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Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit 2
Day 1
Lecture 1 Defining an ABAQUS Model Workshop 1 Basic Input and Output Lecture 2 Linear Static Analysis Workshop 2 Linear Static Analysis of a Cantilever Beam:
Multiple Load Cases Lecture 3 Nonlinear Analysis in ABAQUS/Standard Workshop 3 Nonlinear Statics Lecture 4 Multistep Analysis in ABAQUS
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit 3
Day 2
Lecture 5 Modeling Contact in ABAQUS Lecture 6 Contact Issues Specific to ABAQUS/Standard Workshop 4 Contact Lecture 7 Introduction to Dynamics Workshop 5 Dynamics Lecture 8 Using ABAQUS/Explicit Workshop 5 Dynamics (continued)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit 4
Day 3
Lecture 9 Contact Issues Specific to ABAQUS/Explicit Workshop 6 Contact with ABAQUS/Explicit Lecture 10 Quasi-Static Analysis in ABAQUS/Explicit Lecture 11 Combining ABAQUS/Standard and
ABAQUS/Explicit Workshop 7 Quasi-Static and Import Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit 5
Additional Material
Appendix 1 Element Selection Criteria
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit 6
Legal Notices
The information in this document is subject to change without notice and should not be construed as a commitment by ABAQUS, Inc.
ABAQUS, Inc., assumes no responsibility for any errors that may appear in this document.
The software described in this document is furnished under license and may be used or copied only in accordance with the terms of such license.
No part of this document may be reproduced in any form or distributed in any way without prior written agreement with ABAQUS, Inc.
Copyright ABAQUS, Inc., 2004.Printed in U.S.A.
All Rights Reserved.
ABAQUS is a registered trademark of ABAQUS, Inc.
The following are trademarks of ABAQUS, Inc.:
ABAQUS/Aqua; ABAQUS/CAE; ABAQUS/Design; ABAQUS/Explicit; ABAQUS/Foundation; ABAQUS/Standard; ABAQUS/Viewer; ABAQUS Interface for MOLDFLOW; ABAQUS Interface for MSC.ADAMS; and the ABAQUS, Inc., logo.
All other brand or product names are trademarks or registered trademarks of their respective companies or organizations.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit 7
Revision Status
Updated for v6.510/04Workshop 6
Updated for v6.510/04Lecture 11
Updated for v6.510/04Workshop 1
Updated for v6.510/04Workshop 7
Updated for v6.510/04Workshop 5
Updated for v6.510/04Workshop 4
Updated for v6.510/04Workshop 3
Updated for v6.510/04Workshop 2
Updated for v6.510/04Appendix 1
Updated for v6.510/04Lecture 10
Updated for v6.510/04Lecture 9
Updated for v6.510/04Lecture 8
Updated for v6.510/04Lecture 7
Updated for v6.510/04Lecture 6
Updated for v6.510/04Lecture 5
Updated for v6.510/04Lecture 4
Updated for v6.510/04Lecture 3
Updated for v6.510/04Lecture 2
Updated for v6.510/04Lecture 1
Updated for v6.510/04Answers 6
Updated for v6.510/04Answers 1
Updated for v6.510/04Answers 7
Updated for v6.510/04Answers 5
Updated for v6.510/04Answers 4
Updated for v6.510/04Answers 3
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Defining an ABAQUS Model
Lecture 1
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.2
Overview
Introduction Components of an ABAQUS Model Details of an ABAQUS Input File ABAQUS Input Conventions ABAQUS Output Example: Cantilever Beam Model Parts and Assemblies (optional)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Introduction
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.4
Introduction
ABAQUS, Inc. Founded in 1978.
Headquarters in Providence, Rhode Island (USA).
Offices and representatives throughout the industrialized world.
Sole activities are the development and the support of simulation software for the analysis of engineering problems.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.5
Introduction
Headquarters: Providence, Rhode IslandBranch offices:
USA: California Indiana Michigan Ohio Rhode Island Texas
Overseas: Austria China FinlandFrance Germany (2) IndiaItaly Japan (2) KoreaNetherlands Sweden UK (2)
Representatives:Overseas: Argentina Australia Brazil
Czech Republic Malaysia New ZealandPoland Russia Singapore South Africa Spain TaiwanTurkey
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.6
Introduction
Course preliminaries This course introduces ABAQUS; basic knowledge of finite element
analysis is assumed.
This course introduces concepts in a manner that gives users a working knowledge of ABAQUS as quickly as possiblethe lecture notes do not attempt to cover all the details of ABAQUS completely.
There are several sources for additional information on the topics presented in this course:
ABAQUS Home Page (available via the Internet at www.abaqus.com). ABAQUS documentationall usage details are covered in the users
manuals.
Extensive library of lecture notes developed by ABAQUS on particular topics (a list is available at www.abaqus.com).
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.7
Introduction
ABAQUS is a suite of finite element analysis modules
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.8
Introduction
ABAQUS/CAE Complete ABAQUS Environment for
modeling, managing, and monitoring ABAQUS analyses, as well as visualizing results.
Intuitive and consistent user interface throughout the system.
Based on the concepts of parts and assemblies of part instances, which are common to many CAD systems.
Parts can be created within ABAQUS/CAE or imported from other systems as geometry (to be meshed in ABAQUS/CAE) or as meshes.
Built-in feature-based parametric modeling system for creating parts.
ABAQUS/CAE main user interface
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.9
Introduction
Solver modules ABAQUS/Standard and ABAQUS/Explicit provide the user with two
complementary analysis tools.
