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Updates

The software is updated with new functionality on a continual basis. The following three types of releases are provided: 1. A major version: Indicated by the four-digit year of the software release (based upon

the Autodesk fiscal year, not the calendar year)

2. A "subscription" version: Customers with a current maintenance subscription are eligible for additional releases that may be made available between major product version releases. These are designated by the addition of the word "Subscription" after the major version number.

3. A service pack: Incorporates minor improvements to a major or subscription release and is indicated by the letters "SP" and a service pack number after the major or subscription version number.

How to Determine the Software Version

Access the HELP pull-down menu in the user interface and select the "About" command. This dialog will display the version that you are using. In addition, the program title bar and the splash screen that appears at each program launch will indicate the major version number of the software. However, as with the start menu group name and program shortcut, it will not indicate the subscription and service pack variants. How to Obtain an Update

Update notifications are provided via the "Communication Center" within the user interface. The Communication Center icon is located at the right end of the program window title bar. The state of the Communication Center icon changes whenever new information is available. The Communication Center provides up-to-date product support information, software patches, subscription announcements, articles, and other product information through a connection to the Internet. Users may specify how frequently the Live Update information will be polled—on-demand, daily, weekly, or monthly. When a program update notification is received, the user will be given the option of downloading and installing it.

Navigating the User Interface

In this section, we will introduce you to the Autodesk Algor Simulation user interface. This interface is the same for each of the available packages, including the foundational Algor Simulation product and the Algor Simulation CFD, MES, and Professional products. The only difference will be with regard to which advanced features or capabilities are enabled. We will begin with an overview of the major components of the graphical user interface. Then, we will discuss the toolbars, keyboard, mouse, ViewCube, and additional view controls. Please note that the behavior of the keyboard, mouse, and ViewCube – as discussed within this manual – are based on the default program settings for a clean installation of the product. Many of the features to be discussed are customizable via tabs and settings within the "Options" dialog, reachable via the "Tools: Options" pull-down menu command. Figure 2 on the next page, along with the legend that follows it, introduces the major components of the user interface. This manual is based on Autodesk Algor Simulation Professional 2011. Users of other versions may encounter differences between their version and the interface described herein.

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Figure 2: Autodesk Algor Simulation User Interface

Interface Legend:

A. Title Bar: The title bar displays the program name and version as well as providing links to the Autodesk Subscription Center and Communication Center.

B. Menu Bar: The menu bar is located just below the title bar and contains the pull-down menus. C. Toolbars: The toolbars provide the user with quick access to many commands. D. Tree View: The tree view has unique contents for each environment of the user interface. For the

FEA Editor, it shows the parts list and the units, various properties, and loads that will be used for the analysis. In the Results environment, you will see a list of results presentations and other post-processing-specific content. The components of the analysis report will be listed in the tree view within the Report environment.

E. ViewCube and Additional View Controls: These tools are used to manipulate the model display position, rotation, zoom, display pivot point, and so on. There is also an optional Compass feature that can be activated, providing a compass heading ring around the base of the ViewCube.

F. Display Area: The display area is where the modeling activity takes place. The title bar of the window displays the current environment and the model name. The FEA Editor environment is used to create the model, add the loads and constraints and perform the analysis. The Results environment is used to view results and to create images, graphs, and animations. The Report environment will be used to produce a formal report of the analysis, including desired results presentations.

G. Miniaxis and Scale Ruler: The miniaxis shows your viewpoint with respect to the three-dimensional working area. The scale ruler gives you a sense of the model size,

H. Status Bar: The status bar displays important messages.

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Toolbars

Autodesk Algor Simulation accesses program functions through pull-down menus, context menus, and toolbars. The available toolbars and menus vary for each program environment (FEA Editor, Results, and Report). By default, the toolbars are positioned at the top of the screen, just under the pull-down menus. As is true for the menus, commands are logically grouped into a number of different toolbars. For example, one toolbar includes predefined view orientations, another includes various selection tools, still another includes structured meshing tools, and so on. These may be displayed, hidden, or repositioned as desired. Most of the toolbars and pull-down menus will not appear until an existing model is opened or a new model is created. To see the toolbars of the FEA Editor at this time, start the program. Dismiss the "What's New" screen if it appears, select the "New" icon in the initial dialog ("Open" / "New"), and click the "New" button. Navigate to a working folder, type in the name of your choice in the "File name:" field, and click the "Save" button. How to Display or Hide Specific Toolbars

To display or hide toolbars or to adjust the icon size or style, access the TOOLS pull-down menu and select the "View Toolbars..." command. To display another toolbar activate the checkbox for that toolbar. Deactivate the checkbox for each toolbar that you prefer to hide. Additional checkboxes are provided for the toolbar size and style options. Press the "Close" button to exit the "Toolbars" screen. How to Dock Toolbars

Toolbars can be docked on the top, bottom, and/or sides of the display area. To dock a toolbar, first click on the title bar and drag it toward one of the edges of the display area. Once you reach the edge, the shape will change to signify that you are at a location where the toolbar may be docked. Release the mouse and the toolbar will dock at the location of the mouse. That is, it will snap to the docked position and the title bar will disappear. This is illustrated in the following images.

Figure 3: Steps to Dock a Toolbar

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Using the Keyboard and Mouse

The keyboard and mouse will both be used to operate within the user interface. The keyboard will be used to enter the required data for loads, constraints, material properties, and so on. It will also be used to modify the behavior of particular mouse operations. That is, certain keyboard keys, when held down, will change the behavior of the mouse.

The software supports a number of different mouse configurations. This document assumes that the default template for a new installation is in effect. However, user settings, or those retained from a prior Autodesk Algor Simulation installation, may cause the behavior to differ from that described herein. To ensure that your mouse actions follow the descriptions in this book, access the "Tools: Options: Mouse Options" dialog and choose the "Algor Simulation" template. The left mouse button will be used to select items. How items are selected will depend upon the selection mode chosen in the "Selection: Shape" pull-out menu or toolbar. The type of objects that are selected (such as lines, vertices, surfaces, parts, edges, or elements) will depend upon the selection mode chosen in the "Selection: Select" pull-out menu or toolbar.

Hold down the <Ctrl> key while left-clicking an object to toggle the selection state of the clicked object. That is, unselected objects will be added to the selection set and previously selected items will be removed from the selection set. Holding down the <Shift> key while left-clicking will only add clicked objects to the selection set (this will have no effect on already selected items). Finally, holding both <Ctrl> and <Shift> while left-clicking will only remove clicked objects from the selection set (this will have no effect on items that are not already part of the current selection set).

Pressing the right mouse button with the cursor hovering over items in the tree view will access a context menu with commands relevant to the item under the cursor. When items are currently selected, either within the tree view or display area, the right-click context menu will display commands and options that are specifically relevant to the selected items. For example, if a surface is selected, only surface-based commands will appear in the context menu. You may right-click anywhere in the display area when items are selected to access the context menu. However, to access the context menu within the tree view area, you must right-click with the cursor positioned on one of the selected headings.

If a mouse has a wheel, rolling the wheel will zoom in or out on the model. Holding down the middle mouse button or wheel and dragging the mouse will rotate the model. Press the <Ctrl> key while holding the middle button and dragging the mouse to pan the model, moving it within the display area. Press the <Shift> key while dragging the mouse with the middle button down to zoom in and out, making the model larger as the mouse is moved upward and smaller as it is moved downward. You will likely find the use of the middle mouse button and wheel to be more convenient than choosing a command like "Rotate" or "Pan," clicking and dragging the mouse, and then pressing <Esc> to exit the command.

Finally, the X, Y, or Z key on the keyboard may be held down while dragging the mouse with the middle button held down. Doing so will rotate the model, as before, but constraining the rotation to be only about the corresponding X, Y, or Z global axis direction. You may also use the left and right cursor keys on the keyboard while holding down X, Y, or Z to rotate about these axes in fixed increments (15 degrees by default). The rotation increment is customizable via the "Tools: Options: Graphics: Miscellaneous" dialog.

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Introduction to the ViewCube

As is true for the mouse, the software also supports a number of different view configurations. This document assumes that the default view options template and view navigation settings for a new installation are in effect. However, user settings, or settings retained from a prior Autodesk Algor Simulation installation, may cause the view orientations and behavior to differ from those described throughout this document. To ensure that your view commands follow the descriptions in this book, access the "Tools: Options: Views Options" dialog and choose the "Algor Simulation" template.

Next, access the "Graphics" tab of the same "Options" dialog, select "Navigation Tools" from the items listed on the left side of the dialog, and click on the "View Cube" button. Click the "Restore Defaults" button followed by “OK” to exit the "ViewCube Properties" dialog.

Finally, click the "Steering Wheel" button. Click the "Restore Defaults" button followed by “OK” to exit the "SteeringWheels Properties" dialog. Click “OK” to exit the "Options" dialog.

The ViewCube will be located in the upper right corner of the display by default but may be relocated. The appearance will change depending upon whether the view is aligned with a global plane and whether the cursor is near the cube or not. The ViewCube, in its various appearances, is shown in Figure 4.

Figure 4: ViewCube Appearance

The six standard view names, as labeled on the cube faces, are the Top, Bottom, Front, Back, Left, and Right. These may be selected by clicking near visible face names on the cube, as shown in Figure 4 (b) or by clicking the triangular arrows pointing towards the adjacent faces, as shown in Figure 4 (c), which shows the cursor pointing to the arrow for the Bottom view. In addition, there are clickable zones at each corner and along each edge of the ViewCube. Clicking on a corner will produce an isometric view in which that particular corner is positioned near the center and towards you. Clicking an edge will produce an oblique view, rotated 45 degrees, half-way between the views represented by the two adjacent faces. When the cursor is near the ViewCube, a "Home" icon will appear above it and to the left, providing easy access to the home view. This is an isometric view having the corner between the Front, Right, and Top Faces centrally positioned and towards you by default. The home view may be redefined by right-clicking the Home icon and choosing the "Set Current View as Home" command while viewing the model positioned as desired. When one of the six standard views is active and the cursor is near the ViewCube, two curved arrows will appear above and to the right of the cube, as seen in Figure 4 (c). These are used to rotate the model to one of the four possible variants of the particular standard view. Each click of an arrow will rotate the model 90 degrees in the selected direction.

(a) Cursor not near the ViewCube

(b) Cursor on ViewCube (view not aligned to a standard face)

(c) Cursor on ViewCube (standard face view)

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When the face being viewed is changed via the ViewCube, the model may move to the selected view in the manner that requires the least amount of motion. For example, say we are first looking at the Right view, with the word "Right" positioned upright (that is in the normal reading position). Now, if we click the downward arrow above the cube, the model will rotate 90 degrees to reveal the top face. The Top view will be rotated 90 degrees clockwise from the upright orientation (that is, the word "Top" will read in the vertically downward direction). Activating the "Keep scene upright" option will cause the Front, Back, Left, and Right views to automatically be oriented in the upright position (Top above, Bottom below) when changing to any of these views. You may, however, rotate the view after initial selection, if desired. Go to "Tools: Options: Graphics: Navigation Tools: View Cube" to locate the "Keep scene upright" setting. It is activated by default. The point of this discussion is that whenever a new face is selected using the ViewCube, the resultant view rotation may differ, depending upon the prior position of the model. If the resultant orientation is not what is desired, simply click one of the curved arrows to rotate the view.

Additional View Controls

Immediately below the ViewCube is a pallet of additional view controls. This consists of seven tools, each of which may be individually enabled or disabled. All are on by default. Figure 5 shows the view control pallet.

From top to bottom, the seven tools are as follows:

• SteeringWheels • Pan • Zoom • Orbit • Center • Previous View • Next View

Each of these icons, except for the Previous and Next commands, function as a toggle—clicking it once to activate a command and again to deactivate it. Several of these tools, such as Pan, Previous, and Next are self-explanatory. The "Zoom" tool includes a fly-out menu allowing the choice of one of four different zooming modes—Zoom, Zoom (Fit All), Zoom (Selected), and Zoom (Window). The first of these causes the model to become larger as the cursor is moved upward in the display area and smaller when it is moved downward. The Fit (All) mode encloses the extents of the whole model. After selecting objects in the display area, the Zoom (Selected) tool fits the selected items into the display area. Finally, after selecting the Zoom (Window) tool, you can click and drag the mouse to draw a window defining the area you wish to expand to fill the display area. The "Orbit" tool has two variants, selectable via a fly-out menu—Orbit, and Orbit (Constrained). The former allows the model to be rotated freely in any direction. The Constrained option causes the model to rotate only about the global Z-axis, similar to pressing the Z key while dragging the mouse with the middle button depressed. The "Center" tool is used to center a point on the model within the display area. Click with the mouse to specify the desired center point after selecting the Center command. This point also becomes the display pivot point, about which the model pivots when being rotated.

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Course Introduction

XVIII FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010

The "SteeringWheels" tool is customizable and, in its default setting, produces the Full Navigation Wheel shown in Figure 6. The full navigation wheel floats above the model view, following the cursor position. It provides an additional access method for several functions found elsewhere on the view tools pallet as well as a few additional functions.

Figure 6: Full Navigation Wheel

The "Rewind" button on the navigation wheel presents a timeline of thumbnails representing various views that have been used during the modeling session. Simply release the mouse button with the cursor positioned at the thumbnail representing the view to which you wish to jump. This is more convenient than pressing the previous or next view buttons multiple times.

For additional information concerning these view controls, consult the User's Guide.

Legacy View Controls in Autodesk Algor Simulation

Traditional view controls and options are also provided via the pull-down menus and toolbars at the top of the user interface window. Options for displaying or hiding the mesh or model shading may be found here as well as eight pre-defined, standard view orientations. The orientations will depend upon the currently active views options template (previously discussed in the "Introduction to the ViewCube" section of this introduction). There is also a "User-defined Views" dialog that may be used to save, modify, or restore custom views. Additional capabilities include a local zoom feature and display toggles for the scale ruler, miniaxis, and perspective mode. The "Local Zoom" feature displays a small rectangle that represents the area to be magnified. A larger rectangle shows an overlay of the magnified region. You may click on and drag the local zoom window to position it anywhere on the model within the display area. The size of the local zoom area and magnified overlay and also the zoom level can be customized via the "Tools: Options: Graphics: Local Zoom" dialog. For additional information concerning the legacy view controls, consult the Help files.

Notes Concerning the ”Steps for Exercises” Section

Exercise descriptions and step-by-step solutions are provided in a separate section at the back of this Instructor Manual. Excerpts from the Steps for Exercises section may be printed and distributed to the students as desired. In addition, please refer to the Forward portion of the Steps for Exercises section for detailed information regarding the necessary program setup parameters. Using the specified configuration at each workstation will ensure the expected software behavior for instructor and student alike.

Presentation Slideshow


2 FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010


FEA in Practice – Instructor Manual – Autodesk® Algor® Simulation Professional 2011 4/30/2010 3

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NOTE: For details concerning beam element orientation, access the “Contents” tab of the Help files, go to “Autodesk Algor Simulation: Setting Up and Performing the Analysis: Setting Up Part 1: Linear: Element Types and Parameters: Beam Elements.” Scroll down the resultant page, and click on the “Beam Element Orientation” heading.

Beam Elements (continued)



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Thermal Analyses

Other Analysis Types

Slide 158:


Thermal Analyses

• Steady-State Heat Transfer• Transient Heat Transfer

The following two types of thermal analysis are available:



Slide 159:


Thermal Elements• Thermal elements are geometrically

identical to the corresponding structural elements. The available types are:– Rod (this is a line element) – 2-D– Plate– Brick

Slide 160:


Thermal Nodal Loads• Initial Temperature

– Specify the temperature of a node(s) at the beginning of the analysis (transient analysis).

• Applied Temperature– Specify a temperature at which a node(s) will be

held during the analysis. A stiffness value specifies the amount of thermal energy (heat source or heat sink) available for maintaining the temperature.



Slide 161:


Thermal Surface Loads• Convection

–Assign a convection coefficient and the ambient temperature.

• Radiation–Assign the radiation function and the ambient

temperature.

• Heat Flux–Assign the amount of heat added or removed per

unit area.

Slide 162:


Thermal Element Loads• Heat Generation

–Enter the amount of volumetric heat generated in a given part.



Slide 163:


Body-to-Body Radiation• Define the surfaces that will exchange heat

through radiation and assign emissivity values.

• Define body-to-body radiation enclosures (i.e., groups of surfaces that will radiate to/from each other).

• The processor will automatically calculate the view factors between elements.

Slide 164:


Thermal Contact• Used to simulate imperfect thermal conduction

between two parts or the resistance of a substance that is not modeled (such as epoxy) between two parts.

• Define contact pairs in the FEA Editor environment.

• Define the resistance value between the surfaces.

• Applicable to 3D CAD, hand-built, and 2-D models.



Slide 165:


Thermal Results• Temperature• Heat flux (energy / time / length2)• Heat rate of face (energy / time)

Slide 166:


Exercise L - Thermal Model

• Objective: Analyzethe thermal effects ofa material containing hot and cold waterpassages. Use a meshsize of 80% of default.

• Material: Steel (ASTM - A514)

• Loads:– Largest Hole: Convection coefficient = 1.4

Ambient temperature= 65°F

– Second Largest Hole: Convection coefficient = 2.8Ambient temperature = 180°F

F sec inlbsin

2 °

F sec inlbsin

2 °



Slide 167:


Electrostatic Analyses


Slide 168:


Electrostatic Analyses

• Electrostatic Field Strength and Voltage• Electrostatic Current and Coltage

The following two types of electrostatic analysis are available:



Slide 169:


Electrostatic Elements• Electrostatic 2-D and brick elements are

geometrically identical to the analogous structural elements.

Slide 170:


Electrostatic Nodal Loads• Applied Voltages

–Specify a certain voltage at which a node(s) will be held, due to a voltage source.

• Temperatures–Specify the temperature of a node(s) to influence

the electrostatic results when temperature-dependent material properties are being used.



Slide 171:


Electrostatic Results• Voltage (Volts or mV)• Current (Amps or mA / length2)• Current Rate of Face (Amps or mA)• Electric field (voltage/length)• Displacement field (force/voltage * length)• Electrostatic force• Electrostatic charge (current * time)

Slide 172:


Electrostatic Analysis Exercise

Refer to the software’s “Help: Tutorials” menu command. Follow the “Radial Comb Motor Electrostatic Analysis” tutorial listed under “Analyzing and Evaluating Results Tutorials” for further information on performing an electrostatic analysis.



Slide 173:


Fluid Flow Analyses


Slide 174:


Fluid Flow Analyses

• Steady Fluid Flow• Unsteady Fluid Flow• Flow Through Porous Media• Open Channel Flow

The following four types of fluid flow analysis are available:



Slide 175:


Fluid Flow Elements• The fluid flow 2-D and brick elements are

geometrically identical to the analogous structural elements.

Slide 176:


Fluid Flow Loads• Prescribed Velocity

–Can be used to specify an inlet velocity or zero velocity along a wall.

• Surface Prescribed Inlet/Outlet• Fan Curves

–Can be used to model flow generated by intake, exhaust or internal fans.

• Rotating Frames of Reference–Can be used to model flow in rotating machinery.

• Gravity



Slide 177:


Fluid Flow Loads (continued)• Pressure/Traction

–Applied normal to the edge of 2-D elements (selected as surfaces since the edges represent surfaces).

–Applied normal to the face of 3-D elements.–Applied in a specified vector direction to the edge

surface of 2-D elements or the face of 3-D elements.• Buoyancy Force

–Apply thermal results from a steady-state heat transfer analysis to a steady fluid flow analysis.