ABAQUS/Standards capabilities: General analyses
Static stress/displacement analysis:
Rate-independent response
Rate-dependent (viscoelastic/creep/viscoplastic) response
Transient dynamic stress/displacement analysis
Transient or steady-state heat transfer analysis
Transient or steady-state mass diffusion analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.10
Introduction
Steady-state transport analysis
Coupled problems:
Thermo-mechanical (sequentially or fully coupled)
Thermo-electrical
Pore fluid flow-mechanical
Stress-mass diffusion (sequentially coupled)
Piezoelectric (linear only)
Acoustic-mechanical
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.11
Introduction
Linear perturbation analyses
Static stress/displacement analysis:
Linear static stress/displacement analysis
Eigenvalue buckling load prediction
Dynamic stress/displacement analysis:
Determination of natural modes and frequencies
Transient response via modal superposition
Steady-state response resulting from harmonic loading
Includes alternative subspace projection method for efficient analysis of large models with frequency-dependent properties (like damping)
Response spectrum analysis
Dynamic response resulting from random loading
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.12
Introduction
ABAQUS/Explicits capabilities: Explicit dynamic response with or without adiabatic heating effects
Fully coupled thermo-mechanical analysis
Structural-acoustic analysis
Annealing for multistep forming simulations
Automatic adaptive meshing allows the robust solution of highly nonlinear problems
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.13
Introduction
Comparing ABAQUS/Standard and ABAQUS/Explicit ABAQUS/Standard
A general-purpose finite element program.
Can solve for true static equilibrium in structural simulations.
Provides a large number of capabilities for analyzing many different types of problems, including many nonstructural applications.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.14
Introduction
ABAQUS/Explicit
Solution procedure does not require iteration.
Solves highly discontinuous high-speed dynamic problems efficiently.
Does not require as much disk space as ABAQUS/Standard for larger problems.
Contact calculations are easier with ABAQUS/Explicit. Applications such as quasi-static metal forming simulations are easier.
Provides an adaptive meshing capability.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.15
Introduction
Interactive postprocessing ABAQUS/Viewer is the
postprocessing module of ABAQUS/CAE.
Available with ABAQUS/CAE or as a stand-alone product
Can be used to visualize ABAQUS results whether or not the model was created in ABAQUS/CAE
Provides efficient visualization of large models
Contour plot of an aluminum wheel hitting a curb in ABAQUS/Viewer
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.16
Introduction
Documentation Unless otherwise indicated, all documentation is available both online
and in print.
ABAQUS Analysis Users Manual ABAQUS/CAE Users Manual ABAQUS Example Problems Manual ABAQUS Benchmarks Manual (online only) ABAQUS Verification Manual (online only) ABAQUS Theory Manual (online only)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.17
Introduction
Additional reference materials Installation and Licensing Guide
(Installation instructions) Release Notes
(Explains changes since previous release) Advanced lecture notes on various topics (print only) Tutorials
Getting Started with ABAQUS Getting Started with ABAQUS/Standard: Keywords Version
(online only) Getting Started with ABAQUS/Explicit: Keywords Version
(online only) ABAQUS Home Pagewww.abaqus.com
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.18
Introduction
What is covered in this course Introduction to the analysis
modules and interactive postprocessing.
Details of using ABAQUS to solve a variety of structural analysis problems:
Linear Static Analysis Workshop 1: Basic Input and
Outputanalysis of forces on a connecting lug
Workshop 2: Linear Static Analysis of a Cantilever Beammultiple load cases
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.19
Introduction
Nonlinear Finite Element Analysis Workshop 3: Nonlinear Statics
large deformation analysis of a skew plate
Simulations with Several Analysis Steps
Contact among Multiple Bodies Workshop 4: Contactcontact
analysis of a plate clamped and displaced by rigid dies
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.20
Introduction
Linear and Nonlinear Dynamic Analysis Workshop 5: Dynamicsfrequency
analysis and implicit and explicit free vibration analysis of a cantilever beam
High-Speed Dynamics in ABAQUS/Explicit
Workshop 6: Contact with ABAQUS/Explicit pipe whip problem
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.21
Introduction
Quasi-Static Combined Analysis in ABAQUS/Standard and ABAQUS/Explicit
Workshop 7: Quasi-Static and Import Analysisdeep drawing of a can bottom, including springback
Nonstructural applicationssuch as heat transfer, soils consolidation, and acousticsare not discussed.
All ABAQUS analysis techniques use the same framework.
The knowledge gained in this course will help in learning to use ABAQUS for other applications.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Components of an ABAQUS Model
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.23
Components of an ABAQUS Model
The ABAQUS analysis modules run as batch programs. The primary input to the analysis modules is an input file, which contains options from element, material, procedure, and loading libraries.
These options can be combined in any reasonable way, allowing a tremendous variety of problems to be modeled.
The input file is divided into two parts: model data and history data.
Model data Geometric optionsnodes, elementsMaterial optionsOther model options
History data Procedure optionsLoading optionsOutput options
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.24
Discretized model geometry
nodes,elements
Material properties
Components of an ABAQUS Model
Model datadefine the physical model
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.25
v0
Fixed constraints
Initial conditions
Components of an ABAQUS Model
Model data pin dof 2 fixedENCASTRE
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.26
Components of an ABAQUS Model
History dataspecify what happens to the model
Types of analysis proceduresstatic, dynamic, soil, heat transfer, etc.
Loadings
Prescribed constraints
Output requestsstresses, strains, reaction forces, contact pressure, etc.
ENCASTRE
X-symmetry
Y-symmetry
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.27
Components of an ABAQUS Model
History subdivided into analysis steps Steps are convenient subdivisions in an analysis history.
Different steps can contain different analysis proceduresfor example, static followed by dynamic.