• Surface Prescribed Turbulence Condition• Surface Prescribed Wall Roughness

Slide 178:


Fluid Flow Results• Velocity (length/time)• Pressure (force/length2)• Stress tensors (force/length2)• Reaction forces



Slide 179:


Fluid Flow Analysis

Refer to the software’s “Help: Tutorials” menu command. Follow the “Ball Valve Fluid Flow Analysis” tutorial listed under “Analyzing and Evaluating Results Tutorials” for further information on performing a fluid flow analysis.

Slide 180:


Mechanical Event

Simulation (MES)




Slide 181:


Mechanical Event Simulation (MES)MES overcomes many limitations of static stress analysis by accounting for…

• Geometric nonlinearity (large deformations that change the load and/or constraint positions and directions)

• Acceleration/inertia• Damping• Motion-enabled contact or impact (that is, surface-to-

surface contact that changes over time due to motion or component deformation)

• Nonlinear material behavior (such as plastic deformation due to exceeding the material yield strength).

Slide 182:


Mechanical Event Simulation (MES)(continued)

Other MES characteristics:

• Loads and results are time-dependent, providing many instantaneous results “snapshots” over a user-defined period of time.

• Load curves are used to define how the given loads vary over time.

• Multiple results time steps are provided for post-processing.

• Results may be graphed versus time. The integral and first or second derivative of the results may also be graphed.



Slide 183:


Comparison of Linear Static Stress and MES

{f} = [K] {d}Where: {f} = force vector, [K] = stiffness matrix, {d} = displacement vector

Previously, we introduced the following governing equation for static stress analysis:

For MES, additional terms are included, resulting in the following equation:

{ } [ ]{ } [ ]{ } }]{[ dmdcdKf ++=Where: [c] = damping matrix, [m] = mass matrix,

= velocity vector (first derivative of displacement),= acceleration vector (second derivative of displacement)

{ }d

{ }d

Slide 184:


MES – Shell Elements• MES shell elements are similar to

linear plate elements. They are triangular or quadrilateral, are planar (or nearly planar), and have three or four corner nodes.

• There are several available formulations (consult the Help files for more information).

• Composites are a subset of shell elements in MES, rather than a separate element type.



Slide 185:


MES – Kinematic Elements• Kinematic elements can be either 2-D or

3-D elements. • Kinematic elements do not experience strains

and do not report stresses. Otherwise, these elements behave just like flexible brick elements.

• They have an advantage over conventional brick elements because of their small contribution to the size of the global stiffness matrix. This results in faster run times.

Slide 186:


MES – Contact Elements• Contact elements can have

different stiffness values in compression and tension.

• These elements can also have a breaking stress at which point the stiffness will be zero.

• These elements can be used to simulate cables.



Slide 187:


MES – Coupling Elements• Coupling elements aid in the

simulation of parts that "couple" at a known length.

• This coupling is modeled by introducing a stiffness when it reaches this length. This stiffness is calculated using the modulus of elasticity, a coupling area, and the length of the element.

Slide 188:


MES – Dashpot Elements• Dashpot elements can be used

to apply local damping to a model.

• You can specify a damping coefficient that will control how much these elements affect motion.



Slide 189:


MES – Actuator Elements• Actuator elements are line

elements whose lengths can change over time.

• They are used to simulate defined movement of a part (such as hydraulic cylinders or solenoids).

Slide 190:


MES – Slider Elements • A slider element consists of two

collinear lines connected at one node.

• The node in the middle will be allowed to move along the line defined by the other two points, letting the node “slide” such as if it were in a guide or slot.



Slide 191:


MES – Pulley Elements• Pulley elements consist

of three nodes: driver, pivot, and slack.

• As the driver node moves toward or away from the pivot, the slack node will move in the opposite direction by a set relationship.

Slide 192:


MES – Pipe Elements• Pipe elements allow you to

model piping systems under internal pressure loads.

• The pipe elements can be either straight sections or bends.



Slide 193:


MES – Hydrodynamic Elements• Hydrodynamic elements

can be either 2-D or 3-D elements.

• These elements allow for the simulation of the interaction of fluids with solids without considering the details of the flow.

Slide 194:


MES – Impact Planes• Specify a wall, floor, or ceiling parallel to

the global X, Y and Z axes.• Objects will not be able to pass through this

plane.



Slide 195:


MES – Surface-to-Surface Contact

• Specify two or more surfaces that may come into contact during the event duration.

• Can include static and dynamic friction effects.• A “slide, no bounce” option is available to

prevent objects from separating once they’ve come into contact.

• Consult the Help files for more information concerning the various surface contact options and parameters.

Slide 196:


Mechanical Event Simulation Example

For an introductory level mechanical event simulation (MES) example, refer to the software’s “Help: Tutorials” menu command. Follow the “Piston Mechanical Event Simulation” tutorial listed under “Analyzing and Evaluating Results Tutorials.”

Also, refer to “Example M” (next slide) for a more complex and challenging MES example involving surface number reassignment and surface-to-surface contact.



Slide 197:


• Center of Joint 1 (0, 0, -0.125) & Joint 2 (1.414214, 0, -0.125): Fixed except for Rz• Center of Joint 3 (0, 0, 0.875) & Joint 4 (1.414214, 0, 0.875): Tx, Ty, Rx & Ry constrained

Exercise M – MES, Geneva Mechanism

Slide 1 of 4

Slide 198:


1. Before meshing, set the default contact = “Free/No Contact” and define a surface contact pair between Part 1 and Part 2, which will prevent mesh matching between the parts (this is desirable for MES contact surfaces).

2. Mesh the model at an absolute mesh size of 0.0625” (1/16th of an inch).3. Modify line attributes to consolidate the contact surfaces. Use surface 100 for

the 1st contact pair, 101 for the 2nd, and 102 for the 3rd – include chamfers. For the drive wheel, surfaces 100 and 101 will each encompass about one-third of the perimeter of the wheel’s C-shaped cylindrical contact surface.

4. From the “General Surface-to-Surface Contact” screen, redefine the first pair to be Part 1/Surface 100 to Part 2/Surface 100. Create two more pair—Part 1/ Surface 101 to Part 2/Surface 101 and Part 1/Surface 102 to Part 2/Surface 102. Set the contact element “Updating” to “Automatic.” Set the contact parameters for all three pair as follows…

• Contact problem type = “High Speed Contact (Impact)”• Contact type = “Surface to Surface”• User specified contact stiffness = 1000 lbf/in• User specified contact tolerance = 0.0011” (eliminates the effects of 0.001” part clearances

and prevents chatter, resulting in a quicker and more stable solution).

Exercise M (continued)

Slide 2 of 4



Slide 199:


5. Create four universal joints, one at each end face of the four stub shafts, entering the specified vertex coordinates from the preceding diagram.

6. In the element definition screen for parts 1 and 2, set the analysis type to “Large Displacement.” Set the material for the drive wheel to “Brass, Red” and for the driven wheel to “Plastic – Nylon Type 6/6.” For all four joints… Change the element type to “Pipe” – In the element definition screen, set the OD to 0.1” and the wall thickness to 0.03” – The material is to be custom defined, E=100e6; all other values remain at zero.

7. Apply the nodal boundary conditions and loads specified on the preceding diagram to the center points of the four joints. For Joint 4’s lumped mass, specify a uniform mass of 0.00088 lbf·s2/in and a mass moment of inertia in the Z-direction of 0.00135 lbf·s2·in. These values simulate a steel disk 1/8” thick with a diameter of 3.5”.Use load curve 1 for the prescribed displacement (rotation) and loadcurve 2 for the nodal moment. Load curve 1 ramps linearly from 0 to 1 in 1 second. Load curve 2 is constant at 1. Set a death time of 1 second in the active range data dialog for the prescribed displacement.


Slide 3 of 4

Slide 200:


8. In the analysis parameters screen, set the event duration to 1 second and the capture rate to 90. This will produce a time step for every two degrees of drive wheel rotation.

9. Under the equilibrium tab of the advanced analysis parameters, uncheck the “Automatic” box for the displacement tolerance and set the value to 0.02.

10. Run the Analysis and review the results. Generate a von Mises stress animation and a plot of displacement magnitude vs. time for two nodes – one on the drive wheel’s indexing pin and one on the perimeter of the driven wheel.

* * *NOTE: Depending upon the computer hardware, this analysis may take several

hours to run. You may wish to allow several steps to converge, stop the analysis, and then load the already completed model from the provided archive file, “Exercise M\Results Archive\Exercise M.ach”.


Slide 4 of 4



Slide 201:


Combining Analysis Types(Multiphysics)


Slide 202:


Multiphysics• A multiphysics analysis combines the effects of

multiple analysis types.• The initial analysis is performed. • Another analysis is set up using the results from

the initial analysis as the loading in the subsequent analysis.

• For some analyses, iterations are required to reach a converged solution.

• Steady or unsteady coupled fluid flow and thermal analyses solve for fluid and thermal results simultaneously.



Slide 203:


Examples of Combining Analysis Types

• Apply temperature results from a heat transfer analysis to a stress analysis to analyze thermal stress.

• Apply boundary forces from a fluid flow analysis to a stress analysis (fluid/structural interaction).

• Apply velocity results from a fluid flow analysis to a heat transfer analysis to analyze the effect of forced convection on the temperature distribution (where the temperature does not significantly influence the flow pattern).

• Apply temperature results from a heat transfer analysis to a fluid flow analysis to drive natural convection (where the flow does not significantly influence the temperature distribution).

Slide 204:


Examples of Combining Analysis Types (continued)

• Apply current results from an electrostatic analysis to a heat transfer analysis to analyze Joule heating.

• Apply electrostatic attraction/repulsion forces from an electrostatic analysis to a stress analysis to determine displacements and stresses (commonly used in the analysis of micro electromechanical systems – MEMS).



Slide 205:


Multiphysics Example:

Analysis of Stresses due to Electrostatic Forces

Refer to the software’s “Help: Tutorials” menu command. Follow the “Radial Comb Motor Static Stress Analysis” tutorial listed under “Analyzing and Evaluating Results Tutorials” for further information on performing a multiphysics analysis of structural stress and displacement due to electrostatic forces.

Slide 206:


Material Models




Slide 207:


Background on Material Models• Material models are subsets of the element

types.• These models allow you to make decisions

on what type of material properties will be used for each part in the model.

• For example, if a part will see the plastic region of a stress versus strain curve, you should select one of the von Mises material models for an elastic/plastic analysis.

Slide 208:


Isotropic• This is the standard material model. The

material properties are independent of direction.



Slide 209:


Orthotropic• This material model can have different

properties in the three orthogonal directions.

• The required properties are identical to the isotropic material model. However, you enter separate values for the three directions.

Slide 210:


Temperature-Dependent• For some elements, the properties for both

isotropic and orthotropic materials can be defined on a temperature-dependent basis.

• The values are linearly interpolated between the specified temperature points.



Slide 211:


Elastic-Plastic (von Mises)• von Mises: This material models is based on a bilinear

simplification of the stress-strain curve. The modulus for the elastic region, the yield point, and the modulus for the plastic region must be defined. If the material library includes the elastic modulus, yield point, ultimate strength, and elongation; the program will automatically calculate the plastic modulus for you.

• von Mises Curve: This material model uses either an approximated stress-strain curve or actual stress-strain data. As above, if the material library includes the elastic modulus, yield point, ultimate strength, and elongation; the approximated stress-strain curve will be generated automatically. Alternately, you may define a table of true stress-strain data (either within the material library manager or the material application screen).

Slide 212:


Elastic-Plastic (von Mises)(continued)

• Isotropic hardening and kinematic hardening variants of the von Mises material models are available.

– Use the “von Mises with Isotropic Hardening” model for non-reversing load conditions.

– The “von Mises with Kinematic Hardening” model is recommended for greater accuracy when reversing strain cycles will occur.



Slide 213:


Hyperelastic and Foam Material Models

• The following rubber-like (hyperelastic) material models are available:–Mooney-Rivlin – Yeoh–Arruda-Boyce – Neo-Hookean–Ogden – Van der Waals

• The following foam-like material models are available:–Blatz-Ko–Hyperfoam (accounts for compressibility)

Slide 214:


Drucker-Prager• This material model is used to model rock

and concrete.



Slide 215:


Viscoelastic and Viscoplastic• These material models are used to account

for rate-dependent material behavior due to dissipative losses from viscous effects. The viscoelastic material models are variants of the previously listed hyperelastic material models.

• A material model that can be used to model thermal creep is also available (“Thermal Creep Viscoelastic”).

Slide 216:


Thermoelastic and Thermoplastic• These material models are used for thermal

stress analyses. The Thermoplastic model is used when stresses beyond the yield point occur.



Slide 217:


Piezoelectric• This material model is for parts that

experience stress due to a voltage distribution.

Slide 218:


Curve• This material model allows you to input a

bulk modulus versus strain curve to control the behavior of the part.



Slide 219:


Reinforced Concrete• This material model allows different tensile

and compressive behaviors. It can simulate cracking and crushing failure of concrete under relatively monotonic loading. A maximum of three independent directions of rebar are allowed for the concrete material. The rebar locations (in height or depth) are not considered; they are treated as "smeared" throughout the part.

Slide 220:


Exercise N - Nonlinear Material Model• Objective: Analyze a cantilever beam

using beam elements and an elastic material model. Determine if yielding occurs. If it does, reanalyze the beam using a plastic material model.

• Geometry: The beam is 10’ longand is 5” x 5” square.

• Material: Steel (ASTM - A36)• Loads: 56,000 pounds in the

-Y direction at the free end.• Constraints: The fixed end is fully

constrained.• Duration: 10 seconds.• Capture rate: 2 steps per second.

Load curve:


Steps for Exercises

Based on Autodesk® Algor® Simulation Professional 2011

SE.2 FEA in Practice – Steps for Exercises – Autodesk® Algor® Simulation Professional 2011 4/30/2010

FEA in Practice – Steps for Exercises – Autodesk® Algor® Simulation Professional 2011 4/30/2010 SE.3

STEPS FOR EXERCISES TABLE OF CONTENTS

Foreword........................................... SE.5 Introductory Example – Motor Mount .................................................................. SE.7 Exercise A – FEA Example by Hand ................................................................... SE.17

Exercise B – Truss Frame Model ........................................................................ SE.23

Exercise C – Support Beam under Gravity ......................................................... SE.33

Exercise D – Axisymmetric Thick-Walled Cylinder.............................................. SE.43

Exercise E – Plate under Uniform Pressure ........................................................ SE.49

Exercise F – Cantilever Beam Model .................................................................. SE.57

Exercise G – Comparing Element Types ............................................................ SE.67

Exercise H – Mesh Convergence ........................................................................ SE.79

Exercise I – Bracket Model .................................................................................. SE.85

Exercise J – Hanger Assembly Model ................................................................ SE.91

Exercise K – Linear Contact Model ..................................................................... SE.97

Exercise L – Thermal Model.............................................................................. SE.105

Exercise M – Mechanical Event Simulation (MES), Geneva Mechanism ......... SE.111 Exercise N – Nonlinear Material Model ............................................................. SE.129



Foreword Starting Autodesk® Algor® Simulation

The software may be started by:

• Accessing the Windows "Start" menu and selecting the "All Programs" pull-out menu, followed by selecting the "Autodesk" group and the "Autodesk Algor Simulation" folder within it. Select the "Autodesk Algor Simulation" command.

• In addition, the program may be started by choosing the "Autodesk Algor Mesh" command within supported CAD solid modeling applications. This method starts the program and transfers-in the CAD solid model in one operation.

Defaults

Each exercise is written using the default program settings, as if the software has been opened for the first time after installation. In this way, a user can work through the exercises in any order. If a user will be working through several exercises during one session, some settings from one exercise may be retained, creating incorrect or invalid steps in the following exercise. To minimize this possibility, exit the program at the end of each exercise and reopen it to begin a new exercise. It is possible for an experienced user to work through several exercises without this precaution, but extra care should be taken to review that input is correct and appropriate. It is important that the user access view commands exactly as described, except as otherwise indicated (that is, from the pull-down menus or toolbars). These commands ensure a constant and repeatable view orientation that is not ensured when using the ViewCube. Specifically, while the displayed plane will be correct, the rotational position may not be as expected when using the ViewCube. Several program settings are global. That is, once set, they will influence the program behavior for every model until the settings are changed again. In particular, the solution steps in this manual may be invalidated if a deviation is made from any of the settings listed below. These are the program settings upon which the solution procedures are based:

• "Tools: Options" …

o "Analysis" … "Automate Analysis" – Activated "Ask to show mesh results after CAD meshing" – Activated "Default Modeling Units…" = English (in)

o "CAD Import: Global CAD Import Options…" … "Knit surfaces on import:" = No Automatically generate contact pairs:" = No

o "Graphics: Navigation Tools: View Cube" … "Fit-to-View on view change" – Activated

o "Mouse Options: Mouse settings templates" = Algor Simulation

o "Views Options: Views settings templates" = Algor Simulation

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Input Files and Archives

The University Course Curriculum is distributed in the form of an executable, self-extracting archive and is delivered electronically. Hardcopies of the curriculum are not available. When the downloaded archive is extracted, various documents and folders will be created within the folder at the extraction location. Along with the Instructor Manual (PDF file) and the presentation slides (PPT file), there is a set of folders containing the example and exercise model input files and results archives. These are clearly identified by the folder structure and naming convention. Discretion should be used with regard to which files and folders are made available to the students via a shared network drive. It is recommended that the instructor only shares the example and exercise model input files and results archives. The Instructor Manual and presentation slideshow should not be shared. However, exercise handouts may be provided for the students by selecting and printing the appropriate pages of the Instructor Manual or by printing excerpts as PDF files and sharing these with the students on a per-assignment basis.

Many of the exercise input files are in the form of CAD universal formats. A number of the input files, and all of the results files for the course examples and exercises, are in the form of Algor Simulation archive files (*.ach). These input files and results archives must be copied to the local computer workstations for each student before they are opened. Do not try to open or run models directly from a shared network drive. This will produce excessive network traffic, slow down the analyses, and some analyses may fail to run across a network connection. For this reason, students who have their “My Documents” folders mapped to a shared network drive, as is a common practice in university settings, should NOT place FEA models in their “My Documents” folder. Instead, a folder for FEA models should be created on each local workstation hard drive. Models can be archived to the shared folder for portability during the setup process or after they have been solved.

Opening Archives

1. Copy the set of folders and files to your local computer from the class directory.

2. Start Autodesk Algor Simulation and select the "Open" icon at the left side of the dialog.

3. Select the "Algor Simulation Archive (*.ach)" option in the Autodesk Algor Files section of the "Files of type:" drop-down box.

4. Double-click to open the desired folder, highlight the desired file, and press the "Open" button.

5. In the "Browse for Folder" screen, select a folder on the hard drive for the location of the restored model files.

6. Click the “OK” button. The model will be restored to the selected folder and automatically opened in the FEA Editor environment. For exercises based on CAD solid models, the input files will be universal formats (such as STEP, IGES, and so on), rather than Algor Simulation archives. These files should be placed in the desired working folder prior to opening them. The FEA files will be created in the folder where the CAD file resides when it is opened.

Printing of Exercise Descriptions and Solution Steps

Individual exercise descriptions and/or solution steps within this manual may be printed and distributed to the students at the instructor's discretion. However, they are not to be distributed beyond or outside of the current class of the university or trade school that owns the Autodesk® Algor® Simulation license.