Distinction between general and linear perturbation steps:
General steps define a sequence of events that follow one another.
The state of the model at the end of the previous general step provides the initial conditions for the start of the next step. This is needed for any history-dependent analysis.
Linear perturbation steps provide the linear response about the base state, which is the state at the end of the most recent general step.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.28
Components of an ABAQUS Model
Example: bow and arrow simulation
Step 1: String the bowStep 2: Pull back on the bow string Step 3: Linear perturbation step to extract the natural frequencies of the system
has no effect on subsequent stepsStep 4: Release the arrow
Step 1 = pretension Step 2 = pull back Step 4 = dynamic release
Step 3 = natural frequency extraction
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Details of an ABAQUS Input File
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.30
Details of an ABAQUS Input File
Option blocks All data are defined in option blocks that describe specific aspects of the
problem definition, such as an element definition, etc. Together the option blocks build the model.
Node option block
Property reference option block
Material option block
Element option block
Boundary conditions option block
Contact option block
Initial conditions option block
Analysis procedure option block Loading option block
Output request option block
Model data
History data
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.31
Details of an ABAQUS Input File
Each option block begins with a keyword line (first character is *). Data lines, if needed, follow the keyword line. Comment lines, starting with **, can be included anywhere. All input lines have a limit of 256 characters.
Names can be up to 80 characters long and must begin with a letter. For example, the following would be a permissible name:nodes_at_the_top_of_the_block_next_to_the_gasket
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.32
Details of an ABAQUS Input File
Keyword lines Begin with a single * followed
directly by the name of the option.
May include a combination of required and optional parameters, along with their values, separated by commas.
Example: A material option block defines a set of material properties.
keyword
*MATERIAL, NAME=material name
parameter parameter value
The first line in a material option block
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.33
Details of an ABAQUS Input File
Data lines Define the bulk data for a given
option; for example, element definitions.
A keyword line may have many data lines associated with it.
Example: An element option block defines elements by specifying the element type, the element numbers, and the nodal connectivity.
*ELEMENT, TYPE=B21560, 101, 102564, 102, 103572, 103, 104
keyword line
data lines
node numbers (as required for beam B21 elements)
element numbers
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.34
*ELASTIC, TYPE=ISOTROPIC200.0E4, 0.3, 20.0150.0E3, 0.35, 400.0
Details of an ABAQUS Input File
Example: The elastic material option block defines the type of elasticity model as well as the elastic material properties.
keyword line
data lines
temperature
Poissons ratio
modulus of elasticity
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.35
Details of an ABAQUS Input File
Ordering of option blocks Each option block belongs in either the model data or the history data
one or the other as specified in the users manual.
The ordering within the model data or history data is arbitrary, except for a few cases.
Examples:
HEADING must be the first option in the input file. ELASTIC, DENSITY, and PLASTIC are suboptions of MATERIAL. As such, they must follow MATERIAL directly. Suboptions have no name references of their own.
STATIC, DYNAMIC, and FREQUENCY must follow STEP to specify the analysis procedure for the step.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.36
Node set TOPNODEScontains nodes 101,102, ...
Boundary condition applied to all nodes in node set TOPNODES.
Details of an ABAQUS Input File
Node sets and element sets
Used for efficient cross referencing.
Allow you to refer to a set all at once instead of each node or element individually.
Example: Node sets*NODE, NSET=TOPNODES101, 0.345, 0.679, 0.223102, 0.331, 0.699, 0.234..*BOUNDARY, TYPE=DISPLACEMENTTOPNODES, YSYMM
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.37
Example: Element sets
*ELEMENT, TYPE=B21, ELSET=SEATPOST560, 101, 102, 564, 102, 103..*BEAM SECTION, SECTION=PIPE, MATERIAL=STEEL,ELSET=SEATPOST0.12, 0.004
pipe radius
wall thickness
These beam cross-section properties apply to all elements in element setSEATPOST.
Element set SEATPOSTcontains elements 560, 564, ...
Details of an ABAQUS Input File
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.38
Details of an ABAQUS Input File
Including data from other files ABAQUS reads data from an include file as if the data were directly in the
ABAQUS input file.
An include file can include any portion of an input file and can contain references to other include files.
Data must be in the same format as required for input file dataall rules that apply to input file syntax apply to data from included files.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.39
Details of an ABAQUS Input File
Example: Input file referencing an include file
*HEADING*INCLUDE, INPUT=node_and_element_numbers.txt..
Contents of include file node_and_element_numbers.txt:*NODE, NSET=TOPNODES101, 0.345, 0.679, 0.223102, 0.331, 0.699, 0.234*ELEMENT, TYPE=B21, ELSET=SEATPOST560, 101, 102, 564, 102, 103
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
ABAQUS Input Conventions
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.41
ABAQUS Input Conventions
Units ABAQUS uses no inherent set of units.
It is the users responsibility to use consistent units.
Example:
N, kg, m, s
or
N, 103 kg, mm, s
etc.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.42
ABAQUS Input Conventions
Time measures ABAQUS keeps track of both total time in an analysis and step time for
each analysis step.
Time is physically meaningful for some analysis procedures, such as transient dynamics.
Time is not physically meaningful for some procedures.
In rate-independent, static procedures time is just a convenient, monotonically increasing measure for incrementing loads.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.43
ABAQUS Input Conventions
Coordinate systems For input of initial nodal locations.
The default is a rectangular Cartesian system.
Specify an alternative system using SYSTEM or NODE, SYSTEM=[RECTANGULAR | CYLINDRICAL | SPHERICAL].