Introductory Example Motor Bracket Assembly Model

Brick Elements

Objective: To perform an analysis on a motor bracket that is loaded with surface forces. Geometry: Use the file MotorMount.stp located in the "Introductory Example\Input File" directory

as the input file for this exercise. Mesh the model at the default mesh size. Loads: Surface force loads of 75 lbf each will be applied to the top of the two brackets. The

direction of the load will be normal to the selected surfaces. Constraints: The two holes at the ends of the shaft will be fully constrained. Elements: Brick Material: Steel (ASTM-A36) – All Parts

Introductory Example




Solution

Meshing the Model

Start Autodesk® Algor® Simulation from the Windows Start menu.

"Open" Select the "Open" icon at the left side of the dialog.

Mouse

"Linear: Static Stress with Linear Material Models "

If the desired analysis type is not already set, click on the arrow button next to the "Choose analysis type:" field, select the "Linear" pull-out menu, and choose "Static Stress with Linear Material Models."

"STEP (*.stp, *.ste, *.step)" Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type" drop-down box. Navigate to the directory where the model is located.

MotorMount.stp Select the MotorMount.stp file in the "Introductory Example\Input File" directory.

"Open" Press the "Open" button.

"Use STEP file units" “OK”

A "Select Length Units" dialog will appear. Choose the "Use STEP file units" option from the pull-down menu if it is not already selected and click the “OK” button.

“OK”

A dialog will appear asking you to choose the analysis type for this model. Click the “OK” button to accept the default of "Static Stress with Linear Material Models". The model will be displayed in the FEA Editor as shown in Figure 0.1.

Figure 0.1: Model in the FEA Editor Environment



Mouse Access the MESH pull-down menu and select the "Model

Mesh Settings…" command. Mouse Move the slider in the "Mesh size" section to 75%.

"Mesh model" Press the "Mesh model" button in the "Model Mesh Settings" dialog.

"No" Press the "No" button when asked to view the mesh results. A mesh will be displayed on the model as shown in Figure 0.2).

Figure 0.2: Meshed Model

Defining the Material Data

Mouse Click on the "Material" heading for Part 1 in the tree view.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the "Material" heading for Part 2 in the tree view.


Mouse Right-click on one of the selected headings.

"Modify Material…" Select the "Modify Material…" command.

"Steel (ASTM - A36)"

Within the "Element Material Specification” dialog, expand the "Steel" branch of the Autodesk Algor Material Library, scroll down towards the bottom of the list, and select the material, "Steel (ASTM - A36)," as shown in Figure 0.3.



Figure 0.3: Defining the Materials

“OK” Click the “OK” button to accept this material for all three parts.

Adding Loads and Constraints

Mouse

Click and hold the middle mouse button to rotate the model view. Drag the mouse to position the model for clear visibility of the top surfaces of the brackets and then release the mouse button.

"Selection: Select: Surfaces" Access the SELECTION pull-down menu and choose the

"Select" pull-out menu. Select the "Surfaces" command. Mouse Click on the top surface of one of the brackets.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the top surface of the other bracket.

Mouse Right-click in the display area.

"Add: Surface Forces…" Select the "Add" pull-out menu and select the "Surface Forces…" command (see Figure 0.4).



Figure 0.4: Applying Surface Loads

75 Type "75" in the "Magnitude" field. This is the force applied per selected surface.

“OK” Click the “OK” button to accept this load.

Mouse Click and hold the middle mouse button to rotate the model view. Drag the mouse to position the model for clear visibility of the holes at each end of the shaft.

Mouse Click on one of the inner surfaces of one of the holes in the shaft.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the remaining three inner surfaces of the two holes.


"Add: Surface Boundary Conditions…"

Select the "Add" pull-out menu and select the "Surface Boundary Conditions…" command.

"Fixed" Press the "Fixed" button in the "Predefined" section.

“OK” Press “OK” to accept these surface boundary conditions.

Running the Analysis

"Analysis: Perform Analysis…"

Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command to run the analysis. At the completion of the analysis, the program will automatically transfer to the Results environment.



Viewing the Results

The von Mises stress contour on the displaced shape will appear as shown in Figure 0.5.

Figure 0.5: von Mises Stress Results

Other types of results can be displayed by accessing the RESULTS pull-down menu and selecting from among the various available results. In addition, the amount of displacement exaggeration may be altered and the undisplaced shape can be overlaid on the displaced shape plot.

"Results: Displacement: Magnitude"

Access the RESULTS pull-down menu, then the "Displacement" pull-out menu, and select the "Magnitude" command. Note the maximum displacement magnitude.

"Results Options: Displaced Model Options…"

Access the RESULTS OPTIONS pull-down menu and select the "Displaced Model Options…" command to access the "Displaced Model Options" dialog.

Mouse

Increase the displacement scale from 5% to 10% by dragging the slider towards the right. The displaced plot will now be exaggerated so that the displacement is approximately 10% of the overall model size.

Mouse Under the Scale Factor heading, activate the "As an Absolute Value" radio button. The scale factor field will now show the actual displacement multiplier.

"Transparent" Select the "Transparent" radio button in the "Show Undisplaced Model As" section.

Mouse Press the button in the upper right corner of the

"Displaced Model Options" dialog.



We will now capture a screen image of the displacement results for inclusion within the analysis report.

“File: Export: Image…” Access the FILE pull-down menu, select the "Export"

pull-out menu, and choose the "Image…" command.

Mouse

Click once in the display area to make this window active and press <Enter> to automatically select the entire display area and open the “Save image as” dialog. (Note that it is also possible to click and drag to select only a portion of the display for capture.)

“Portable network graphics file (*.png)”

Choose “Portable network graphics file (*.png)” from the drop-down list in the “Save as type:” field.

“Motor Mount – Displacement”

Type “Motor Mount – Displacement” in the “File name:” field.

“Save” Click the “Save” button.

Generating an HTML Report

"Tools: Report" Access the TOOLS pull-down menu and select the

"Report" command to change to the Report environment. Mouse Right-click on the "HTML Report" heading in the tree view.

"Configure Report" Select the "Configure Report" command.

Mouse Activate the “Logo” checkbox. Drag the horizontal scroll bar towards the right to see the full logo. The “Configure Report” dialog will now appear as shown in Figure 0.6.

Figure 0.6: Report Configuration Utility

NOTE: When selecting portions of the report to modify, click on the item name and not on the checkbox. Clicking on the checkbox will toggle the inclusion state of the item (that is, whether it is to be included or excluded from the HTML report).



Mouse Select the "Project Name" heading.

Mouse: Introductory Exercise

Click and drag the mouse to select the text "Design Analysis" and type "Introductory Exercise" to replace it.

Mouse: Analysis of a Motor Mount under a 150 lbf Load.

Click and drag the mouse to select the text "Project Title Here" and replace this text by typing "Analysis of a Motor Mount under a 150 lbf Load".

Mouse Select the "Title and Author" heading.

Your Name Type your name into the "Author" field.

Your Department Type your department name into the "Department" field.

Mouse Deselect the "Executive Summary" item by clicking on the associated checkbox. This item will be excluded from the report.

NOTES

: Text can be added as desired within the "Executive Summary" section using the built-in word processor features. A variety of font and paragraph styles are included, such as bullet or numbered lists, tables, tabs, and various text justification settings.

The following sections are automatically generated and cannot be modified. The analyst may only include or exclude these items or alter their order of appearance within the report:

• Summary • Analysis Parameters • Parts • Element • Material • Loads • Constraints • Probes • Rotating Frames (applicable to fluid flow analysis) • Results Presentations • Processor Log Files Group • Code Checking – General • Code Checking – Detailed

We will now deactivate the default results presentation image and instead add the displacement image that we captured previously. We will position the image within the report just before the processor log files.

Mouse Deselect the "Results Presentation" item by clicking on the associated checkbox to exclude it from the report.

“Tree: Add Image File(s)…” Access the TREE pull-down menu and choose the “Add Image File(s)…” command.

“Portable Network Graphics (.png)”

Choose “Portable Network Graphics (.png)” from the drop-down list to the right of the “File name:” field.

“Motor Mount – Displacement.png”

Browse to and select the file, “Motor Mount – Displacement.png” that was previously created.

“Open” Click the “Open” button. A heading matching the image name will appear at the bottom of the report tree view. Also, the default header text will match the filename.



Mouse

Click on the “Motor Mount – Displacement” heading and drag it upward in the tree view to reposition this item within the report. Release the button with the cursor over the “Processor Log Files” heading. The image will now precede the log files.

"Generate Report" Press the "Generate Report" button. This will automatically bring up the report, which will appear as shown in Figure 0.7. You can scroll through and review the full report.

Figure 0.7: Completed Report

NOTES

: The default title image is the model as it currently appears within the FEA Editor environment. A different image may be substituted for this one and/or the image may be resized using the report configuration utility. To resize the image, click and drag the handles that appear around the image border while it is selected within the report configuration utility.

Within the folder where any given model resides there will be a subfolder named "modelname.ds_data" (in this case, "MotorMount.ds_data"). Within this folder, there will be one numbered subfolder for each design scenario that was built and analyzed. In this case, only the folder ("1") will exist, since only the first design scenario was used. Finally, within the numbered design scenario folder there will be a subfolder named "ds_rpt." This folder contains the HTML report and all of its attachments, style sheet, and table of contents. This folder may be zipped and sent to anyone who wishes to review the report. They do not need to have the Algor Simulation software installed on the system in order to review the report. The HTML document may be opened in a web browser (like Internet Explorer). Merely extract the report and double-click on the file "modelname.htm" to open it in the default web browser. Note that the report can also be saved in a variety of other formats—Word 97, Word 2007, PDF (Adobe portable document format), and RTF (rich text format).

To review a completed archive of this exercise, refer to the file MotorMount.ach in the "Introductory Example\Results Archive" directory.


Exercise A FEA Example by Hand

Truss Elements

Objective: Construct and analyze a system of three trusses supporting a vertical load. Geometry: Draw the trusses in the XY plane (Top View).

L = 10 feet Cross-sectional area = 2 in2 θ = 45°

Loads: F = 10,000 pounds Constraints: Fully fixed at nodes 2, 3 and 4. Constrain translation in the Z direction at point 1. Elements: Truss Material: Modulus of elasticity = 30e6 psi

Exercise A – FEA Example by Hand




Solution

Building the Model


"New" Select the "New" icon at the left side of the dialog.

Mouse



"New" Press the "New" button.

Exercise A

Type "Exercise A" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.

"Save" Press the "Save" button.

"Geometry: Add: Line…" Access the GEOMETRY pull-down menu and select the

"Add" pull-out menu. Select the "Line…" command. Mouse Deactivate the "Use as Construction" checkbox.

120<Enter> Type "120" in the "Y:" field in the "Vertex" section of the "Define Geometry" dialog and press <Enter> to define the point (0, 120, 0) as the first vertex.

<Enter> Press <Enter> to define the origin as the next vertex.

120<Enter> Type "120" in the "X:" field in the "Vertex" section of the "Define Geometry" dialog and press <Enter> to define the point (120, 0, 0) as the next vertex.

<Esc> Press <Esc> to begin a new line.

<Enter> Press <Enter> to define the origin as the first vertex.

120<Tab>120<Enter>

Type "120" in the "X:" field in the "Vertex" section of the "Define Geometry" dialog, press <Tab>, type "120" and press <Enter> to define the point (120, 120, 0) as the final coordinate.

Mouse Press the button in the upper right corner of the "Define

Geometry" dialog to close it.

"View: Orientation: Top View"

Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Top View" command.

Defining the Element and Material Data

Mouse Right-click on the "Element Type" heading for Part 1 in the tree view.

"Truss" Select the "Truss" command.



Mouse Right-click on the "Element Definition" heading for Part 1 in the tree view.

"Modify Element Definition…" Select the "Modify Element Definition…" command.

2 Type "2" in the "Cross-Sectional Area" field.

“OK” Click the “OK” button.

Mouse Right-click on the "Material" heading for Part 1 in the tree view.


"Edit Properties" Press the "Edit Properties" button.

30e6 Type "30e6" in the "Modulus of Elasticity" field.

“OK” Click the “OK” button to close the “Element Material Specification” dialog.

“OK” Click the “OK” button to close the “Element Material Selection” dialog.


"Selection: Select: Vertices" Access the SELECTION pull-down menu and choose the

"Select" pull-out menu. Select the "Vertices" command. Mouse Click on the vertex at point 1.


"Add: Nodal Force…" Select the "Add" pull-out menu and select the "Nodal Force…" command.

-10000 Type "-10000" in the "Magnitude" field.

"Y" Select the "Y" radio button in the "Direction" section.


Mouse With point 1 still selected, right-click again in the display area.

"Add: Nodal Boundary Condition…"

Select the "Add" pull-out menu and select the "Nodal Boundary Condition…" command.

Mouse Activate the "Tz" checkbox in the "Constrained DOFs" section.


Mouse Click on the vertex at point 2.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the vertices at points 3 and 4.


"Add: Nodal Boundary Conditions…"

Select the "Add" pull-out menu and select the "Nodal Boundary Conditions…" command.

"Fixed" Press the "Fixed" button in the "Predefined" section of the dialog.







Viewing the Results

"Results: Displacement: X"

Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Select the "X" command. The maximum displacement in the X direction is about 0.00414 inches.

"Results: Displacement: Y"

Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Select the "Y" command. The maximum displacement in the Y direction is about -0.01586 inches.

"Results: Stress: Beam and Truss: Axial Stress (Local 1 Direction)"

Access the RESULTS pull-down menu and select the "Stress" pull-out menu. Select the "Beam and Truss" pull-out menu and select the "Axial Stress (Local 1 Direction)" command.

"Inquire: Results" Access the INQUIRE pull-down menu and select the "Results" command.

Mouse Click on the fixed end of the horizontal truss. The axial stress should be about -1,036 psi (compression).

Mouse Click on the fixed end of the vertical truss. The axial stress should be about 3,964 psi (tension).

Mouse Click on the fixed end of the diagonal truss. The axial stress should be about 1,464 psi (tension).

To review a completed archive of this exercise, refer to the file Exercise A.ach in the "Exercise A\ Results Archive" directory.




Exercise B Truss Frame Model

Truss Elements

Objective: Construct and analyze a frame of truss elements loaded with forces. Geometry: Model is built in the XY plane (Top View).

Cross-sectional area = 1 in2

Loads: A nodal force of 2,000 pounds downward will be applied to point C. A nodal force of 1,000 pounds downward will be applied to point E. Constraints: Fully fixed at point A. Translation in the Y and Z directions will be constrained at point G. The rest of the model will be constrained against translation in the Z direction. Elements: Truss Material: Aluminum 6061-T6

Exercise B – Truss Frame Model




Solution

Building the Model



Mouse




Exercise B

Type "Exercise B" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.




"Geometry: Add: Line…"

Access the GEOMETRY pull-down menu and select the "Add" pull-out menu. Select the "Line…" command to bring up the "Define Geometry" dialog.

Mouse Deactivate the "Use as Construction" checkbox.

<Enter> Press <Enter> to accept (0, 0, 0) as the coordinate for the initial vertex at joint A.

432<Enter> Type "432" in the "X" field and press <Enter> to accept (432, 0, 0) as the coordinate for joint G.

<Esc> Press <Esc> to terminate the current line segment and start a new one.

72<Tab>96<Enter> Type "72" in the "X" field, press <Tab>, type "96" in the "Y" field and then press <Enter> to accept (72, 96, 0) as the coordinate for the initial vertex at joint B.

360<Tab>96<Enter> Type "360" in the "X" field, press <Tab>, type "96" in the "Y" field and then press <Enter> to accept (360, 96, 0) as the coordinate for the vertex at joint F.

<Esc> Press <Esc> to terminate the current line segment.

<Esc> Press <Esc> to exit the line command.

"View: Enclose"

Access the VIEW pull-down menu and select the "Enclose" command. Your screen should now look like Figure B1.

NOTE: For images of this model, the "Draw thicker lines" option has been enabled for better visibility

of the trusses. This setting is found under "Tools: Options: Graphics: Miscellaneous."



Figure B1: Adding Line Segments

"Selection: Select: Lines" Access the SELECTION pull-down menu and choose the

"Select" pull-out menu. Select the "Lines" command. Mouse Click on the upper horizontal line.

"Geometry: Tools: Divide" Access the GEOMETRY pull-down menu and select the

"Tools" pull-out menu. Select the "Divide" command. “OK” Click the “OK” button to divide the line into two segments.

Mouse Click on the lower horizontal line.


"Tools" pull-out menu. Select the "Divide" command. 3 Type "3" in the "Number of Lines:" field.

“OK” Click the “OK” button to divide the line into three segments.

"View: Options: Endpoint Vertices"

Access the VIEW pull-down and select the "Options" pull-out menu. Select the "Endpoint Vertices" command. Blue Xs will appear on the vertices.



Mouse

Move the mouse cursor to the left end of the bottom line segment (joint A) as shown in Figure B2. When the cursor is in the vicinity of the vertex (i.e. endpoint), a "lock" icon will appear. When the "lock" icon is visible, click to start a new line segment at the endpoint.



Figure B2: Vertex at Joint A

Mouse

Move the mouse cursor to the left end of the upper line segment (joint B) as shown in Figure B3. When the "lock" icon is visible, click to create the next vertex at the existing endpoint.

Figure B3: Vertex at Joint B



Mouse Continue this process, working in a "zigzag" fashion to add the remaining lines to joints C, D, E, F, and G to complete the mesh for the truss assembly.


<Esc> Press <Esc> to exit the line command. Your screen should now look like Figure B4.

Figure B4: Completed Truss Mesh



"Truss" Select the "Truss" command.


"Modify Element Definition..." Select the "Modify Element Definition…" command.

1 Type "1" in the "Cross-Sectional Area" field.

“OK” Click the “OK” button to accept the change.



"Aluminum 6061-T6; 6061-T651"

Highlight the material "Aluminum 6061-T6; 6061-T651" within the "Aluminum" folder of the "Element Material Selection" dialog. The associated material properties for this material are shown in the right half of the dialog.

“OK” Click the “OK” button to accept the selected material. After assigning the material properties, all red Xs and red text should now be removed from the tree view, indicating that the elements are completely defined.




"Selection: Select: Vertices"

Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Vertices" command. This will allow you select vertices.

Mouse Click on the vertex at point A. When selected, the vertex will turn to a magenta color to signify that it is part of the current selection set.




"Fixed" Press the "Fixed" button. Note that checkmarks appear in all six boxes in the "Constrained DOFs" section.

“OK” Click the “OK” button to apply these constraints to the selected vertex. A red triangle will now appear at the location of the vertex, indicating that it is fully constrained.

Mouse Click on the vertex at point G.



Select the "Add" pull-out menu and select the "Nodal Boundary Condition…" option.

Mouse Activate the "Ty" checkbox in the "Constrained DOFs" section to constrain the translation in the Y direction.

Mouse Activate the "Tz" checkbox in the "Constrained DOFs" section to constrain the translation in the Z direction.

“OK” Click the “OK” button to apply these constraints. A red circle will now appear at the location of the vertex, indicating that it is partially constrained.

"Selection: Shape: Rectangle"

Access the SELECTION pull-down menu and select the "Shape" pull-out menu. Select the "Rectangle" command. This will allow you to select multiple vertices with a rectangle selection box.

Mouse Draw a box around the entire model except for the vertices at points A and G (see Figure B5).

Figure B5: Rectangle Select of Vertices






Mouse Activate the "Tz" checkbox in the "Constrained DOFs" to activate the constraint in the Z direction.

“OK” Click the “OK” button to apply these constraints to the selected vertices.

"Selection: Shape: Point"

Access the SELECTION pull-down menu and select the "Shape" pull-out menu. Select the "Point" command. This will allow you select an object by clicking on it.

Mouse Click on the vertex at joint C.



-2000 Type "-2000" in the "Magnitude" field to specify a force of 2000 pounds acting in a negative direction.

"Y" In the "Direction" section, select the "Y" radio button to specify that the force will be applied in the Y direction.

“OK” Click the “OK” button to apply the force to the selected vertex.

Mouse Click on the vertex at joint E.




"Y" In the "Direction" section, select the "Y" radio button to specify that the force will be applied in the Y direction.

“OK” Click the “OK” button to apply the force to the selected vertex.

Analysis



Viewing the Results


Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Select the "Magnitude" command.

"Results Options: Displaced Model Options…"

Access the RESULTS OPTIONS pull-down menu and select the "Displaced Model Options…" command to bring up the "Displaced Model Options" dialog.



"Mesh" Select the "Mesh" radio button in the "Show Undisplaced Model As" section of the dialog.

Mouse

Press the button in the upper right corner of the "Displaced Model Options" dialog to close it. Your screen should now look similar to the one shown in Figure B6.

Figure B6: Displacement Results

"Results: Element Forces and Moments: 1) Axial Force"

Access the RESULTS pull-down menu and select the "Element Forces and Moments" pull-out menu. Select the "1) Axial Force" command.

"Display Options: Show Element Numbers"

Access the DISPLAY OPTIONS pull-down menu and select the "Show Element Numbers" command. Note that the truss element connecting joints C and D is number 8.

"Inquire: Results…" Access the INQUIRE pull-down menu and select the "Results…" command to bring up the "Inquire: Results" dialog.

Mouse Click on the node at joint D. The "Inquire: Results" dialog indicates that the axial force for element number 8 is 416.667 lbf ,as shown in Figure B7.

"Close" Press the "Close" button to close the "Inquire: Results" dialog.



Figure B7: Inquire Results Dialog

Validation of Results

The force in truss CD can be verified using the method of sections. First, the vertical reaction force at joint A is determined by summing the moments about joint G.

∑Mz = 0 1000(144) + 2000(288) - RA(432) = 0

RA = 1666.667 lbs. Then, the truss assembly is sectioned though trusses BD, CD, and CE and the vertical forces are balanced.

∑Fy = 0 1666.667 – 2000 + FCD(8/10) = 0

FCD = 416.667 lbs.

Comparison of Results

Theoretical Algor Simulation % Difference

416.667 416.667 0.00%

This completes the exercise. To review a completed archive of this exercise, refer to the file Exercise B.ach in the "Exercise B\Results Archive" directory.


Exercise C Support Beam under Gravity

Beam Elements

Objective: Determine the maximum deflection of the beam due to its own weight. Geometry: The beam is parallel to the X axis.

Cross-section: W10 x 100.

Loads: Gravity is applied in the -Y direction. Constraints: Far end is constrained against all degrees of freedom except for rotation about the Z axis.

Near end is constrained against all degrees of freedom except for translation in the X-direction and rotation about the Z axis.

Elements: Beam Material: Steel (AISI 4130)

Exercise C – Support Beam Under Gravity




Solution

Building the Model



Mouse




Exercise C

Type "Exercise C" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.






Mouse Deselect the “Use as Construction” checkbox.

<Enter> Press <Enter> to accept (0, 0, 0) as the coordinate for the initial vertex.

480<Enter> Type "480" in the "X:" field and press <Enter> to accept (480, 0, 0) as the coordinate for the next vertex.



"View: Enclose" Access the VIEW pull-down and select the "Enclose"

command.


"Select" pull-out menu. Select the "Lines" command. Mouse Click on the line that was just created to select it.

"Geometry: Tools: Divide…"

Access the GEOMETRY pull-down menu and select the "Tools" pull-out menu. Select the "Divide" command to bring up the "Divide Lines" dialog.

10 Type "10" in the "Number of Lines:" field in the "Divide Lines" dialog.

“OK” Click the “OK” button to divide the single line segment into 10 line segments.





"Beam" Select the "Beam" option.



Mouse In the "Element Definition" dialog, click anywhere in the "Layer 1" row to select it.

"Cross-Section Libraries…" Press the "Cross-Section Libraries…" button.

"aisc2005" In the "Cross-Section Libraries" dialog, select the "aisc2005" option in the "Section database:" drop-down box.

"W" Select the "W" option in the "Section type:" drop-down box.

w10 Type "w10" in the "Section name:" field to automatically scroll down to the start of the W10 cross-sections.

"W10X100" Select the "W10X100" item in the "Section name:" area.

“OK” Click the “OK” button to accept the properties and close the "Cross-Section Libraries" dialog.

“OK” Click the “OK” button to accept the changes and close the "Element Definition" dialog.



"Steel (AISI 4130)"

Highlight the "Steel (AISI 4130)" item within the “Steel” folder of the “Autodesk Algor Material Library.” The properties of the selected material will appear in the right side of the “Element Material Selection” dialog.

“OK” Click the “OK” button to accept the selected material. After assigning the material properties, all red Xs and red text should now be removed from the tree view, indicating that the elements are completely defined.



"Select" pull-out menu. Select the "Vertices" command. Mouse Click on the vertex at the left end of the beam.




"Fixed" Press the "Fixed" button in the "Predefined" section of the dialog.

Mouse Deactivate the "Rz" checkbox in the "Constrained DOFs" section of the dialog.



“OK” Click the “OK” button to apply the constraints to the selected vertex. A red circle will now appear, indicating that the vertex is partially constrained.

Mouse Click on the vertex at the right end of the beam.




"Fixed" Press the "Fixed" button.

Mouse Deactivate the "Tx" and "Rz" checkboxes.

“OK” Click the “OK” button to apply the constraints to the selected vertex.

Mouse

Expand the "Analysis Type" branch in the tree view by clicking on the plus sign to the left of the icon (if it is not already expanded). Double-click on the "Gravity/ Acceleration" heading.

"Set for standard gravity" Press the "Set for standard gravity" button to automatically apply the standard acceleration due to gravity constant.

-1 Type "-1" in the "Y multiplier" field to indicate that gravity will act in the negative Y direction.

0 Type "0" in the "Z multiplier" field to disable gravity from acting in the Z direction.

“OK” Click the “OK” button to accept the changes.

"Yes" Press the "Yes" button to set the gravity multiplier.

Analysis



Viewing the Results



Mouse

Use the ViewCube to reposition the model for a Y-up isometric view of the beam. Specifically, click just inside the upper-right corner of the "Top" face of the cube. A light blue square at the corner will mark the proper clicking zone.

"View: Display: Shaded with Mesh"

Access the VIEW pull-down menu and select the "Display" pull-out menu. Choose the "Shaded with Mesh" command to enhance the 3-D visualization of the beam shape.


Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Select the "Magnitude" command. The maximum displacement is indicated as 0.305 in, as shown in Figure C1.



Figure C1: Displacement Results

"Selection: Shape: Rectangle" Access the SELECTION pull-down menu and select the

"Shape" pull-out menu. Select the "Rectangle" command.

"Selection: Select: Elements" Access the SELECTION pull-down menu and choose the

"Select" pull-out menu. Select the "Elements" command. Mouse Draw a box enclosing the entire model.

"Inquire: Add Shear Diagrams (Axis 2)"

Access the INQUIRE pull-down menu and select the "Add Shear Diagrams (Axis 2)" command to display the shear diagram.

"Results: Element Forces and Moments: Local 2 Force"

Access the RESULTS pull-down menu and select the "Element Forces and Moments" pull-out menu. Choose the "Local 2 Force" command.

The element force results in the local 2 direction and the shear diagram for the same direction should now appear as shown in Figure C2.



Figure C2: Shear Diagram

"Inquire: Clear Beam Diagrams"

With the beam elements still selected, access the INQUIRE pull-down menu and select the "Clear Beam Diagrams" command to remove the display of the shear diagram.

"Inquire: Add Moment Diagrams (Axis 3)"

Access the INQUIRE pull-down menu and select the "Add Moment Diagrams (Axis 3)" to display the moment diagram as shown in Figure C3.

"Results: Element Forces and Moments: Local 3 Moment"

Access the RESULTS pull-down menu and select the "Element Forces and Moments" pull-out menu. Choose the "Local 3 Moment" command.

The element moment results about axis 3 and the corresponding moment diagram should now appear as shown in Figure C3.



Figure C3: Moment Diagram




Reference Mark’s Standard Handbook for Mechanical Engineers, Tenth Edition, McGraw-Hill, 1996, page 5-23, Table 5.2.2. Theoretical Solution f is the maximum displacement for a simply supported beam with a uniform load.

EIWlf

3845 3

=

The actual total load from gravity can be calculated as follows:

W = (cross-sectional area)(mass density)(gravitational constant)(beam length)

W = (29.4)(0.000732)(386.4)(480)

W = 3991.5 lb *

* Note that this differs slightly from the nominal specific weight of the beam times its length (100 lb/ft. * 40 ft. = 4,000 lb.)

Variable Value Units Comments W 3991.5 lb Calculated total load l 480 in Length of beam E 30E6 lb/in2 Modulus of elasticity I 623 in4 Moment of inertia



0.30753 0.30507 0.8%

This completes the exercise. To review a completed archive of this exercise, refer to the file Exercise C.ach in the "Exercise C\Results Archive" directory.




Exercise D Axisymmetric Thick-Walled Cylinder

2-D Elements

Objective: Determine the hoop stress at the inner radius of the cylinder from the applied pressure load.

Geometry: Model is built in the YZ plane (Right View).

The axis of the cylinder is parallel to the Z axis. Cross-sectional area = 24 in2.

Loads: Uniform internal pressure of 10,000 psi. Constraints: The bottom surface will be constrained against translation in the Z direction. Elements: 2-D Axisymmetric Material: Steel (AISI 4130)

Exercise D – Axisymmetric Thick-walled Cylinder




Solution

Building the Model

Start Autodesk® Algor® Simulation from the Windows Start menu. The mesh for the 2-D elements will be generated from a sketch in the FEA Editor environment.


Mouse




Exercise D

Type "Exercise D" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.

"Save" Press the "Save" button. Mouse Right-click on the "Plane 2 < YZ(+X) >" heading in the

tree view. "Sketch" Select the "Sketch" command.

"Geometry: Add: Rectangle…"

Access the GEOMETRY pull-down menu and select the "Add" pull-out menu. Select the "Rectangle…" command.

7 <Enter> Type "7" in the "Y:" field and press <Enter> to define the point (0, 7, 0) as the first corner of the rectangle.

10 <Tab> 8 <Enter> Type "10" in the "Y:" field, press <Tab>, type "8”, and press <Enter> to define the point (0, 10, 8) as the opposite corner.

"Apply" Press the "Apply" button.

<Esc> Press <Esc> to exit the rectangle command.

"View: Enclose" Access the VIEW pull-down menu and select the

"Enclose" command.

Mouse Right-click on the "Plane 2 < YZ(+X) >" heading in the tree view.

"Sketch" Deselect the "Sketch" command.

Mouse Right-click on the "1 < YZ(+X) >" heading in the tree view under Part 1.

"Create 2D Mesh…" Select the "Create 2D Mesh…" command.






"2-D' Select the "2-D"' command. Mouse Right-click on the "Element Definition" heading for Part 1

in the tree view. "Modify Element Definition..." Select the "Modify Element Definition..." command.

"Axisymmetric" In the "Element Definition" dialog, select the "Axisymmetric" option in the "Geometry Type" drop-down box.

“OK” Click the “OK” button to accept the change. Mouse Right-click on the "Material" heading for Part 1 in the tree

view. "Modify Material…" Select the "Modify Material…" command.

"Steel (AISI 4130)" Highlight the material, "Steel (AISI 4130)", from the list of available materials within the “Steel” folder. The properties of this material can be seen in the right side of the dialog.

“OK” Click the “OK” button to accept the selected material. After assigning the material properties, all red Xs and red text should now be removed from the tree view.



"Select" pull-out menu. Select the "Surfaces" command.

Mouse Select the bottom surface of the model. The chain of lines along the bottom edge of the mesh should turn magenta.




Mouse Activate the "Tz" checkbox in the "Constrained DOFs" section to add the constraint in the Z direction.

“OK” Click the “OK” button to apply these constraints to the selected vertices. A red circle will appear on each vertex along the bottom to indicate that it is partially constrained.

Mouse Click on the left vertical edge of the rectangle.


"Add: Surface Pressure/Traction…"

Select the "Add" pull-out menu and select the "Surface Pressure/Traction…" command.

10000 Type "10000" in the "Magnitude" field.

“OK” Click the “OK” button to apply the pressure.






Mouse

Click the "Toggle Load and Constraint Display" toolbar button to turn off the display of these items, if they are not already hidden.

Results Evaluation and Presentation

The hoop stress is in the tangential (X) direction, which is normal to the plane formed by the radial (Y) and axial (Z) directions.

"Results: Stress: Stress Tensor: 1) XX"

Access the RESULTS pull-down menu and select the "Stress" pull-out menu. Select the "Stress Tensor" pull-out menu and select the "1) XX" command. Your screen should now look like Figure D1.

Figure D1: Hoop Stress Results

To compare the results with the theoretical value, the hoop stress should be obtained from a node at a distance removed from free ends or constraints. This will avoid local effects, which the theoretical solution does not take into account. When comparing FEA results with closed form solutions, it is important to be aware of any assumptions or limitations of the theoretical solution. We will inquire on the nodal stresses at the mid-height of the ring (that is, at Z = 4”).




Mouse

Click on the node at the middle of the inner radius. The "Inquire: Results" dialog indicates that node number 71, at coordinates (0, 7, 4), has a stress value of approximately 29,188 psi.

Mouse

Click on the node at the middle of the outer radius. The "Inquire: Results" dialog indicates that node number 30, at coordinates (0, 10, 4), has a stress value of approximately 19,208 psi.



Reference Roark, R. J. and Young, W. C., Roark's Formulas for Stress and Strain, Fifth Edition, New York, McGraw-Hill, 1975, page 504, Table 32, Case 1A. Theoretical Solution σ2 is the normal stress in the hoop or tangential direction at radius r.

−+

= 22

22

2

2

2 bara

rqbσ

Variable Value Units Comments a 10 in. Outer radius b 7 in. Inner radius q 10,000 psi Internal pressure r - in. Radial location at which

results are calculated.

For r = 7": σ2 = 29,216 psi. For r = 10”: σ2 = 19,216 psi.


r Theoretical Algor Simulation % Difference

7 29,216 29,188 -0.10%

10 19,216 19,208 -0.04%

This completes the exercise. To review a completed archive of this exercise, refer to the file Exercise D.ach in the "Exercise D\Results Archive" directory.


Exercise E Plate under Uniform Pressure

Plate Elements

Objective: Determine the maximum stress in the plate from the applied pressure load. Use the 4 Point structured meshing tool to make the plate.

Geometry: Model is built in the XY plane (Top View) with the long side parallel to the X axis.

Plate is 10" x 5" x 0.25".

Loads: Uniform pressure of 50 psi Constraints: The two long edges will be constrained against translation in the Y and Z directions and

rotation in the Z direction.

One of the short edges will be constrained against translation in the X and Z directions. Elements: Plate Material: Steel (AISI 4130)

Exercise E – Plate Under Uniform Pressure




Solution

Building the Model



Mouse




Exercise E

Type "Exercise E" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.


"Mesh: Structured Mesh: 4 Point Rectangular…"

Access the MESH pull-down menu and select the "Structured Mesh" pull-out menu. Select the "4 Point Rectangular…" command.

20 Type "20" in the "AB:" field.

10 Type "10" in the "BC:" field.

<Enter> Press <Enter> to define the origin as the first point.

10 <Enter> Type "10" in the "X:" field and press <Enter> to define the point (10 ,0, 0) as the second point.

10 <Tab> 5 <Enter> Type "10" in the "X:" field, press <Tab>, type "5”, and press <Enter> to define the point (10, 5, 0) as the third point.

5 <Enter> Type "5" in the "Y:" field and press <Enter> to define the point (0, 5, 0) as the fourth point.

"Apply" Press the "Apply" button to create the mesh.

<Esc> Press <Esc> to exit the mesh command.


Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Top View" command. The mesh will appear as shown in Figure E1.



Figure E1: Plate Element Mesh



"Plate" Select the "Plate" command.


"Modify Element Definition…" Select the "Modify Element Definition..." command.

0.25 In the "Element Definition" dialog, type "0.25" in the "Thickness" field.

100 Type "100" in the "Normal Point (Z)" field. This will be used to control the direction of the uniform pressure load.

“OK” Click the “OK” button to accept the change and close the dialog.



"Steel (AISI 4130)" Highlight the material, "Steel (AISI 4130)", from the list of available materials within the “Steel” folder.

“OK” Click the “OK” button to accept the selected material. After assigning the material properties, all red Xs should now be removed from the tree view.





"Select" pull-out menu. Select the "Vertices" command. Mouse Click on the vertex at the bottom left corner of the plate.

<Ctrl> Mouse Holding down the <Ctrl> key, click on the vertex at the upper left corner of the plate to add it to the selection set.




"Pinned" Press the "Pinned" button to activate the translation constraints in the X, Y, and Z directions.

“OK” Click the “OK” button to apply these constraints to the selected vertices. A red circle will appear on each vertex to indicate that it is partially constrained.



Mouse Draw a box enclosing all of the vertices along the top edge except for the one at the upper left corner (see Figure E2).

Figure E2: Rectangle Select of Upper Vertices

<Ctrl>Mouse Holding down the <Ctrl> key, draw a box enclosing all of the vertices along the bottom edge except for the one at the lower left corner.




Mouse Activate the "Ty" checkbox in the "Constrained DOFs" section to constrain the translation in the Y direction.




Mouse Activate the "Rz" checkbox in the "Constrained DOFs" section to constrain the rotation in the Z direction.


Mouse Draw a box enclosing the left edge except for the lower left and upper left corners.




Mouse Activate the "Tx" checkbox in the "Constrained DOFs" section to constrain the translation in the X direction.



Mouse Click on the + next to the "Surfaces" heading for Part 1 in the tree view to expand this branch.

Mouse Right-click on the "Surface 1" heading for Part 1 in the tree view.




“OK” Click the “OK” button to apply the pressure.

Analysis



Viewing the Results

The maximum stress is in a direction parallel to the free edge, which for this example is the Y direction.

"View: Orientation: Isometric View"

Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Isometric View" command.

"Results: Stress: Stress Tensor: 2) YY"

Access the RESULTS pull-down menu and select the "Stress" pull-out menu. Select the "Stress Tensor" pull-out menu and select the "2) YY" command. The maximum stress is indicated as 15,772 psi.

Mouse

To verify the location of boundary conditions and the orientation of the pressure, press the "Toggle Load and Constraint Display" toolbar button near the bottom of the screen. Your screen should now look similar to the one shown in Figure E3.



Figure E3: Stress Tensor Results




Reference Roark, R. J. and Young, W. C., Roark's Formulas for Stress and Strain, Fifth Edition, New York, McGraw-Hill, 1975, page 389, Table 26, Case 2A. Theoretical Solution σmax is parallel to the free edge.

2

2

maxσt

Bqb= = 15,800 psi

Variable Value Units Comments a 10 in. Length of long side b 5 in. Length of short side q 50 psi Uniform pressure t 0.25 in. Thickness B 0.79 - Parameter from

reference based on a/b ratio of 2.



15,800 15,772 0.18%

This completes the exercise. To review a completed archive of this exercise, refer to the file Exercise E.ach in the "Exercise E\Results Archive" directory.