Do not affect loading or output because automatically converted internally to the global rectangular Cartesian system.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.44
ABAQUS Input Conventions
For nodal loads, boundary conditions, initial conditions, and output.
The default is a rectangular Cartesian system.
Specify an alternative system using the TRANSFORM option.
These directions do not rotate with the material in large-displacement analyses.
Example: Boundary conditions on a skew edge.
Use TRANSFORM on these nodes with YSYMM boundary conditions
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.45
ABAQUS Input Conventions
For material point directions (directions associated with each elements material or integration points).
Affect input: Anisotropic material directions.
Affect output: Stress/strain output directions.
The default depends on the element type.
Solid elements use a global rectangular Cartesian system.
Shell and membrane elements use a projection of the global Cartesian system onto the surface.
Default material directions for shell and membrane elements
Default material directions for solid elements
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.46
ABAQUS Input Conventions
Specify a local material coordinate system using the ORIENTATION option.
These directions rotatewith the material in large-displacement analyses.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.47
ABAQUS Input Conventions
Degrees of freedom Primary solution variables at the nodes.
Available nodal degrees of freedom depend on the element type.
Each degree of freedom is labeled with a number: 1=x-displacement, 2=y-displacement, ..., 11=temperature.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
ABAQUS Output
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.49
ABAQUS Output
Output Four types of output are available:
Neutral binary output can be written to the output database (.odb) file using the OUTPUT option and related suboptions.
Printed output can be written to the printed output (.dat) file. This is available only for ABAQUS/Standard.
Restart output can be written to the restart (.res) file using the RESTART option for the purpose of conducting restart analyses (discussed in Lecture 4).
Results (.fil) file output can be written for third-party postprocessing.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.50
ABAQUS Output
Output to the output database file The output database file is used by ABAQUS/Viewer. An application
programming interface (API) is available in Python and C++ to use for external postprocessing (e.g., to add data to display in ABAQUS/Viewer).
Two types of output data: field and history data.
Field data is used for model plots (deformed, contour, etc.):*OUTPUT, FIELD ABAQUS/Standard: Specify the output frequency in increments.
ABAQUS/Explicit: Specify the number of intervals during which output is written.
History data is used for XY plots:*OUTPUT, HISTORY Specify the output frequency in increments (both
ABAQUS/Standard and ABAQUS/Explicit) or the time interval between output (ABAQUS/Explicit only).
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.51
ABAQUS Output
The VARIABLE=PRESELECT parameter is optional for either history or field output. It indicates that the default output variables will be written to the output database.
Additional output variables can be selected using any of the following suboptions of OUTPUT:
NODE OUTPUTELEMENT OUTPUTENERGY OUTPUTCONTACT OUTPUTINCREMENTATION OUTPUT (ABAQUS/Explicit only)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.52
ABAQUS Output
Output to the printed output file These options allow tabular data to be written to an ASCII file that can
be read with a text editor.
These options are available only for ABAQUS/Standard. Syntax:
*NODE PRINT*EL PRINT*ENERGY PRINT
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.53
ABAQUS Output
Output to the restart file If a simulation stops prematurely, the restart data can be used to start
the simulation from some intermediate point without repeating any calculations.
*RESTART, WRITE This option is discussed further in Lecture 4.
Output to the results file The results file can be used by third-party postprocessors.
*FILE OUTPUT (This option required for ABAQUS/Explicit only.)*NODE FILE*EL FILE*ENERGY FILE
Select specific output variables
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Example: Cantilever Beam Model
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.55
Example: Cantilever Beam Model
Finite element model using beam elements
boundary conditions node number element number
point load
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.56
Example: Cantilever Beam Model ABAQUS input file with some annotations
Model data*HEADINGCANTILEVER BEAM EXAMPLEUNITS IN MM, N, MPa*NODE 1, 0.0, 0.0..11, 200.0, 0.0*NSET, NSET=END11,*ELEMENT, TYPE=B21, ELSET=BEAMS1, 1, 3..5, 9, 11*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT150.0, 5.0** Material from XXX testing lab*MATERIAL, NAME=MAT1*ELASTIC2.0E5, 0.3*BOUNDARY1, ENCASTRE
comment line
property reference option block
heading option block
node option block
node set definition
element option block
material option block
fixed boundary condition option block
This line will appear on each page of output.
elastic option block
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.57
History data
*STEPAPPLY POINT LOAD*STATIC*CLOAD 11, 2, -1200.0*OUTPUT, FIELD, FREQUENCY=10*ELEMENT OUTPUT, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*NODE OUTPUT, NSET=ENDU*EL PRINT, FREQUENCY=10S, E*NODE FILE, FREQUENCY=5U*END STEP
Example: Cantilever Beam Model
The history data begin with the first *STEP option.
The history data end with the last *END STEP option.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.58
Property references using set names*ELEMENT, TYPE=B21, ELSET=BEAMS1, 1, 3*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT150.0, 5.0*MATERIAL, NAME=MAT1 *ELASTIC2.0E5, 0.3 The property reference BEAM SECTION associates the element set BEAMS with the material definition MAT1.
The option can also provide geometric information. In this case the cross-section type is rectangular (RECT); the width is 50.0; and the height is 5.0.
All elements in a model must have an appropriate property reference. Solid elements reference SOLID SECTION; shell elements reference SHELL SECTION; etc.
Example: Cantilever Beam Model
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.59
Example: Cantilever Beam Model
Material data*MATERIAL, NAME=MAT1*ELASTIC2.0E5, 0.3
Definition for an isotropic linear elastic material
ABAQUS interprets the options following a MATERIAL option as part of the same material option block until the next MATERIAL option or the next nonmaterial property option, such as the NODE option, is encountered.