Exercise F Cantilever Beam Model

Brick Elements

Objective: Determine the maximum bending stress in the beam from the applied load. Geometry:

Loads: 10,000 pounds will be applied downward at the free end of the beam. This should be

distributed between the nodes in the center horizontal row. The two end nodes will have half the force that is applied to the other nodes.

Constraints: The center row of nodes (running in the Y-direction) at the fixed end will be fully

constrained. The remaining nodes at the fixed end will be constrained only against translation in the X-direction.

Elements: Brick Material: Steel (AISI 4130)

Exercise F – Cantilever Beam Model




Solution

Building the Model



Mouse




Exercise F

Type "Exercise F" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.

"Save" Press the "Save" button. We will create a mesh with four elements across the width of the cantilever cross-section and six elements across the height of the cross-section. Since the bending stresses vary, and in fact reverse, across the cross-section height, the higher element count in this direction will help to ensure that these bending stresses are accurately captured. We will then extrude the cross-sectional mesh into a solid mesh, using twenty-four elements along the length of the cantilever.





<Enter> Press <Enter> to define the origin as the first point.

4 <Enter> Type "4" in the "Y:" field and press <Enter> to define the point (0, 4, 0) as the second point.

4 <Tab> 4 <Enter> Type "4" in the "Y:" field, press <Tab>, type "4”, and press <Enter> to define the point (0, 4, 4) as the third point.

4 <Enter> Type "4" in the "Z:" field and press <Enter> to define the point (0, 0, 4) as the fourth point.



"View: Orientation: Right View"

Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Right View" command. The mesh will appear as shown in Figure F1.



Figure F1: Four-Point Rectangular Mesh

Mouse Right-click on the "4-Point Mesh 1" heading in the tree view.

"Move or Copy…" Select the "Move or Copy…" command.

Mouse Activate the "Copy" checkbox.

24 Type "24" in the "Copy" field.

Mouse Activate the "Join" checkbox.

24 Type "24" in the "Total distance" field.

“OK” Click the “OK” button to perform the operation.


Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Isometric View" command. The model should appear as shown in Figure F2.

Figure F2: Brick Mesh



Note that the solid mesh could also have been constructed using the 8 Point 3-D structured meshing tool.



"Brick" Select the "Brick" command.



"Steel (AISI 4130)" Highlight the material, "Steel (AISI 4130)", from the list of available materials within the "Steel" folder.

“OK” Click the “OK” button to accept the selected material. After assigning the material properties, all red Xs and red text should now be gone from the tree view.


"View: Orientation: Front View"

To get a profile of the ends of the beam, access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Front View" command.


Access the SELECTION pull-down menu and choose the "Shape" pull-out menu. Select the "Rectangle" command.


"Select" pull-out menu. Select the "Vertices" command.

Mouse Draw a box around the top three rows of vertices at the left end of the model to select them (see Figure F3).

Figure F3: Rectangle Select of Vertices

<Ctrl>Mouse Holding down the <Ctrl> key, draw a box around the bottom three rows of vertices at the left end of the model to also select these. Only the middle row should remain unselected.






Mouse Activate the "Tx" checkbox in the "Constrained DOFs" section.

“OK” Click the “OK” button to apply this constraint to the selected vertices.

Mouse Draw a box around the center row of vertices at the left end of the model.




"Fixed" Press the "Fixed" button to activate all constraints.

“OK” Click the “OK” button to apply these constraints to the selected vertices. A red triangle will appear on each vertex to indicate that it is fully constrained.


Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Isometric View" command.

"Selection: Shape: Point" Access the "Selection" pull-down menu and select the

"Shape" pull-out menu. Select the "Point" command.

Mouse Click on the vertex at the left side of the center row of vertices at the free end (the face opposite of the end with the boundary conditions).

<Ctrl> Mouse Holding down the <Ctrl> key, click on the vertex at the right side of the center row of vertices at the free end.


"Add: Nodal Forces…" Select the "Add" pull-out menu and select the "Nodal Forces…" command.


"Z" In the "Direction" section, select the "Z" radio button to specify that the force will be applied in the Z direction.

“OK” Click the “OK” button to apply the forces to the selected vertices.

Mouse Click on one of the 3 vertices between the two vertices with the nodal forces.

<Ctrl> Mouse Holding down the <Ctrl> key, click on the other two vertices in between the two vertices with the nodal forces.




"Z" In the "Direction" section, select the "Z" radio button to specify that the force will be applied in the Z direction.

“OK” Click the “OK” button to apply the forces to the selected vertices. The model should now appear as shown in Figure F4.

Note that the total force is 10,000 lbf and that the edge node forces are half the magnitude of the interior node forces (-1,250 = -2,500/2) and (2 * -1,250 + 3 * -2,500 = -10,000).



Figure F4: Completed Brick Element Model

Analysis



Viewing the Results

We will look at the stress tensor in the X-direction, since this is the direction of the bending stress for this cantilever. The stress inquiry will be performed at a node far removed from the beam corners to avoid local effects.

"Results: Stress: Stress Tensor: 1) XX"

Access the RESULTS pull-down menu and select the "Stress" pull-out menu. Select the "Stress Tensor" pull-out menu and select the "1) XX" command. The maximum stress is indicated as 22,321 psi as shown in Figure F5.



Figure F5: Stress Tensor Results


Mouse

Click on the node at the top middle of the constrained end which is highlighted in Figure F6. The "Inquire: Results" dialog indicates that the stress for node number 15 at (0, 2, 4) is 22,099 psi.



Figure F6: Inquire Results Dialog

Mouse

Click on the nodes at (1, 2, 4), (2, 2, 4), (3, 2, 4), (4, 2, 4), (5, 2, 4) and (6, 2, 4) down the middle of the beam to obtain the stress values at each node. These values will be used in the validation of the results in the next section.





Reference Mischke, C. R. and Shigley, J. E., Mechanical Engineering Design, Fifth Edition, McGraw-Hill, 1989, page 44. Theoretical Solution

M = F·L = 10,000 * 24” = 240,000 in.lb.

IMc

bending =σ = 22,500 psi

Variable Value Units Comments

M 240,000 in.lb. Bending moment

c 2 in. Distance to neutral axis

I 21.333 in.4 Moment of inertia (I = bh3/12)


Theoretical (psi)

Algor Simulation

(psi)

% Difference

22,500 22,424 -0.34%

This completes the exercise. To review a completed archive of this exercise, refer to the file Exercise F.ach in the “Exercise F\Results Archive” directory.


Exercise G Comparing Element Types

Beam, 2-D, Plate and Brick Elements

Objective: Analyze a beam model using different element types and compare the results. Geometry:

Loads: 100 psi downward along the top. Constraints: Fixed at left end and simply supported at right end. Elements: 2-D: The pressure is applied as a 100 psi surface load along the top edge.

Beam: Convert the 100 psi load over the 0.25 in width to a 25 lb/in distributed load.

Plate: Model the 10" x 0.5" dimensions and enter a thickness of 0.25". The pressure must be converted to forces on the top edge as follows:

• (Length/# elements along edge) * Width * Pressure = Force • Force/2 located at the end (i.e., corner) nodes

Plate: Model the 10" x 0.25" dimensions and enter a thickness of 0.5". The pressure is applied as a -100 psi traction load in the Z direction.

Brick: The pressure is applied as a 100 psi surface load.

Material: Steel (AISI 4130) Note

: This exercise must be performed using two design scenarios or two different analysis models. The 2-D element model must be analyzed separately from the rest of the models because 2-D elements cannot be included in any model that has nodes outside of the YZ plane (X=0).

Exercise G – Comparing Element Types




Solution

Building the 2-D Model



Mouse




Exercise G

Type "Exercise G" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.


Mouse "Rename"

Right-click on the "Design Scenario 1" heading in the tree view and select the "Rename" command.

2-D Model Type "2-D Model" in the "Description" field.






1<Enter> Type "1" in the "Z:" field and press enter to define the point (0, 0, 1) as the first corner of the rectangle.

<Tab>10<Tab>1<Enter> Press <Tab>, type "10", press <Tab>, type "1", and press enter to define the point (0, 10, 1) as the second corner of the rectangle.

<Tab>10<Tab>1.5<Enter> Press <Tab>, type "10", press <Tab>, type "1.5", and press enter to define the point (0, 10, 1.5) as the third corner of the rectangle.

<Tab><Tab>1.5<Enter> Press <Tab> twice, type "1.5", and press enter to define the point (0, 0, 1.5) as the fourth corner of the rectangle.




Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Right View" command.


Access the SELECTION pull-down menu and select the "Shape" pull-out menu. Select the "Rectangle" command.




"Select" pull-out menu. Select the "Lines" command. Mouse Draw a box around the top edge of the model.

"Geometry: Tools: Modify Attributes…"

Access the GEOEMTRY pull-down menu and select the "Tools" pull-out menu. Select the "Modify Attributes…" command.

2 Type "2" in the "Surface:" field.


Applying Loads and Constraints


"Select" pull-out menu. Select the "Vertices" command. Mouse Draw a box around the left end of the model.






Mouse Draw a box around the center node of the right end of the model.




Mouse Activate the "Tx" checkbox.

Mouse Activate the "Tz" checkbox.

Mouse Activate the "Ry" checkbox.

Mouse Activate the "Rz" checkbox.




"2-D" Select the "2-D" command.



0.25 Type "0.25" in the "Thickness" field.






"Steel (AISI 4130)" Highlight the material, "Steel (AISI 4130)", from the list of available materials within the “Steel” folder.


Mouse Click on the + next to the "Surfaces" heading for Part 1.

Mouse Right-click on the "Surface 2" heading.







Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command. The model will be analyzed and then displayed in the Results environment.

Viewing the Results

Inquire on the result types listed in the “Results” table at the end of the exercise solution (page SE.77) See how the listed 2-D part values compare with your results.

Building the 3-D Model

We will create a second design scenario in which to build the 3-D model, since we cannot mix 2-D and 3-D elements within a single analysis. However, the remaining three variants may all be constructed within the second design scenario.

"Tools: FEA Editor" Access the TOOLS pull-down menu and select the "FEA

Editor" command. Mouse Right-click on the "1 <2-D Model>" heading in the tree view.

"Copy" Select the "Copy" command. A new design scenario heading will appear in the tree view and it will become the current design scenario.

Mouse "Rename"

Right-click on the "2 <2-D Model>" heading in the tree view and select the "Rename" command.

3-D Model Type "3-D Model" in the "Description" field.

“OK” Click the “OK” button. The mesh copied from the 2-D analysis can be used to model the 0.25” thick plate elements. We will have to delete the pressure load from the top of this part. We will apply equivalent nodal forces later.



Mouse “Plate”

Right-click on the “Element Type” heading for Part 1 in the tree view and choose “Plate.”

Mouse Double-click on the “Element Definition” heading for Part 1.

0.25 Type “0.25” in the “Thickness” field.


Mouse Click on the “+” sign to the left of the “FEA Object Groups” heading in the tree view to expand this branch.

Mouse “Delete”

Right-click on the “3 < Surface Pressure/Tractions >” heading and choose “Delete.”

Next, we will build the geometry for the beam part, the 0.5” thick plate part, and the brick element part.




2 Type "2" in the "Part:" field.


<Enter> Press <Enter> to define the origin as the first end point.

<Tab>10<Enter> Press <Tab>, type "10" in the “Y:” field, and press <Enter> to define the second end point as (0, 10, 0).

<Esc> Press <Esc> to end the current line.


"Selection: Shape: Point" Access the SELECTION pull-down menu and select the



"Select" pull-out menu. Select the "Lines" command. Mouse Click on the line you just drew.


"Tools" pull-out menu. Select the "Divide" command. 34 Type "34" in the "Number of Lines:" field.

“OK” Click the “OK” button to create the divisions.

Mouse

Click just inside the top edge of the “Right” face of the ViewCube, near the middle of the edge. A light-blue rectangle will indicate when you are within the proper clicking zone. This will provide an oblique view that will allow us to see the mesh for the next part.









3 <Enter> Type "3" in the "Z:" field and press <Enter> to define the point (0, 0, 3) as the first point.

<Tab> 10 <Tab> 3 <Enter> Press <Tab>, type "10" in the “Y:” field, press <Tab>, type "3" in the “Z:” field, and press <Enter> to define the point (0, 10, 3) as the second corner of the rectangle.

0.25 <Tab> 10 <Tab> 3 <Enter>

Type "0.25" in the “X:” field, press <Tab>, type "10" in the “Y:” field, press <Tab>, type "3" in the “Z:” field, and press <Enter> to define the point (0.25, 10, 3) as the third corner of the rectangle.

0.25 <Tab> <Tab> 3 <Enter>

Type "0.25" in the “X:” field, press <Tab> twice, type "3" in the “Z:” field, and press <Enter> to define the point (0.25, 0, 3) as the fourth corner of the rectangle.




4 <Enter> Type "4" in the "Z:" field and press <Enter> to define the point (0, 0, 4) as the first point.

<Tab> 10 <Tab> 4 <Enter> Press <Tab>, type "10" in the “Y:” field, press <Tab>, type "4" in the “Z:” field, and press <Enter> to define the point (0, 10, 4) as the second corner of the rectangle.

<Tab> 10 <Tab> 4.5 <Enter>

Press <Tab>, type "10", in the “Y:” field, press <Tab>, type "4.5" in the “Z:” field, and press <Enter> to define the point (0, 10, 4.5) as the third corner of the rectangle.

<Tab> <Tab> 4.5 <Enter> Press <Tab> twice, type "4.5" in the “Z:” field, and press <Enter> to define the point (0, 0, 4.5) as the fourth corner of the rectangle.



Mouse Right-click on the "4-Point Mesh 3" heading in the tree view.

"Move or Copy…" Select the "Move or Copy…" command.

Mouse Activate the "Copy" checkbox.

2 Type "2" in the "Copy" field.

Mouse Activate the "Join" checkbox.

0.25 Type "0.25" in the "Total distance" field.

"DX" Select the "DX" radio button.

“OK” Click the “OK” button to perform the operation.




"Shape" pull-out menu. Select the "Rectangle" command. Mouse Draw a box enclosing the top edge of Part 4 (light-blue).

"Geometry: Tools: Modify Attributes…"

Access the GEOMETRY pull-down menu and select the "Tools" pull-out menu. Select the "Modify Attributes…" command.






Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Isometric View" command to verify that the model appears correctly.

Applying Loads and Constraints





Draw a box enclosing the left endpoint of the bottom (beam) part (Part 2).

Mouse Holding down the <Ctrl> key, draw a box around the left end of the two top parts (Parts 3 and 4).






Mouse Draw a box around the right end of the bottom (beam) part (Part 2).

<Ctrl> Mouse Holding down the <Ctrl> key, draw a box around the right end of Part 3.

<Ctrl> Mouse Holding down the <Ctrl> key, draw a box around only the center node of the right end of Part 4.




Mouse Activate the "Tx" checkbox.

Mouse Activate the "Tz" checkbox.

Mouse Activate the "Ry" checkbox.

Mouse Activate the "Rz" checkbox.


Mouse Draw a box around the top edge of Part 1 (second part from the bottom), excluding the two corner nodes.



-250/34= Type "-250/34=" in the "Magnitude" field. The resultant force per node of -7.35294 lbf will be shown.

"Z" Select the "Z" radio button.




The leftmost and rightmost nodes will see a force half the magnitude of the remaining nodes along the top edge. However, since the node at the top left corner is fully constrained, a force there will have no effect. We will therefore omit this particular nodal force and apply the reduced force only to the top right corner node.

Mouse Draw a box around the node at the top right corner of Part 1 (second part from the bottom).



-250/68= Type "-250/68=" in the "Magnitude" field. The resultant force per node of -3.67647 lbf will be shown.



Defining the Remaining Element and Material Data


"Beam" Select the "Beam" command.



Mouse Click in one of the fields for Layer 1 in the "Sectional Properties" table.

"Cross-Section Libraries…" Press the "Cross-Section Libraries…" button.

"Rectangular" Select the "Rectangular" option in the “User-Defined” drop-down box in the upper right corner.

0.25 Type "0.25" in the "b" field.

0.5 Type "0.5" in the "h" field.

“OK” Click the “OK” button to exit the “Cross-Section Libraries” dialog.

“OK” Click the “OK” button to exit the “Element Definition” dialog.






"Select" pull-out menu. Select the "Lines" command. Mouse Draw a rectangle around all of the beam elements.


"Add: Beam Distributed Loads…"

Select the "Add" pull-out menu and select the "Beam Distributed Loads…" command.







"Plate" Select the "Plate" command.



0.5 Type "0.5" in the "Thickness" field.










"Traction" Select the "Traction" radio button.

-100 Type "-100" in the "Z Magnitude" field.



"Brick" Select the "Brick" command.















Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command. The model will be analyzed and then displayed in the Results environment.

Viewing the Results

Mouse Click on the heading for Part 2 in the tree view.

<Shift>Mouse Holding down the <Shift> key, right-click on the heading for Part 4 in the tree view.

"Hide" Select the "Hide" command. The legend will be updated to only show the range for the stress in Part 1. You can use this command to view the results for each part individually.

“Results: Displacement: Magnitude”

Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Choose the "Magnitude" command.

Mouse “Show” and/or “Hide”

Right-click on the various parts in the tree view and alternately “Show” and/or “Hide” them until you have reviewed the individual stress results for each part. Also, review the various applicable results for each part (bending and shear stresses and reactions. Compare your results for the various parts to each other and to those listed in the table below.

Results

Element Type Displacement Magnitude (inch)

X-Reaction Moment * (in-lb)

Shear Force * (lb)

σ y * Max. (psi)

σ y * at mid-span (psi)

σ yz Max. (psi)

2-D 0.01751 ** ** 28,349 14, 976 1,625 First Plate Model (0.25" Thick) 0.01751 ** ** 28,349 14,976 1,625

Beam 0.01761 311.9 156.2 29,933 15,024 ** Second Plate Model (0.5" Thick) 0.01722 313.5 *** ** 30,413 14,929 **** **

Brick 0.01741 ** ** 29,331 14,912 **** 1,814

Values above are magnitudes. Actual results may be positive or negative.

Notes

σ

: * For the beam element part, the “Local 3 Moment” corresponds to the X-Reaction Moment; the "Local 2 Force" corresponds to the Shear Force; and the "Bending Stress in Local 3 Direction" corresponds to the bending stress ( y).

** This result type is not calculated for this element type.

*** The X-Reaction moment for the 0.5” thick plate is the sum the reactions for all fixed nodes.

**** This stress was determined at the node in the middle of the 0.25” thickness.



To review a completed archive of this exercise, refer to the file Exercise G.ach in the "Exercise G\Results Archive" directory.


Exercise H Mesh Convergence

2-D Elements

Objective: To perform a static stress analysis with linear material models on a classical problem, utilizing different meshes densities to determine where convergence occurs. Use mesh density settings of 200, 400, 800, 1600, 3200, and 6400. Increase the 2-D mesh generation "Angle" from the default value of 15 to 30 degrees. This will ensure that the mesh density controls the element size for all cases, otherwise the angle would control the element size for coarser meshes.

Geometry: The part shown below is 1" thick.

Loads: 1,000 psi on the right edge. Constraints: Fully fixed at the left end. Elements: 2-D Plane Stress Material: Stainless Steel (AISI 302) Cold-rolled

Exercise H – Mesh Convergence


Solution

Building the Model

The mesh for the 2-D elements will be generated from a sketch in the FEA Editor environment. Start Autodesk® Algor® Simulation from the Windows Start menu.


Mouse




Exercise H

Type "Exercise H" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.



"Sketch" Select the "Sketch" command.

"Geometry: Add: Rectangle…"

Access the GEOMETRY pull-down menu and select the "Add" pull-out menu. Select the "Rectangle…" command.

<Enter> Press <Enter> to define the origin as the first corner of the rectangle.

4 <Tab> 1.5 <Enter> Type "4" in the "Y:" field, press <Tab>, type "1.5”, and press <Enter> to define the point (0, 4, 1.5) as the opposite corner.


<Esc> Press <Esc> to exit the rectangle command.

"Geometry: Add: Circle: Center and Radius…"

Access the GEOMETRY pull-down menu and select the "Add" pull-out menu. Select the "Circle" pull-out menu and select the "Center and Radius…" command.

2 <Enter> Type "2" in the "Y:" field and press <Enter> to define the point (0, 2, 0) as the center of the circle.

2.45 <Enter> Type "2.45 in the "Y:" field and press <Enter> to define the point (0, 2.45, 0) as a point on the circle.


<Esc> Press <Esc> to exit the circle command.

"View: Enclose" Access the VIEW pull-down and select the "Enclose"

command.

"Selection: Select: Construction Objects"

Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Construction Objects" command.

"Geometry: Tools: Trim" Access the GEOMETRY pull-down menu and select the

"Tools" pull-out menu. Select the "Trim" command.




Mouse Click on the circle.

Mouse Click on the lower half of the circle. It will be removed from the sketch.

Mouse Click on the semicircle.


Mouse Click on the part of the horizontal line inside the circle. It will be removed from the sketch.

<Esc> Press <Esc> to exit the trim command.

"Geometry: Add: Line…" Access the GEOMETRY pull-down menu and select the

"Add" pull-out menu. Select the "Line…" command.

0.75 <Enter> Type "0.75" in the "Z:" field and press <Enter> to define the point (0, 0, 0.75) as the beginning of the line.

4 <Tab> 0.75 <Enter> Type "4" in the "Y:" field, press <Tab>, type "0.75" and press <Enter> to define the point (0, 4, 0.75) as the end of the center line.

<Esc> <Esc> Press <Esc> twice to exit the line command.

Mouse Click on the semicircle.

"Geometry: Tools: Mirror" Access the GEOMETRY pull-down menu and select the

"Tools" pull-out menu. Select the "Mirror" command. "Pick…" Press the "Pick…" button.

Mouse Click on the middle horizontal line.


"Geometry: Tools: Trim" Access the GEOMETRY pull-down menu and select the

"Tools" pull-out menu. Select the "Trim" command. Mouse Click on the upper semicircle.

Mouse Click on the upper horizontal line.

Mouse Click on the part of the horizontal line inside the circle. It will be removed from the sketch.

<Esc> Press <Esc> to exit the trim command.

Mouse Click on the middle horizontal line.

"Edit: Delete" Access the EDIT pull-down menu and select the "Delete"

command.


"Sketch" Select the "Sketch" command.

Mouse Right-click on the "1 < YZ(+X) >" heading for Part 1 in the tree view.

"Create 2D Mesh…" Select the "Create 2D Mesh…" command.

200 Type "200" in the "Mesh Density" field.

"Apply" Press the "Apply" button to generate the mesh.



Defining the Element Parameters


"2-D" Select the "2-D" command.



1 Type "1" in the "Thickness" field.


Mouse Right-click on the "Material" heading in the tree view under Part 1.

"Modify Material…" Select the "Modify Material…" command in the menu.

"Stainless Steel (AISI 302) Cold-rolled"

Select the material, "Stainless Steel (AISI 302) Cold-rolled", from the list of available materials in the “Steel” folder.


Adding the Loads and Constraints


"Select" pull-out menu. Select the "Surfaces" command. Mouse Click on the surface at the right end.



In the menu, select the "Add" pull-out menu and select the "Surface Pressure/Traction…" command.



Mouse Click on the surface at the left end.


"Add: Surface Boundary Condition…"

In the menu, select the "Add" pull-out menu and select the "Surface Boundary Condition…" command.





Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command. The model will be analyzed and will be loaded in the Results environment.



Viewing the Results

"Results: Stress: Stress Tensor: 2) YY"

Access the RESULTS pull-down menu and select the "Stress" pull-out menu. Select the "Stress Tensor" pull-out menu. Select the "2) YY" command. The accepted value for the stress in this direction is 3,560 psi based upon known stress concentration behavior.

Record the stress value in the following table so that the results for each trial mesh density setting may be easily compared:

Mesh Density Maximum YY Stress (psi)

200 400 800

1,600 3,200 6,400

Analyzing the Model with Different Mesh Sizes


Editor" command. Mouse Right-click on the "2-D Mesh 1" heading in the tree view.

"Modify" Select the "Modify" command.

value "Apply"

Type the next mesh density value in the "Mesh Density" field and press the "Apply" button.

Repeat the steps from "Running the Analysis" through the end of the exercise until the stress results for all specified mesh densities have been obtained and recorded.

To review a completed archive of this exercise, refer to the file Exercise H.ach in the "Exercise H\Results Archive" directory. All six trials have been combined into a single model and design scenario for easy comparison.




Exercise I Bracket Model

Brick Elements

Objective: Determine the maximum stress in the bracket from a load applied at the hole. Use default mesh settings.

Geometry: Use the Exercise I.igs file located in the "Exercise I\Input File" directory. Use the default

mesh settings.

Loads: 40 pounds will be applied downward at the hole (that is, in the –Y direction). Constraints: The back surface (-X end of bracket) is fully constrained. Elements: Brick Material: Steel (ASTM - A514)

Apply 40 pound load downward (-Y) at hole.

Fully constrain the back surface.

Exercise I – Bracket Model




Solution

Meshing the Model


"Open" Select the "Open" icon at the left side of the dialog

Mouse



"IGES (*.igs, *.iges)" Select the "IGES (*.igs, *.iges)" option in the CAD Files section of the "Files of type" drop-down box. Navigate to the directory where the model is located.

Exercise I.igs Select the Exercise I.igs file in the "Exercise I \Input File" directory.


Mouse "Linear: Static Stress with Linear Material Models"

If the desired analysis type is not already selected, click on the arrow button to the right of the analysis type field. Select the “Linear” pull-out menu and choose the “Static Stress with Linear Material Models" option.


"Mesh: Generate Mesh" Access the MESH pull-down menu and select the

"Generate Mesh" command. "No" Press the "No" button when asked to view the mesh results.



"Modify: Material…" Select the "Modify Material…" command. "Steel (ASTM - A514)" Highlight the material, "Steel (ASTM - A514)" near the

bottom of the list of available materials in the "Steel” folder. “OK” Click the “OK” button to accept the selected material.



Access the VIEW pull-down menu, select the "Orientation" pull-out menu, and choose the “Right View” command.

"Selection: Select: Surfaces"

Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Surfaces" command. This will allow you to select the surfaces.



Mouse Click on the large square surface, which is the base of the bracket.


"Add: Surface Boundary Condition…"

Select the "Add" pull-out menu and select the "Surface Boundary Condition…" command.


“OK” Click the “OK” button to apply these constraints.

Mouse

Click just inside the right edge of the ViewCube face, about midway between the top and bottom corners. A light-blue rectangle will indicate the correct clicking zone. This will reposition the model to an oblique view in which the two half-cylindrical surfaces of the hole through the bracket will both be visible.

Mouse Click on one of the two surfaces on the inside of the hole.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the second surface.


"Add: Surface Forces…" Select the "Add" pull-out menu and select the "Surface Forces…" command.

-20

Type "-20" in the "Magnitude" field to specify a force of 20 pounds in the negative Y direction on each of the surfaces. This force will be evenly distributed across each of the surfaces so that the total magnitude will be 40 pounds.

Mouse Select the "Y" radio button, in the "Direction" section, to specify that the force will be applied in the Y direction.

“OK” Click the “OK” button to apply these surface forces.


Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Top View" command. Your model should now look like Figure I1.

Figure I1: Bracket with Constraints and Loads Applied



Analysis



Viewing the Results

"View: Orientation: Axonometric View"

Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Axonometric View" command. The model should look like Figure I2.

Figure I2: Displaced Model Showing von Mises Stresses

To review a completed archive of this exercise, refer to the file Exercise I.ach in the "Exercise I\Results Archive" directory.




Exercise J Hanger Assembly Model

Brick Elements

Objective: Determine the maximum stress in the hanger assembly from a load applied at the center of the shaft.

Geometry: Use the Exercise J.ach file located in the "Exercise J\Input File" directory. Mesh the

model at 90% of the default mesh size.

Loads: 100 pounds will be applied in the downward (-Y) direction. Apply the load to a full ring

of nodes at the center of the shaft span. Constraints: The bottom surfaces of the brackets will be fully constrained. Elements: Brick Material: Brackets: Iron, Fe Shaft: Steel (AISI 4130)

Exercise J – Hanger Assembly Model




Solution

Meshing the Model



"Algor Simulation Archive (*.ach)"

Select the "Algor Simulation Archive (*.ach)" option in the Algor Simulation Files section of the "Files of type" drop-down box. Navigate to the directory where the model is located.

Exercise J.ach Select the Exercise J.ach file in the "Exercise J \Input File" directory.

"Open" Press the "Open" button. “OK” Select the location where you want the model to be

extracted and Click the “OK” button.

"Mesh: Model Mesh Settings…"

Access the MESH pull-down menu and select the "Model Mesh Settings…" command to mesh the model using default settings.

Mouse "90%"

Move the "Mesh size" slider towards the right until the indicator shows "90%."

"Mesh model" Press the "Mesh model" button.

"No" Press the "No" button when asked to view the mesh results. A mesh will be displayed at this time.


Mouse Click on the "Material" heading for Part 1 in the tree view.




"Iron, Fe" Highlight the material, "Iron, Fe", from the list of available materials within the “Iron” folder.

“OK” Click the “OK” button to accept the selected material.


"Modify Material…" Select the "Modify Material…" command. "Steel (AISI 4130)" Highlight the material, "Steel (AISI 4130)", from the list

of available materials within the "Steel” folder. “OK” Click the “OK” button to accept the selected material.





Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Surfaces" command. This will allow you to select the surfaces.

Mouse Click on the bottom of one of the brackets.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the bottom of the other bracket.








"Selection: Shape: Rectangle" Access the SELECTION pull-down menu and choose the



Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Vertices" command. This will allow you to select the vertices.

Mouse

Click and drag the mouse to enclose the ring of vertices nearest to the middle of the shaft’s span. Distributing the total load over these nodes will prevent a local stress exaggeration at the point of load attachment. Hint

: The Z-coordinate at the mid-span of the shaft is 7.465".

Mouse Right-click in the display.


-100/16=

Note the number of nodes listed in the "Creating Nodal Force Object" dialog box (16). Type "-100/16=" in the "Magnitude" field. This will calculate and enter the resultant force of -6.25 lbs. per node.

"Y" Select the "Y" radio button in the "Direction" section to specify that the force will be applied in the Y direction.

“OK” Click the “OK” button to apply this force. The model should now look like Figure J1.



Figure J1: Bracket with Constraints and Loads Applied

Analysis


Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command to run the analysis.

“OK” Click the “OK” button to dismiss the pop-up message at the completion of the analysis. The model will be displayed within the Results environment.

Viewing the Results


Access the VIEW pull-down menu and select the "Orientation" pull-out menu. Select the "Isometric View" command. The model should look like Figure J2.



Figure J2: von Mises Stress, Displaced Model

To review a completed archive of this exercise, refer to the file Exercise J.ach in the "Exercise J\Results Archive" directory.


Exercise K Linear Contact Model

Brick Elements

Objective: Determine the stress in the assembly for a maximum upward load of 1000 pounds applied at the bottom of the exposed end of the latch.

Geometry: Use the Exercise K.stp file located in the "Exercise K\Input File" directory.

Loads: 1,000 pounds upward force will be applied at the extended underside of the sliding latch. Constraints: The four bolt holes will be fully constrained. "Rigid" boundary elements with a stiffness of 100 lbf/in will be applied in the X, Y, and

Z directions to the back end surface of the sliding latch. Elements: Brick – An absolute mesh size of 0.15 in. will be used. Material: Sliding Latch: Iron, Fe Handle: Brass, Red

Housing & Base Plate: Steel (ASTM - A36) Contact: The default contact is bonded. Two surface contact pairs should be created:

1. Between the sliding latch and the housing 2. Between the sliding latch and the base plate

Exercise K – Linear Contact Model




Solution

Meshing the Model



"STEP (*.stp, *.ste, *.step)" Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type" drop-down box. Navigate to the directory where the model input file is located.

Exercise K.stp Select the Exercise K.stp file in the "Exercise K \Input File" directory.



Choose the option to "Use STEP file units" if it is not already selected and click the “OK” button. The original STEP file length unit is inches.

Mouse "Linear: Static Stress with Linear Material Models"

If the desired analysis type is not already selected, click on the arrow button to the right of the analysis type field. Select the “Linear” pull-out menu and choose the “Static Stress with Linear Material Models" option.

“OK” Click the “OK” button. For the latch assembly, the contact areas include the interface between the sliding latch and the housing and between the sliding latch and the base plate. For the purpose of this example, the remaining part interfaces will be bonded. The default contact option of "Bonded" will be kept and two contact pairs will be defined as "Surface Contact," overriding the default. This type of contact will prevent the surfaces from penetrating each other, but will allow them to pull away from each other or slide relative to each other with no resistance. Mouse Click on the heading for Part 2 in the tree view (the housing).

<Ctrl> Mouse Holding down the <Ctrl> key, click on the heading for Part 4 in the tree view (the sliding latch).


"Contact: Surface Contact" <Enter>

Select the "Contact" pull-out menu and select the "Surface Contact" command. Press the <Enter> key to accept the default contact pair name and to complete the command.

Mouse Click on the heading for Part 3 in the tree view (the base plate).

<Ctrl> Mouse Holding down the <Ctrl> key, click on the heading for Part 4 in the tree view (the sliding latch).


"Contact: Surface Contact" <Enter>

Select the "Contact" pull-out menu and select the "Surface Contact" command. Press the <Enter> key to accept the default contact pair name and to complete the command.


Access the MESH pull-down menu and select the "Model Mesh Settings…" command.

"Options" Click on the "Options" button.



"Absolute mesh size" Select "Absolute mesh size" from the "Type" pull-down menu.

0.15 Enter "0.15" in the "Size" field.

“OK” Click on the “OK” button to exit the options dialog.

"Mesh model" Press the "Mesh model" button to create the mesh.

"No" Press the "No" button when asked to view the mesh results.

Defining Element and Material Data

Mouse Double-click on the "Material" heading for Part 1 in the tree view. This will open the material selection screen.

"Brass, Red" Highlight the material, "Brass, Red", within the “Brass” folder of the Autodesk Algor Material Library..

“OK” Click the “OK” button to accept this material for the handle.

Mouse Select the "Material" heading for Part 2 in the tree view.



"Modify: Material…" Select the "Modify" pull-out menu and select the "Material…." command.

"Steel (ASTM-A36)" Highlight the material, "Steel (ASTM-A36)", near the bottom of the list of available materials within the “Steel” folder.

“OK” Click the “OK” button to accept this material for the housing and base plate.

Mouse Double-click on the "Material" heading for Part 4 in the tree view.

"Iron, Fe" Highlight the material, "Iron, Fe", from the list of available materials within the “Iron” folder.

“OK” Click the “OK” button to accept this material for the sliding latch.

After assigning the material properties, all red Xs should now be removed from the tree view.



Access the VIEW pull-down menu, select the "Orientation" pull-out menu, and choose the "Top View" command.

"Selection: Shape: Circle"

Access the SELECTION pull-down menu and select the "Shape" pull-out menu. Select the "Circle" command. This will allow you select objects within a circular selection zone.


Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Surfaces" command. This will set a filter to allow you to select surfaces.

Mouse Click near the center of one of the bolt holes and drag the mouse to make a circular selection area large enough to encompass the ID surfaces of one bolt hole.



<Ctrl>Mouse

While holding down the <Ctrl> key, repeat this selection procedure for the remaining three holes. Since you are looking at the edge of the surface, the magenta coloring indicating that the surface has been selected may not be readily apparent unless you rotate the view.






Mouse

Click just inside the top edge of the ViewCube face, about midway between the top corners. A light blue rectangle will indicate the correct clicking zone. This will provide an oblique view of the assembly with the back of the sliding latch visible.

"Selection: Shape: Point"

Access the SELECTION pull-down menu and select the "Shape" pull-out menu. Select the "Point" command. This will allow you select objects by clicking on them.

Mouse Click on the surface at the back end of the sliding latch.


"Add: Surface Rigid Boundaries…"

Select the "Add" pull-out menu and select the "Surface Rigid Boundaries…" command.

Mouse "X," "Y," and "Z"

Activate the checkboxes to apply the boundary elements in the "X," "Y," and "Z" directions.

100

Enter "100" in the "Stiffness" field. This soft boundary provides stability during the contact solution by preventing rigid-body motion but is small enough to produce an insignificant reaction at the surface for the converged solution.


"View: Orientation: Bottom View"

Access the VIEW pull-down menu, select the "Orientation" pull-out menu, and choose the "Bottom View" command.

Mouse Click on the surface at the extended underside of the sliding latch.


"Add: Surface Force…" Select the "Add" pull-out menu and select the "Surface Force…" command.

1000 Enter "1000" in the "Magnitude" field.

Mouse Activate the "Z" direction radio button.

“OK” Click the “OK” button to apply this force.


Access the VIEW pull-down menu, select the "Orientation" pull-out menu, and choose the "Isometric View" command.

Analysis


Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command to run the analysis.



“OK” Click “OK” to dismiss the pop-up message when the analysis has finished. The model will be displayed in the Results environment.

Viewing the Results

There are many options available in the Results environment to customize the presentation of results. For this exercise, the stress range and the legend box precision and font will be modified. "Display Options:

Plot Settings…" Access the DISPLAY OPTIONS pull-down menu and select the "Plot Settings…" command.

Mouse Select the "Legend Properties" tab.

Mouse Using the down-arrow next to the "Precision" field, decrease the precision from 7 to "5".

"Font…" Press the "Font …" button. "16" Select the "16" option in the "Size:" field. Note that you

can also change the font to any of the TrueType fonts listed.

“OK” Click the “OK” button to accept the changes to the legend box font.

Mouse Select the "Range Settings" tab.

Mouse Deactivate the "Automatically calculate value range" checkbox.

0 Type "0" in the "Low" field.

20000

Type "20000" in the "High" field. Any areas with stresses larger than this value will now be rendered using the highest color in the legend box (typically red). One common use of this feature is to set the value to the yield stress of the material in order to quickly see what areas of the model may have yielded. Another is to bring out the full range of colors when focusing on more lowly stressed regions of the model.

“OK” Click the “OK” button and your presentation should now look similar to the one shown in Figure K1.



Figure K1: Stress Results

This completes the exercise. To review a completed archive of this exercise, refer to the file Exercise K.ach in the "Exercise K\Results Archive" directory.




Exercise L Thermal Model

Brick Elements

Objective: To analyze the thermal effects of a block that has hot and cold water passages running through it.

Geometry: Use the Exercise L.ach file located in the "Exercise L\Input File" directory. Use 80% of

the default mesh size.