Options such as ELASTIC are called suboptions and must be used in conjunction with the MATERIAL option.
Poissons ratio
elastic modulus
material name
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.60
Example: Cantilever Beam Model
Fixed boundary conditions*BOUNDARY1, 1, 6
Fixed boundary condition constraints are applied to active degrees of freedom.
Prescribed nonzero boundary conditions can be included only in the history data.
ABAQUS activates only the necessary degrees of freedom at a node. Thus, for this two-dimensional example with only degrees of freedom 1, 2, and 6 active, the following are equivalent input data:1, 1, 21, 6, 6or1, 1, 6or1, ENCASTRE
The batch preprocessor will issue a warning about inactive degrees of freedom.
node or node setrange of degrees of freedom or type of BC (pinned, encastre, symmetry, antisymmetry)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.61
History definition*STEPAPPLY POINT LOAD*STATIC
The STEP option block can include a title of any length. The procedure definition must be the first option after STEP.
Begins the history data
Example: Cantilever Beam Model
This line appears on every page of resultsSpecifies a static analysis procedure
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.62
Loading Definition of a concentrated load in the global negative 2-direction:
*CLOAD 11, 2, -1200.0
Many distributed loadings are also available, including surface pressure, body forces, centrifugal and Coriolis loads, etc.
node or node set
degree of freedom
Example: Cantilever Beam Model
magnitude
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.63
Output requests
*OUTPUT, FIELD, FREQUENCY=10*ELEMENT OUTPUT, VARIABLE=PRESELECT*OUTPUT, HISTORY, FREQUENCY=1*NODE OUTPUT, NSET=ENDU, In this case we have requested field output of a preselected set of the most
commonly used output variables.
We have also requested history output of displacements for the previously defined node set END.
Since history output is usually requested at relatively high frequencies, the sets should be as small as possible.
Each output request includes a FREQUENCY parameter. If the analysis requires many increments, the FREQUENCY parameter specifies how often results will be written to the requested file.
Example: Cantilever Beam Model
output to the output database file
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.64
Example: Cantilever Beam Model
*EL PRINT, FREQUENCY=10S, E*NODE FILE, FREQUENCY=5U Tabular output is printed to the data (.dat) file for visual inspection using
the EL PRINT option. In this case we have requested output of the stress (S) and strain (E)
components.
Binary output is written to the legacy ABAQUS results file for postprocessing in other postprocessors using the NODE FILE option.
In this case we have requested output of the displacement (U) components.
Printed output to the data file
Output to the results file
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.65
End of step
*END STEP Each analysis step ends with the END STEP option. The final option in the input file is the END STEP option for the final
analysis step.
ends the analysis step
Example: Cantilever Beam Model
Video Clip
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Introduction to ABAQUS/Standard and ABAQUS/Explicit
Parts and Assemblies
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.67
Parts and Assemblies
The input file can be defined in terms of parts, part instances, and an assembly.
An ABAQUS model uses the same terminology in the input file as in ABAQUS/CAE.
Future enhancements to ABAQUS will take advantage of the concept of parts and assemblies.
Provides an inherent means of referring to distinct regions of the model. The user need not define separate sets for this purpose.
Allows reuse of part definitions, which is valuable for creating large, complex models.
Labelsnode and element numbers, set namesneed be unique only within the level in which they are defined.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.68
Parts and Assemblies
Defining parts A part is defined by using the PART and END PART options, which must
appear outside of the assembly definition. Each part must have a unique name.
Defining part instances A part instance is defined by using the INSTANCE and END INSTANCE
options within the assembly definition. Each part instance must have a unique name.
Defining an assembly The assembly is defined by using the ASSEMBLY and END ASSEMBLY
options. Only one assembly can be defined in a model.
Additional sets and surfaces, as well as constraints and rigid body definitions, must appear in the assembly definition.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.69
Parts and Assemblies
*HEADING...*PART, NAME=Tire
Node, element, section, set, and surface definitions*END PART*PART, NAME=Rim
Node, element, section, set, and surface definitions*END PART...*ASSEMBLY, NAME=Tire_and_rim
*INSTANCE, NAME=I_Tire, PART=Tire
set and surface definitions (optional)*END INSTANCE*INSTANCE, NAME=I_Rim, PART=Rim
set and surface definitions (optional)*END INSTANCEAdditional set and surface definitions*NSET, NSET=OutputI_Tire.514, I_Tire.520I_Rim.101, I_Rim.102
*END ASSEMBLY
...*MATERIAL, NAME=Rubber*AMPLITUDE*INITIAL CONDITIONS*PHYSICAL CONSTANTS...*STEP*STATIC
*BOUNDARYTire_and_rim.I_Rim.101, 1, 3, 0.0*CLOADTire_and_rim.I_Tire.514, 2, 1000.0
*OUTPUT, HISTORY, FREQUENCY=10*NODE OUTPUT, NSET=Tire_and_rim.OutputRF, CF
*END STEP
Example assembly input file
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.70
Parts and Assemblies
Node labels for parts and the assembly
node label: 101
Part: Rim
Part: Tire
node label: 514
Assembly: Tire_and_rimnode label: I_Tire.514
node label: I_Rim.101
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Workshop 1: Basic Input and Output
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.72
Workshop 1: Basic Input and Output
Workshop tasks1. Use some of the ABAQUS utility programs.