Loads: Largest Hole:

Water temperature (ambient): T = 65 °F

Convection coefficient: H = 1.4 F sec in

lbsin 2 °

Second Largest Hole:

Water temperature (ambient): T = 180 °F

Convection coefficient: H = 28 F sec in

lbsin 2 °

Elements: Brick Material: Steel (ASTM - A514)

Exercise L – Thermal Model




Solution

Meshing the Model



"Algor Simulation Archive (*.ach)"

Select the "Algor Simulation Archive (*.ach)" option in the Algor Simulation Files section of the "Files of type" drop-down box. Navigate to the directory where the model is located.

Exercise L.ach Select the Exercise L.ach file in the "Exercise L\Input File" directory.


“OK”

Select the location where you want the model to be extracted and click the “OK” button. Note that the analysis type has already been set to Steady-State Heat Transfer for the input archive.


Access the MESH pull-down menu and select the "Model Mesh Settings…" command.

Mouse "80%"

Move the "Mesh size" slider towards the right until the indicator shows "80%."

"Mesh model" Press the "Mesh model" button. "No" Press the "No" button when asked to view the mesh results.

Defining the Element Data


"Modify Material…" Select the "Modify Material…" command. "Steel (ASTM - A514)" Highlight the material, "Steel (ASTM - A514)", from the

list of available materials within the “Steel” folder. “OK” Click the “OK” button.


"Select" pull-out menu. Select the "Surfaces" command. Mouse Click on one of the surfaces of the largest hole.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the second surface of the largest hole. Rotate the model slightly, if desired, to clearly see both surfaces of the hole.

Mouse Right-click in the display area. "Add: Surface Convection

Loads…" Select the "Add" pull-out menu and select the "Surface Convection Loads…" command.

1.4 Type "1.4" in the "Temperature Independent Convection Coefficient" field.



65 Type "65" in the "Temperature" field. “OK” Click the “OK” button. Mouse Click on one of the surfaces of the second largest hole.

<Ctrl>Mouse Holding down the <Ctrl> key, click on the other surface of the second largest hole. Rotate the model slightly, if desired, to clearly see both surfaces of the hole.

Mouse Right-click in the display area. "Add: Surface Convection

Loads…" Select the "Add" pull-out menu and select the "Surface Convection Loads…" command.

28 Type "28" in the "Temperature Independent Convection Coefficient" field.

180 Type "180" in the "Temperature" field. “OK” Click the “OK” button.



Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command. The model will be displayed in the Results environment and solved.

Viewing the Results


Access the VIEW pull-down menu, select the "Orientation" pull-out menu, and choose the "Isometric View" command.

Mouse

The small circles on the surfaces of the two largest holes indicate the applied surface convection loads. Click the "Toggle Load and Constraint Display" toolbar button to turn off the display of the load and constraint symbols. Your screen should now look similar to Figure L1.



Figure L1: Temperature Results

We will now check the temperature of the top surface of the block.

"Inquire: Results…" Access the INQUIRE pull-down menu and select the "Results…" command.

Mouse

Click on a node on the top face (hot end) of the model. The "Inquire: Results" dialog will report that the temperature is somewhere between 174.3 and 176.6 degrees, depending upon which node was selected.

To review a completed archive of this exercise, refer to the file "Exercise L.ach" in the "Exercise L\Results Archive" directory.




Exercise M Mechanical Event Simulation (MES), Geneva Mechanism

Brick and Pipe Elements

Objective: Create universal joints for the rotation, loading, and constraining of two CAD-based parts. Define surface to surface contact to produce the proper component interaction. The drive wheel will be rotated one-half of a revolution to produce a single, 90º indexing movement of the driven wheel. Produce a von Mises stress animation as well as a graph showing the displacement magnitude versus time at the drive wheel's indexing pin and at the OD of the driven wheel.

Geometry: Use the Exercise M.stp file located in the "Exercise M\Input File" directory. See

next page for meshing, geometry modification, and contact setup instructions.

• Joint 1 center vertex location; (0, 0, -0.125) • Joint 2 center vertex location; (1.414214, 0, -0.125) • Joint 3 center vertex location; (0, 0, 0.875) • Joint 4 center vertex location; (1.414214, 0, 0.875)

Loads: Initial velocity of 30 rpm about axis through Joints 1 and 3 (parallel to Z-axis)

applied to the Drive Wheel (Part 1)

Prescribed displacement of a half-revolution in one second (30 rpm) at Joint 3.

Constant 2 lbf.in. nodal Z-moment at Joint 4 (Assign to Load Curve 2 and set a "Death Time" of 1 second for Active Range 1 to ensure that the displacement remains active for the entire simulation event.)

Nodal lumped mass at Joint 4 – Uniform mass of 0.00088 lbf s2/in and a mass moment of inertia in the Z-direction of 0.00135 lbf s2 in. These values simulate a steel disk 1/8” thick with a diameter of 3.5”

Exercise M – Mechanical Event Simulation (MES), Geneva Mechanism


Constraints: Center vertices of Joints 1 and 2 – Fixed except for Rz

Center vertices of Joints 3 and 4 – Tx, Ty, Rx and Ry Elements: Drive and Driven Wheels – Brick, Analysis Type = "Large Displacement" Joints – Pipe, O.D. = 0.1", Wall Thickness = 0.03" Materials: Drive Wheel (Part 1) – Brass, Red

Driven Wheel (Part 2) – Plastic- Nylon Type 6/6 All Joints – Custom – Density=0.0, Modulus of Elasticity =100E6, Poisson's = 0.0, Shear Modulus of Elasticity = 0.0

Analysis Parameters: Duration = 1 second Capture rate = 90 (This will produce a resultant time step for every 2° of drive

wheel rotation.)

Displacement Tolerance = 0.02 (found under the "Equilibrium" tab of the advanced analysis parameters dialog. Disable "Automatic" tolerance control.)

Load Curve Information:

Load Curve 1 (Prescribed Rotation)…

Load Curve 2 (Nodal Moment)…

Meshing, Geometry Modification, and Surface Contact Setup Instructions:

1. Set the default contact = “Free/No Contact” and define a surface contact pair between Part 1 and Part 2, which will prevent mesh matching between the parts (this is desirable for MES contact surfaces).

2. Mesh the model at an absolute mesh size of 0.0625”. 3. Modify line attributes to consolidate the contact surfaces. Use surface 100

for the 1st contact pair, 101 for the 2nd, and 102 for the 3rd. For the drive wheel, surfaces 100 and 101 will each encompass approximately one-third of the perimeter of the wheel’s C-shaped cylindrical contact surface.

4. From the “General Surface-to-Surface Contact” settings, redefine the first pair to be Part 1/Surface 100 to Part 2/Surface 100. Create two more pair; Part 1/Surface 101 to Part 2/Surface 101 and Part 1/Surface 102 to Part 2/Surface 102. Set the contact element “Updating” to “Automatic.” Set the contact parameters for all three pair as follows…

• Contact problem type = “High Speed Contact (Impact)” • Contact type = “Surface to Surface” • User specified contact stiffness = 1000 lbf/in • User specified contact tolerance = 0.0011” (eliminates clearance and

chatter).

Time (s)

Multiplier

0 0 1 1

Time (s)

Multiplier

0 1 1 1



Solution

Meshing the Model


"Open" Select the "Open" icon at the left side of the dialog.

"STEP (*.stp, *.ste, *.step)"

Select the "STEP (*.stp, *.ste, *.step)" option in the CAD Files section of the "Files of type" drop-down box. Navigate to the directory where the model input file is located.

Exercise N.stp Select the Exercise M.stp file in the "Exercise M\Input File" directory.



Choose the option to "Use STEP file units" if it is not already selected and click the “OK” button. The original STEP file length unit is inches.

"Nonlinear: MES with Nonlinear Material Models"

From the analysis type pull-out menu, choose "Nonlinear: MES with Nonlinear Material Models."


Mouse "Free/No Contact"

Right-click on the "Contact (Default: Bonded)" heading at the bottom of the tree view and select "Free/No Contact" as the default contact type.

Mouse Click on the Part 1 heading in the tree view.

<Ctrl>Mouse Hold the <Ctrl> key and click on the Part 2 heading in the tree view.

Mouse "Contact: Surface Contact" <Enter>

Right-click on one of the selected two headings, access the "Contact" pull-out menu, and select the "Surface Contact" command. Hit <Enter> to complete the command without entering a description for the contact pair.

Nonlinear contact occurs between a node and an element face rather than between pairs of nodes, as is the case for linear contact. For this reason, it is best if the meshes between adjacent contact parts are not matched. By default, meshes are not matched for MES contact pairs. That's why it's important to define surface contact between parts 1 and 2 prior to meshing. Later, we will modify the geometry and the contact definitions, localizing the contact calculations to include only those surface pairs where contact will actually occur. This will be done to minimize the number of contact calculations the solver must perform and to speed up the analysis. We will also specify an absolute mesh size of 0.0625". The program's default geometry-based mesh sizing function will automatically provide finer elements around the circumference of the small pin, resulting in an acceptable mesh without further refinement.

"Mesh: Model Mesh Settings" Access the MESH pull-down menu and select the "Model

Mesh Settings" command. "Options" Click on the "Options" button.



Mouse "Absolute mesh size"

Under the "Mesh size" heading, click on the pull-down menu button at the right end of the "Type" field. Select "Absolute mesh size."

0.0625 Enter "0.0625" in the "Size" field.


"Mesh model" Click the "Mesh model" button.

“No” Click “No” when prompted to view the meshing results.

Modifying the Model

We will now select lines on the surface of the wheels and modify their surface number attribute so that they are conveniently grouped into the desired contact surfaces.



Mouse Click and drag the middle mouse button to temporarily enter the rotate view mode. Rotate the model so that the underside of the wheels can be seen.

Mouse "Hide"

Click on the bottom surface of the drive wheel (the disk and not the shaft – Part 1, Surface 29). Then right-click and choose the "Hide" command.


Access the VIEW pull-down menu and choose the "Orientation" pull-out menu. Select the "Top View" command.

"Selection: Shape: Polyline" Access the SELECTION pull-down menu and choose the

"Shape" pull-out menu. Select the "Polyline" command.


"Select" pull-out menu. Select the "Lines" command.

Mouse <Enter>

Refer to Figure M1. Clicking multiple times with the mouse, draw a selection polyline enclosing all of the lines of the first contact pair surfaces (including both the drive and the driven wheel). Hit <Enter> to draw the final segment and to close the polyline loop. Be sure to include the chamfers on both wheels. The lines should be highlighted in magenta as shown in Figure M1. The yellow outline represents the selection polyline.



Figure M1: Selection Polyline (Yellow) and Lines Selected for Modification of Attributes (Magenta)


"Modify Attributes" Select the "Modify Attributes" command.

<Tab> 100 Press <Tab> once to jump to the "Surface" field and type "100" in this field.


"Yes" Click the "Yes" button when asked if you want to proceed.

Mouse <Enter>

Refer to Figure M2. Clicking multiple times with the mouse, draw a selection polyline enclosing all of the lines of the second contact pair surface that belong to the drive

wheel). Hit <Enter> to draw the final segment and to close the polyline loop. Be sure to include the chamfer.

Mouse <Ctrl> <Enter>

Clicking multiple times with the mouse, draw another selection polyline enclosing all of the lines of the second contact pair surface that belong to the driven

wheel). While holding the <Ctrl> key, hit <Enter> to draw the final segment and to close the polyline loop. Be sure to include the two chamfers. The lines should be highlighted in magenta as shown in Figure M2. The yellow outlines represent the selection polylines.

Note: If you close the polyline by clicking again on the starting point, rather than by hitting the <Enter> key before reaching it; you must hold the <Ctrl> key when clicking so that the second group of lines is added

to the selection set. Otherwise, the prior selection will be discarded.



Figure M2: Selection Polylines (Yellow) and Lines Selected for Modification of Attributes (Magenta)






Access the VIEW pull-down menu and choose the "Orientation" pull-out menu. Select the "Right View" command.

"Selection: Shape: Point" Access the SELECTION pull-down menu and choose the




Mouse Click on the upper left half of the indexing pin's cylindrical surface.

<Ctrl> Mouse Holding down the <Ctrl> key, click on the upper right half of the indexing pin's cylindrical surface.

Mouse "Select Subentities: Lines"

Right-click in the display area and choose the "Select Subentities" pull-out menu. Select the "Lines" command.




Mouse "Hide"

In the tree view, right-click of the heading for Part 1 and select the "Hide" command.


Access the VIEW pull-down menu and choose the "Orientation" pull-out menu. Select the "Top View" command.



Mouse Click once anywhere within the model display area, making this the active window, rather than the previously accessed tree view area.

Holding <Z>… <Cursor Left> <Cursor Left> <Cursor Left>

While holding the <Z> key, press the <Cursor Left> key three times. This action will rotate the view about the Z-axis, 45 degrees clockwise (15 degrees per keystroke).



Mouse

Click and drag the mouse to create a selection box enclosing the driven wheel's lines that belong to the third contact surface. This will be the slot at the left side of the display. Include the chamfers at the outside end of the slot but not at the inside end. The lines should be highlighted in magenta as shown in Figure M3. The yellow outline represents the selection box.

Figure M3: Selection Box (Yellow) and Lines Selected for Modification of Attributes (Magenta)





Mouse "Show"

Right-click on the Part 1 heading and select the "Show" command, restoring the visibility of this previously hidden part.

Mouse "Show All Surfaces"

Right-click on the "Surfaces" heading under Part 1 in the tree view. Select the "Show All Surfaces" command. The bottom surface of the drive wheel will reappear.




Access the VIEW pull-down menu and choose the "Orientation" pull-out menu. Select the "Isometric View" command.

"Selection: None" Access the SELECTION pull-down menu and select the "None" command to deselect all items, whether in the display area or tree view.

"File: Save"

Before proceeding further, save the work performed thus far by accessing the FILE pull-down menu and selecting the "Save" command.

Defining Surface Contact Pairs and Parameters

Now that the proper surface line assignments have been applied to the model, we will go into the "MES: Surface-to-Surface Contact" dialog and set up the three contact pairs and their specified parameters.

Mouse "General Surface-to-Surface Contact…"

Right-click in the display area and select the "General Surface-to-Surface Contact…" command.

Mouse "100"

Using the pull-down menu in the "First Surface" field at the top of the dialog, select surface "100."

Mouse "100"

Using the pull-down menu in the "Second Surface" field, select surface "100."

"Add Row" Click on the "Add Row" button.

Mouse "1"

Using the pull-down menu in the "First Part" field, select part "1."

Mouse "101"

Using the pull-down menu in the "First Surface" field, select surface "101."

Mouse "2"

Using the pull-down menu in the "Second Part" field, select part "2."

Mouse "101"


"Add Row" Click on the "Add Row" button.

Mouse "1"

Using the pull-down menu in the "First Part" field, select part "1."

Mouse "102"

Using the pull-down menu in the "First Surface" field, select surface "102."

Mouse "2"

Using the pull-down menu in the "Second Part" field, select part "2."

Mouse "102"


Mouse "Automatic"

Access the pull-down menu at the "Updating" field and choose "Automatic." The active contact elements will be reevaluated as the wheels move to different positions.

Mouse In the first row (Pair 1) of the Contact Pairs table, click on the "Parameters" column (currently showing "Default").

Mouse "High Speed Contact (Impact)"

Change the "Contact problem type" to "High Speed Contact (Impact)" using the provided pull-down menu.

Mouse "Surface to Surface"

Change the "Contact type" to "Surface to Surface" using the provided pull-down menu.

"Advanced" Click on the "Advanced" button.



Mouse Mouse

Activate the checkboxes for both "User-specified contact stiffness" and "User-specified contact tolerance."

1000 Enter "1000" into the "Contact stiffness" field.

0.0011 Enter "0.0011" into the "Contact tolerance" field.

“OK” Click the “OK” button to exit the "Advanced Controls and Parameters for Contact Pair" screen.

“OK” Click the “OK” button to exit the "Controls and Parameters for Contact Pair" screen.

Mouse "All"

To conveniently duplicate these contact settings for the remaining two pairs, access the pull-down menu at the "To Pair" field and select "All."

"Copy" Click on the "Copy" button.

"Yes"

Click the "Yes" button to verify that you want the parameters copied from the source pair (#1) to all other pairs. Note that the Parameters column in the Contact Pairs table will now show "Custom" for all pairs.

“OK” Click the “OK” button to exit the "MES: Surface to Surface Contact" screen.

Creating the Joints

We will next create the four joints used to rotationally mount the two Geneva wheels.





Mouse Click and drag the middle mouse button to temporarily enter the rotate view mode. Rotate the model so that the underside of the wheels can be seen.

Mouse Click on the bottom, end surface of the drive wheel's center shaft (Part 1, Surface 21).

"CAD Mesh Options: Create Joint…"

Right-click in the display area, select the "CAD Mesh Options" pull-out menu, and choose the "Create Joint…" command.

"Universal Joint (lines to axis midpoint)"

Access the pull-down menu at the "Joint" field and choose "Universal Joint (lines to axis midpoint)."

Mouse Activate the "Manual axis/center-point specification" radio button.

<Tab> <Tab> <Tab> -0.125 Press <Tab> three times and type in "-0.125" for the Z-coordinate of the center-point.

“OK” Click the “OK” button to create the first joint.

Mouse Click on the bottom, end surface of the driven wheel's center shaft (Part 2, Surface 4).








<Tab> 1.414214 <Tab> once and type in "1.414214" for the X-coordinate of the center-point.

<Tab> <Tab> -0.125 <Tab> twice and type in "-0.125" for the Z-coordinate of the center-point.

“OK” Click the “OK” button to create the second joint.



Mouse Click on the top, end surface of the drive wheel's center shaft (Part 1, Surface 9).






<Tab> <Tab> <Tab> 0.875 <Tab> three times and type in "0.875" for the Z-coordinate of the center-point.

“OK” Click the “OK” button to create the third joint.

Mouse Click on the top, end surface of the driven wheel's center shaft (Part 2, Surface 18).



Mouse "Universal Joint (lines to axis midpoint)"



<Tab> 1.414214 <Tab> once and type in "1.414214" for the X-coordinate of the center-point.

<Tab> <Tab> 0.875 <Tab> twice and type in "0.875" for the Z-coordinate of the center-point.

“OK” Click the “OK” button to create the fourth and final joint.


Next, we'll define the element type for the joints and the element definitions and materials for each part of the assembly. The element type for the Geneva wheels will have already been set to brick.

Mouse Click on the "Element Definition" heading under Part 1

in the tree view.

<Ctrl> Mouse Holding the <Ctrl> key, click on the "Element Definition" heading under Part 2

in the tree view. Mouse "Modify Element Definition"

Right-click on one of the selected headings and choose the "Modify Element Definition" command.

Mouse "Large Displacement"

Use the pull-down menu in the "Analysis Type" field and select "Large Displacement."



“OK” Click the “OK” button to clear the resulting pop-up message (if the setting had been changed from small to large displacement).

“OK” Click the “OK” button to exit the “Element Definition” screen.

Mouse Double-click on the "Material" heading under Part 1

in the tree view.

Mouse Click on the plus sign to the left of the "Brass" folder to expand this branch.

"Brass, Red" Select the material, "Brass, Red", within the “Brass” folder of the Autodesk Algor Material Library.

“OK” Click on the “OK” button to close the “Element Material Selection” screen.

Mouse Double-click on the "Material" heading under Part 2

in the tree view.

"Plastic- Nylon Type 6/6" Select the material, "Plastic- Nylon Type 6/6", from the list of available materials within the “Plastic” folder.

“OK” Click the “OK” button to close the Element Material Selection screen.

We will set the element type, element definition, and material properties for all four joints simultaneously.

Mouse Click on the "Part 3" heading in the tree view.

<Ctrl> <Shift> "M" Holding down the <Ctrl> and the <Shift> keys, press the "M" key to collapse the tree view's parts list.