2. Open the online documentation, and search for useful information.
3. Use the online documentation to determine the syntax for variousoptions.
4. Add some details to an existing input file to complete the model of a connecting lug.
50 MPa pressure load 30 kN/(2 0.015m 0.02m)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L1.73
Workshop 1: Basic Input and Output
5. Submit analyses a few different ways (datacheck only, complete analysis, interactive, and batch submission).
6. View the results using ABAQUS/Viewer.
7. Become familiar with the contents of the printed output files.
8. Modify the model, and understand the changes to the results.
Video Clip
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Introduction to ABAQUS/Standard and ABAQUS/Explicit
Linear Static Analysis
Lecture 2
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.2
Overview
Linear and Nonlinear Procedures Linear Static Analysis and Multiple Load Cases Multiple Load Case Usage Examples
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Linear and Nonlinear Procedures
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.4
Linear and Nonlinear Procedures
In ABAQUS/Standard there are two kinds of analysis steps:
General analysis steps:response can be linear or nonlinear.
Linear perturbation steps:response can only be linear.
Step 1 = pretension Step 2 = pull back Step 4 = dynamic release
Step 3 = natural frequency extraction
Video Clip
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.5
In this context linear analysis is a linear perturbation about a base state, which can be either the initial or the current configuration of the model.
The response prior to reaching the base state, when that is the current configuration of the model, can be nonlinear.
But the model must be in static equilibrium (the DYNAMIC option can be used only if it is followed by a STATIC step to achieve static equilibrium before the perturbation analysis is performed).
Further nonlinear analysis steps after a perturbation step are also allowed.
In ABAQUS/Explicit there are only general analysis steps.
Linear and Nonlinear Procedures
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.6
The purely linear perturbation procedures in ABAQUS/Standard are:
BUCKLE (eigenvalue buckling analysis)FREQUENCY (eigenvalue extraction)MODAL DYNAMIC (transient linear dynamic analysis)RANDOM RESPONSE (response of structure to random excitation)RESPONSE SPECTRUM (peak linear response to dynamic loads)STEADY STATE DYNAMICS (steady-state dynamic response to
harmonic excitation)
A *STATIC step can be either a linear perturbation or a general procedure.
Discussed further in the next section.
Linear and Nonlinear Procedures
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.7
Linear and Nonlinear Procedures
Default amplitude references Different defaults for different
analysis procedures
AMPLITUDE=RAMP for procedureswithout natural time scales:
STATICHEAT TRANSFER, STEADY STATECOUPLED TEMPERATURE-DISPLACEMENT, STEADY STATESOILS, STEADY STATECOUPLED THERMAL-ELECTRICAL, STEADY STATESTEADY STATE TRANSPORT
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.8
AMPLITUDE=STEP for procedures with natural time scales:
DYNAMICVISCOHEAT TRANSFER (transient)COUPLED TEMPERATURE-DISPLACEMENT (transient)DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICITCOUPLED THERMAL-ELECTRICAL (transient)SOILS, CONSOLIDATIONSTEADY STATE DYNAMICSRANDOM RESPONSE MODAL DYNAMIC
A nonzero displacement boundary condition prescribed in an explicit dynamic procedure (DYNAMIC, EXPLICIT) must refer to an amplitude option.
Linear and Nonlinear Procedures
Note: Frequency domain proceduresamplitude references define load versus frequency.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Linear Static Analysis and Multiple Load Cases
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.10
Static analyses are the only procedures that can be performed as either a general or perturbation step:
*STEP*STATICor
*STEP, PERTURBATION*STATIC
When investigating the linear static responses of a structure subjected to distinct sets of loads and boundary conditions, it is convenient (and generally more efficient) to use multiple load cases in a single perturbation step rather than using multiple perturbation steps.
A load case includes a single set of loads and boundary conditions.
Linear Static Analysis and Multiple Load Cases
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.11
Linear Static Analysis and Multiple Load Cases
Multiple load cases are advantageous when analyzing components that are subjected to many different types of loads.
Common in many industries.
For example, an aircraft experiences different loads during take-off, climb, cruise, decent, landing, and taxiing.
Each load case is applied independently.
If the stiffness of the structure is assumed constant over all phases of the loading history (linear assumption), a multiple load case analysis is an attractive option to determine the loading envelope.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.12
Linear Static Analysis and Multiple Load Cases
Multiple *LOAD CASE Multiple STEP, PERTURBATION
Element loop(stiffness/
multiple RHS)
Primary factorization(w/ possibly multiplesmall factorizations)
Simultaneousbacksubstitution
Element loop(simultaneous
recovery)
Element loop(stiffness/
single RHS)
Factorization(or read factorized
matrix from .fct)
Backsubstitution
Element loop(recovery)
Next *STEP
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.13
Linear Static Analysis and Multiple Load Cases
Example: An agricultural implement This is an agricultural implement attached to and towed behind a tractor
through a 3-point hitch.
The purpose of the hitch is to transfer towing loads to the implement, but otherwise to allow the implement to float and move more or less independently of the tractor.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.14
Linear Static Analysis and Multiple Load Cases
Three load cases The connection is very flexible and the loads on the implement are not well
defined, but are a combination of many different types of loads.
Vertical Loads
Lateral Loads
Forward Loads
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Introduction to ABAQUS/Standard and ABAQUS/Explicit
Multiple Load Case Usage
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.16
Multiple Load Case Usage
The following procedures support load cases:
*STEP, PERTURBATION*STATIC
*STEADY STATE DYNAMICS, DIRECT A load case may contain the following load types:
Concentrated and distributed loads
Boundary conditions (may change from load case to load case)
Inertia relief
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.17
Multiple Load Case Usage
...*Step, perturbation*Static*Load Case, name="Bending A"*Boundaryright, 1, 6*Cloadleft, 3, 1.*End Load Case *Load Case, name="Bending B"*Boundaryleft, 1, 6*Cloadright, 3, 1.*End Load Case*End Step
Node set left
Node set right
Bending A
Bending B
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.18
Multiple Load Case Usage
Additional rules Load case names (LOAD CASE, name=name) must be unique Load options specified outside of load cases apply to all load cases
Base state boundary conditions propagate to all load cases Rules for using OP=NEW
If used anywhere in a load case step, must be used everywhere inthat step
If used on any BOUNDARY in a load case step, propagated boundary conditions will be removed in all load cases
LOAD CASE options do not propagate
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.19
Multiple Load Case Usage
Changing boundary conditions from load case to load case No performance penalty when boundary conditions change only in
magnitude.
Limit number of boundary conditions which change location from load case to load case.
Depending on number and distribution of boundary conditions which change location, multiple load case analysis may be significantly slower than equivalent multiple step analysis (very problem dependent).
If in doubt, run datacheck analyses (multiple step vs. multiple load case) and compare solver information in data (.dat) file (e.g., memory requirements, number of floating point operations, etc.).
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.20
Multiple Load Case Usage
Problem size Combination of number of degrees of freedom and number of load cases
determines problem size.
Multiple load case analyses may require more:
memory than equivalent multiple step analyses (e.g., all right-hand-sides must be kept in core during backsubstitution).
disk space (element and nodal databases).
When possible, set: standard_memory to minimize I/O (see data file). standard_memory_policy to MAXIMUM.
If necessary, spread load cases over several steps to reduce memory/disk usage per step.
Worst case: resort to multiple perturbation steps (again, compare solver information in data file).
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.21
Multiple Load Case Usage
Output Output requested per step (not per
load case)
Available for the output database (.odb) and printed output (.dat) files
For the output database file:
All output variables for a load case are mapped to a frame
Similar to the way increments are mapped to frames
Frame contains load case name
Field output only (no history output)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.22
Multiple Load Case Usage
Postprocessing with ABAQUS/Viewer
Operations on entire frames supported
For selected frames, can create:
Linear combinations (e.g., linear combination of load cases)
Min/Max envelope (e.g., find max stresses over all load cases)
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.23
Multiple Load Case Usage
Mises stress: Bending A Mises stress: Bending B
Max value of Mises stress over both frames
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Introduction to ABAQUS/Standard and ABAQUS/Explicit
Examples
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.25
Examples
Square plate benchmark
Number of load cases: 8 and 16 *Static, perturbation Changing boundary condition
locations at corners
Default output
Changing BCs15060065013
2424062012
33840067514
612061011
# variables(# DOF)# nodes/edgeModel
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.26
Examples
Performance results: Total CPU time
0.E+00
1.E+04
2.E+04
3.E+04
4.E+04
0.E+00 1.E+06 2.E+06 3.E+06 4.E+06Number of variables
CPU
time
(sec
)
8 Steps8 Load Cases16 Steps16 Load Cases
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.27
Examples
Performance: Details for 751 751 model
Relative CPU Time 3.4 M variable case
7.485.04Total
14.37.52Solver
16 Steps/16 Load cases8 Steps/8 Load cases
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.28
Examples
Modify 501 501 model 8 load cases
Boundary conditions on opposite edges changing per load case
Relative total CPU time: ~0.153 (multiple load case ~6.6 slower!)
Watch number and location of changing boundary conditions!
Changing BCs
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.29
Examples
Chassis-bracket mobility analysis:Number of variables: 534,000
Number of equations: 483,000
Number of load cases: 60*Steady-state dynamics, direct
(10 frequency points)
Output: U (output database)
CPU time (sec)
11,600 (10 faster)1965 60 = 117,600Total1990 (39 faster)1290 60 = 77,400Solver
60 load cases60 steps (projected based on 1 step)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Workshop 2: Linear Static Analysis of a Cantilever Beam
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L2.31
Workshop 2: Linear Static Analysis of a Cantilever Beam
Workshop tasks1. Use multiple load cases to analyze the bending response of the beam.
2. Compare the solution and analysis times obtained using a single step with multiple load cases and multiple steps with single load cases.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Nonlinear Analysis in ABAQUS/Standard
Lecture 3
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.2
Overview
Nonlinearity in Structural Mechanics Solving Equilibrium Equations Nonlinear Input File Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Nonlinearity in Structural Mechanics
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.4
Nonlinearity in Structural Mechanics
Some examples of material nonlinearity
Sources of nonlinearity Material nonlinearities:
Nonlinear elasticity
Plasticity
Material damage
Failure mechanisms
Etc.
Note: Material dependencies on temperature or field variables do not introduce nonlinearity if the temperature or field variables are predefined.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.5
Nonlinearity in Structural Mechanics
An example of self-contact:Example Problem 1.1.16, Compression of a jounce bumper
Boundary nonlinearities: Contact problems
Boundary conditions change during the analysis.
Extremely discontinuous form of nonlinearity.
Video Clip
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.6
Nonlinearity in Structural Mechanics
Geometric nonlinearities: Large deflections and
deformations
Large rotations
Structural instabilities (buckling)
Preloading effects
An example of geometric nonlinearity: elastomeric keyboard dome
Video Clip
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Introduction to ABAQUS/Standard and ABAQUS/Explicit
Solving Equilibrium Equations
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Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.8
Solving Equilibrium Equations
Typical nonlinear problems have all three forms of nonlinearity.
Must include the nonlinear terms in the equations.
Generally, the nonlinear equations for each degree of freedom are coupled.