<Shift> Mouse Holding the <Shift> key, click on the "Part 6" heading in the tree view. Parts 3 through 6 should now be highlighted.


"Modify: Element Type: Pipe" Access the "Modify" pull-out menu, choose the "Element Type" pull-out menu, and select "Pipe" from the list.

Mouse "Modify: Element Data…"

Once again, right-click on a selected heading, access the "Modify" pull-out menu, and select the "Element Data" command.

Mouse 0.1

Double-click in the "Outside diameter" field and type the value "0.1".

<Tab> 0.03 <Tab> once and enter the value "0.03" into the "Wall thickness" field.

“OK” Click on the “OK” button.

Mouse "Modify: Material…"

One more time, right-click on a selected heading, access the "Modify" pull-out menu, and select the "Material…" command.

"Edit Properties" Press the "Edit Properties" button.

Mouse 100e6

Double-click in the "Modulus of Elasticity" field and enter the value "100e6". All other values remain at zero.

“OK” Click the “OK” button to exit the “Element Material Definition” screen.

“OK” Click the “OK” button to exit the “Element Material Selection” screen.

"File: Save"





Next, we will define the specified loads and constraints. These consist of the nodal loads and constraints at the joint center-points and the part-based load (initial velocity) to be applied to the drive wheel.

"View: Orientation: Front View"

Access the VIEW pull-down menu and choose the "Orientation" pull-out menu. Select the "Front View" command.





Mouse Click and drag the mouse to draw a selection window enclosing the two center-nodes of the bottom two joints (#1 and #2).

Mouse "Add: Nodal Boundary Conditions…"

Right-click in the display area, access the "Add" pull-out menu and select the "Nodal Boundary Conditions…" command.

"Fixed" Click on the "Fixed" button.

"Rz" {deselect} Deselect

the "Rz" checkbox to release this DOF.


Mouse Click and drag the mouse to draw a selection window enclosing the two center-nodes of the top two joints (#3 and #4).

Mouse "Add: Nodal Boundary Conditions…"

Right-click in the display area, access the "Add" pull-out menu and select the "Nodal Boundary Conditions…" command.

"Tx", "Ty", "Rx", "Ry" Activate the "Tx", "Ty", "Rx" and "Ry" checkboxes.




Mouse Click on the center-point of Joint #3 (upper-left). Be sure to select the vertex and not the previously applied boundary condition.

Mouse "Add: Nodal Prescribed Displacement…"

Right-click in the display area, access the "Add" pull-out menu, and select the "Nodal Prescribed Displacement…" command.

"Rotation" Activate the "Rotation" radio button.

<Tab> 0.5 <Tab> once and enter "0.5" in the "Magnitude" field.

"Scalar Z" Activate the "Scalar Z" radio button.

"Curve…" Press the "Curve…" button.

“OK” Click the “OK” button to accept the default load curve (ramp from 0 to 1 in 1 second).

"Data…" Press the "Data…" button.



Mouse 1

Type "1" in the "Death Time" column for Index 1 (the only displayed row). This value ensures that the prescribed displacement remains active throughout the simulation event.

“OK” Click the “OK” button to accept the active range.

“OK” Click the “OK” button to close the “Nodal Prescribed Displacement” dialog.

Mouse Click on the center-point of Joint #4 (upper-right). Be sure to select the vertex and not the previously applied boundary condition.

Mouse "Add: Nodal Moment…"

Right-click in the display area, access the "Add" pull-out menu, and select the "Nodal Moment…" command.

2 Enter "2" in the "Magnitude" field.

"Z" Activate the "Z" direction radio button.

Mouse "2"

Using the up-arrow to the right of the "Load Case / Load Curve" field, increment the load curve number to "2."

"Curve…" Press the "Curve…" button.

"Add Row" Press the "Add Row" button.

Mouse Click in the "Multiplier" column for Time = 0.0 (first row).

1 Type "1" in the Row 1 “Multiplier” column.

<Tab> <Tab> 1 <Tab> twice and type "1" in the Row 2 “Time” column.

<Enter> Press the <Enter> key to update the load curve graph.

“OK” Click the “OK” button to accept Load Curve 2.

“OK” Click the “OK” button to close the “Nodal Moment Object” dialog.

Mouse "Add: Nodal Lumped Mass…"

While the joint 4 center-point is still selected, right-click again, access the "Add" pull-out menu, and select the "Nodal Lumped Mass…" command.

<Tab> 0.00088 <Tab> once and type "0.00088" in the "X Direction" field under the "Mass/Weight" heading.

<Tab> <Tab> <Tab> 0.00135

<Tab> three times and type "0.00135" in the "Z Direction" field under the "Mass Moment of Inertia" heading.

<Tab> 3.5 inch diameter, 1/8 inch thick steel disk.

<Tab> once and type "3.5 inch diameter, 1/8 inch thick steel disk." in the "Description" field.


Mouse "Add: Initial Velocity…"

Right-click on the heading for Part 1

in the tree view. Access the "Add" pull-out menu and select the "Initial Velocity…" command.

Mouse 30

Double-click in the "Z" field under the "Rotational Magnitude" heading and type "30" in this field.




"File: Save"




This completes the application of constraints, loads, element properties, and materials to the assembly. We will now define the analysis parameters.

Defining the Analysis Parameters

"Analysis: Parameters…" Access the ANALYSIS pull-down menu and select the

"Parameters…" command.

Mouse 90 Double-click in the "Capture Rate" field and enter "90".

"Advanced" Click on the "Advanced" button.

Mouse Deselect the "Automatic" checkbox to the right of the "Displacement Tolerance" field.

Mouse 0.02

Double-click in the "Displacement Tolerance" field and enter "0.02".

“OK” Click the “OK” button to close the “Advanced” analysis parameters screen.

“OK” Click the “OK” button to close the “Analysis Parameters” screen.



Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command.

NOTE

: Depending upon the computer hardware, this analysis may take an hour or several hours to run. If time is limited, you may wish to allow several steps to converge, stop the analysis, and then load the already completed model from the provided archive file, “Exercise M\Results Archive\Exercise M.ach”.

Viewing the Results

We will review the stress results for time step 44 (when the peak stress occurs), create and export a graph showing the displacement magnitude as a function of time, and create an animation showing the stress results for the whole simulation. We will also turn off the display of contact diagnostic probes so that they will not appear within the animation. These probes mark areas of node/surface penetration and/or chatter and are useful for troubleshooting a model that is having difficulty converging. They do not necessarily indicate a problem, since slight, localized penetration is not uncommon and may be insignificant. Contact behavior is influenced by the mesh density, mesh smoothness, and contact stiffness. Chatter is generally the result of excessive contact stiffness and makes convergence more difficult.

Mouse

Click the "Toggle Load and Constraint Display" toolbar button to turn off the display of the load and constraint symbols. Your screen should now look similar to Figure L1.

Mouse Disable the displaying of “Contact Diagnostic Probes” by

clicking the associated toolbar icon.



"Results Options: Load Case: Set…"

Access the RESULTS OPTIONS pull-down menu, select the "Load Case" pull-out menu, and choose the "Set…" command.

44 “OK” Type "44" and Click the “OK” button.

Mouse Click on the “Maximum Result Probe” toolbar icon. This

will place a flag at the peak von Mises stress location. Mouse Click on the heading for Part 2 in the tree view.

<Shift> Mouse While holding the <Shift> key, click on the Part 6 heading in the tree view.

Mouse "Hide"

Right-click on a selected heading and choose the "Hide" command. This will improve the visibility of the peak stress, which is on the drive wheel's indexing pin.

Mouse

Click and drag the middle mouse button to temporarily enter the rotate view mode. Rotate the model for a better view of the peak stress area. If desired, roll the wheel to zoom in somewhat.

The annotation and legend will indicate the maximum stress value. This stress should be approximately 5,000 to 5,200 psi and will be in the contact area of the indexing pin. Contact stresses are rather sensitive to surface mesh and contact settings changes, so expect different peak values for modeling variants. The screen image should resemble Figure M4.

Figure M4: Peak von Mises Stress Plot – Time Step 44

Mouse "Show"

Right-click on the Part 2

heading in the tree view and choose the "Show" command.

Mouse Click the “Maximum Result Probe” toolbar icon to toggle off this flag.



"View: Enclose" Access the VIEW pull-down menu and select the

"Enclose" command.


Access the RESULTS pull-down menu, select the "Displacement" pull-out menu, and choose the "Magnitude" command.

Mouse Click on a node on the top, end face of the drive wheel's indexing pin. Choose the node that is furthest from the centerline of the wheel.

<Ctrl> Mouse Holding the <Ctrl> key, select a node at the OD of the driven wheel, for example, one at the outer edge of one of the slot chamfers.

Mouse "Graph Values"

Right-click in the display area and select the "Graph Values" command.

Mouse "Font Size: Large"

Right-click in the graph display area, access the "Font Size" pull-out menu and select the "Large" option. The resulting plot should look like Figure M5.

Figure M5: Displacement versus Time Graph

Mouse "Export Dialog…"

Right-click in the graph display area and select the "Export Dialog…" command.

"PNG" Select the "PNG" radio button under the "Export" heading.

"File" Select the "File" radio button under the "Export Destination" heading.

"Browse…" Exercise M – Displacement Graph.png

Click on the "Browse…" button, accept the default file location and type "Exercise M – Displacement Graph.png" into the "File name" field.



"Save" Click on the "Save" button to return to the Exporting dialog.

Mouse 1024

Double-click on the "Width" field under the "Export Size" heading and enter "1024".

<Tab> 768 <Tab> once and enter "768" in the "Height" field.

Mouse "100"

Using the pull-down menu in the "DPI" field, choose "100," which is the closet value to the typical computer screen's resolution.

"Export" Click on the "Export" button to create the PNG file.

Mouse Click on the first heading, "1 < Stress >," listed under the “Presentations” heading in the tree view to return to the color contour plot.

“Selection: None” Access the SELECTION pull-down menu and choose "None" to deselect the two nodes.

"Results: Stress: von Mises" Access the RESULTS pull-down menu, select the "Stress" pull-out menu, and choose the "von Mises" command.

Before making the stress animation, let's override the default legend range for the plot. This will be done for the following two reasons:

1. To make the correlation between stress level and plot color consistent for all video frames—otherwise, the stress range in the legend will be recalculated for each frame based on the minimum and maximum stress result at that time step only.

2. Because the high contact stresses are localized and the typical stresses in the two wheels are much lower—changing the display range to a lesser maximum value will bring out a broader range of color throughout the assembly and reveal the more typical and lower stress values.

"Display Options: Plot Settings" Access the DISPLAY OPTIONS pull-down menu and select the "Enclose" command.

"Range Settings" Click on the "Range Settings" tab.

Mouse Deactivate the "Automatically calculate value range" checkbox.

<Tab> 0 <Tab> once and enter "0" in the "Low" field under the Current Range heading.

<Tab> 2000 <Tab> once and enter "2000" in the "High" field.

“OK” Click on the “OK” button.

Mouse

Click and drag the middle mouse button to temporarily enter the rotate view mode. Rotate the model to a good viewpoint for creating the animation (AVI file). Also, roll the mouse wheel to zoom in or out as desired.

<Ctrl> Mouse If necessary, reposition the view by holding the <Ctrl> key and clicking and dragging the middle mouse button to temporarily enter the pan view mode.

"Animation: Save as AVI"

Access the ANIMATION pull-down menu and select the "Save as AVI…" command. Or, click on the Export Animation toolbar icon.

We will keep the default settings for frames per second, start and end steps, step increment, and video compression. We will however change the resolution to a standard 4/3 format of 1024 x 768 (assuming it is not already set to that resolution) and we'll change the filename.



Mouse Deactivate the "Lock" checkbox under the “Target Resolution” heading.

Mouse 1024 Double-click in the "Width" field and type "1024".

<Tab> 768 <Tab> once and type "768" in the "Height" field.

Mouse - von Mises Stress

Click twice (slowly) in the "File name" field at the end of the default name, the first click selects the name, the second one positions the cursor just before the point. Append the text, " – von Mises Stress" to the end of the "Exercise M" default filename.

"Save" Click on the "Save" button to generate the AVI file.

"Yes" Click the "Yes" button when asked if you want to view the animation now.

Mouse

Use the Analysis Replay controls to play, pause, or rewind the animation. Click on the button in the upper right corner of the “Analysis Replay” control screen to close both it and the animation window.

To review a completed archive of this exercise, refer to the file "Exercise M\Results Archive\Exercise M.ach”.


Exercise N Nonlinear Material Model

Beam Elements

Objective: First, analyze a cantilever beam using an elastic material model. If the stress exceeds the yield stress of 36,000 psi, run another analysis using a plastic material model.

Geometry: The beam shown below is 10 feet long. The cross section is a 5" x 4”, with the

beam oriented for maximum strength and stiffness for the applied load direction.

Loads: 56,000 pound force downward (-Y direction) at the free end. Constraints: Fully constrained at one end. Elements: Beam (use the “Large Displacement” analysis type option in the “Element

Definition” dialog) Material: Steel (ASTM-A36) Analysis Parameters: Duration = 10 seconds Capture rate = 2 Load Curve Information:

Time (s)

Multiplier

0 0 10 1

Exercise N – Nonlinear Material Model




Solution

Building the Model



Mouse Click on the arrow button to the right of the analysis type field.

"Nonlinear: MES with Nonlinear Material Models "

Select the "Nonlinear" pull-out menu and select the "MES with Nonlinear Material Models" option.


Exercise N

Type "Exercise N" in the "File name:" field in the "Save As" dialog. Note the default folder location where the analysis files will be created. This location can be changed by navigating to an alternate working folder if desired.





Access the GEOMETRY pull-down menu and select the "Add" pull-out menu. Select the "Line…" command to access the "Define Geometry" dialog.


<Enter> Press <Enter> to accept (0, 0, 0) as the coordinate for the initial vertex.

120<Enter> Type "120" in the "X:" field and press <Enter> to accept (120, 0, 0) as the coordinate for the next vertex.



"View: Enclose" Access the VIEW pull-down and select the

"Enclose" command.

"Selection: Select: Lines"

Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Lines" command.

Mouse Click on the line that was just created to select it.

"Geometry: Tools: Divide…"

Access the GEOMETRY pull-down menu and select the "Tools" pull-out menu. Select the "Divide…" command to bring up the "Divide Lines" dialog.

20 Type "20" in the "Number of Lines:" field in the "Divide Lines" dialog.

“OK” Click the “OK” button to divide the single line segment into 20 line segments.





"Beam" Select the "Beam" command. Mouse Right-click on the "Element Definition" heading

for Part 1 in the tree view. "Modify Element Definition..." Select the "Modify Element Definition…" command. “Large Displacement” Select the “Large Displacement” option from the drop-

down list in the “Analysis Type” field. “OK” Click “OK” to dismiss the pop-up message. Mouse Click any cell within the Layer 1 row of the “Sectional

Properties” table to select this row. "Cross-Section Libraries…" Press the "Cross-Section Libraries…" button. "Rectangular" Select the "Rectangular" option in the drop-down

box in the upper right corner. 4 Type "4" in the "b" field. 5 Type "5" in the "h" field. “OK” Click the “OK” button to exit the “Cross-Section

Libraries” dialog. “OK” Click the “OK” button to exit the “Element

Definition” dialog.


Access the SELECTION pull-down menu and select the "Shape" pull-out menu. Select the "Rectangle" command.

Mouse Draw a box enclosing the entire model. Mouse Right-click in the display area. "Beam Orientations: New…" Select the "Beam Orientations" pull-out menu and

select the "New…" command.

0 <Tab> 10 <Enter>

Type”0” in the “X:” field, press <Tab>, type "10" in the "Y:" field, and press <Enter>. This defines an auxiliary vertex (0, 10, 0) that orients the local 2 axis of the beam elements, corresponding to the direction for the 5 inch dimension.



"Steel (ASTM-A36)" Highlight the material, "Steel (ASTM-A36)", near the bottom of the list of available materials within the “Steel” folder.

“OK” Click the “OK” button to accept the selected material.





Access the SELECTION pull-down menu and choose the "Select" pull-out menu. Select the "Vertices" command.

Mouse Draw a box around the vertex at the left end of the beam.





“OK” Click the “OK” button to apply the constraint.

Mouse Draw a box around the vertex at the right end of the beam.




"Y" Select the "Y" radio button.

“OK” Click the “OK” button to apply the force.

Mouse Right-click on the "Analysis Parameters" heading in the tree view.

"Modify Analysis Parameters…" Select the "Modify Analysis Parameters…" command.

10 Type "10" in the "Duration" field.

100 Type "100" in the "Capture rate" field.

10 Type "10" in the second row of the “Time” column within the “Load Curve” table.

“OK” Click the “OK” button to accept the changes.



Access the ANALYSIS pull-down menu and select the "Perform Analysis…" command. The model will be displayed in the Results environment while the solution is progressing.

Viewing the Results

"Results: Beam and Truss: Worst Stress"

Access the RESULTS pull-down menu and select the "Beam and Truss" pull-out menu. Choose the "Worst Stress" command.



The maximum stress is about 40,300 psi, which is well over the yield stress of 36,000 psi. Therefore, a nonlinear material model is necessary. We will create a second design scenario within the model for the non-linear run. Before doing so, we will check the displacement magnitude to compare with the later results, which will consider plastic deformation.


Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Choose the "Magnitude" command.

The maximum displacement magnitude should be about 2.67 inches. We expect this number to be less than the actual displacement with plastic deformation considered.

Creating a New Design Scenario


Editor" command.

Mouse Right-click on the "Design Scenario 1" heading in the tree view and select the "Copy" command.

Mouse Right-click on the "Design Scenario 1" heading in the tree view and select the "Rename" command.

"Elastic Material" Type "Elastic Material" into the "Description" field.


Mouse Right-click on the "Design Scenario 2" heading in the tree view and select the "Rename" command.

"Nonlinear Material" Type "Nonlinear Material" into the "Description" field.

“OK” Click the “OK” button. You now have two design scenarios defined within the model, one for the elastic (isotropic) material model and one for the non-linear (von Mises with isotropic hardening) material model. Double-clicking on an inactive scenario heading will make it the active scenario. We will now modify the element data for the second design scenario to specify the non-linear material model.

Modifying the Element Data



"von Mises with Isotropic Hardening"

Select the "von Mises with Isotropic Hardening" option in the "Material Model" drop-down box.

“OK” Click the “OK” button. Since the material model has been changed, we will revisit the material selection dialog to refresh the properties for the selected material.

Mouse Double-click on the "Material" heading for Part 1 in the tree view.

"OK" Verify that a non-zero “Strain Hardening Modulus” is shown in the material properties list and click "OK."




"Analysis: Perform Analysis…" Access the ANALYSIS pull-down menu and select

the "Perform Analysis…" command.

Viewing the Results

"Results: Stress: Beam and Truss: Worst Stress"

Access the RESULTS pull-down menu and select the "Stress" pull-out menu. Select the "Beam and Truss" pull-out menu and select the "Worst Stress" command. The maximum stress (~37,287 psi) is now below the previous value. Therefore the effect of the lower modulus that was used after yield is obvious.


Access the RESULTS pull-down menu and select the "Displacement" pull-out menu. Choose the "Magnitude" command. The displacement with plasticity of the material taken into account (~4.65 inches) is approximately 2 inches greater than the prior displacement.

To review a completed archive of this exercise, refer to the file "Exercise N.ach" in the "Exercise N\Results Archive" directory. The results archive contains both the elastic and the nonlinear variants of the exercise.



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