The basic statement of static equilibrium is that the internal forces exerted on the nodes, I, resulting from the element stresses and external forces, P, acting at every node must balance:
0)()( = uIuP (Eq. 3.1)
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.9
Solving Equilibrium Equations
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.10
Solving Equilibrium Equations
To solve for equilibrium in nonlinear problems, ABAQUS/Standard uses an incremental-iterative solution, based on the Newton-Raphson technique.
Assume that the solution to the previous load increment, u0, is known.
Assume that after an iteration, i, an approximation, ui, to the solution has been obtained. Let ci+1 be the difference between this solution and the exact solution to the discrete equilibrium equation, Equation 3.1, so that
Expanding the left-hand side of Equation 3.2 in a Taylor series about the approximate solution, ui, then gives
(Eq. 3.2)
(Eq. 3.3)
.0)()( 11 =++ ++ iiii cuIcuP
1( ) ( )( ) ( ) .... 0i ii i i
P u I uP u I u cu u +
+ + = .
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.11
By ignoring higher-order terms, the equation can be written as
where is the tangent stiffness.
The next approximation to the solution is
Note that if the load depends on displacement (e.g., pressure on a surface that rotates), the stiffness matrix includes a load stiffness contribution.
Solving Equilibrium Equations
,)()(1 iiii uIuPcK =+
uuP
uuIK iii
= )()(
.11 ++ += iii cuu
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.12
Solving Equilibrium Equations
Static equilibrium in a mesh1. Apply an increment of
prescribed load.
2. Iterate until the sum of all forces acting on each node is small.
3. Update the state once equilibrium has been satisfied.
4. Go back to Step 1, and apply the next load increment.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.13
Single degree of freedom example
Nonlinear spring
Find u(P) or P(u)typically, load ramped from 0 to PFINALduring the step.
Time will usually vary from 0 to 1.
Solving Equilibrium Equations
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.14
Solving Equilibrium Equations
Newton-Raphson solution technique
Iteration 1 (i=1) Assume that the solution u0, P0
at the end of the previous converged increment is known.
A small increment of load, P, is applied to the structure during the current increment.
ABAQUS determines the displacement correction, c1, based on the tangent stiffness,K0, at u0; the total load, PTOTAL; and the internal forces at the end of the previous increment,
.: 0100 IPcKI TOTAL =
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.15
ABAQUS forms K1 and calculates I1 based on the updated state of the model, u1.
The difference between the total applied force, PTOTAL, and the internal force, I1, is called the force residual, R1: R1= PTOTAL I1.
If R1 is very small (within the tolerance limit) at every degree of freedom in the model, the structure is in equilibrium.
The default tolerance is that R1 must be less than 0.5% of the time averaged force in the structure.
ABAQUS automatically calculates the time averaged force.
If the iteration does not produce a converged solution, ABAQUS will perform another iteration in an attempt to find a converged solution.
Solving Equilibrium Equations
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.16
Iteration 2 (i=2) A new displacement
correction, c2, is calculated based on the updated stiffness, K1, and
The new residual, R2, is compared with the tolerances to see if the solution, u2, is converged.
Solving Equilibrium Equations
.1211 : IPcKI TOTAL =
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.17
Solving Equilibrium Equations
This procedure is repeated until force residuals are within the tolerance limits. Each iteration, i, requires:
1. Formulation of tangent stiffness, Ki.
2. Solution of simultaneous system of equations for ci+1.
Update the estimate of the solution: ui+1 = ui + ci+1.
3. Calculation of internal force vector Ii+1 based on ui+1.4. Judgment of equilibrium convergence:
Is Ri+1 within the tolerance?
Is#
11
iter
i jj
c c+=
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Nonlinear Input File
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.20
Nonlinear Input File
*HEADINGCANTILEVER BEAM EXAMPLE--LARGE DISPLACEMENT*NODE 1, 0., 0.11, 200., 0.*NGEN1, 11, 1*ELEMENT, TYPE=B211, 1, 3*ELGEN, ELSET=BEAMS1, 5, 2, 1*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT150., 5.*MATERIAL, NAME=MAT1*ELASTIC2.E5, .3*BOUNDARY1, 1, 6*AMPLITUDE, NAME=RAMP0.0, 0.0, 0.5, 0.3, 1.0, 1.0
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.21
*RESTART, WRITE,FREQ=3*STEP, NLGEOM,INC=25APPLY POINT LOAD*STATIC0.1, 1.0, 0.001, 1.0*CLOAD, AMPLITUDE=RAMP11, 2, -1200. *NODE PRINT, FREQ=1U, RF*EL PRINT, FREQ=10S, E*NODE FILE, FREQ=5U*END STEP
major differences from linear input
minimum time increment
maximum time increment
time period of the step
initial suggested time increment
previously defined amplitude function for load application
major differences from linear input
Nonlinear Input File
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.22
Step and procedure input
*STEP, NLGEOM, INC=25 NLGEOM: include all nonlinear geometric effects due to:
Large deflections, rotations, deformation.
Preloading (initial stresses).
Load stiffness.
If the above are not important, the answer will be the same as without NLGEOM but the analysis will be more expensive.
INC=25: maximum of 25 increments allowed in this example:
The code will stop if the maximum number of increments is reached before the total load is applied.
Keeps the analysis from running too longyou can always restart.
Default value is 100.
Nonlinear Input File
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.23
Nonlinear Input File
Similar time incrementation data exist for all transient procedures, which are
STATICDYNAMICHEAT TRANSFERVISCOCOUPLED TEMPERATURE-DISPLACEMENTSOILSMODAL DYNAMIC (allows only fixed time incrementation)COUPLED THERMAL-ELECTRIC
Physical or normalized time scale depending on the procedure and the presence of time-dependent or rate-dependent behavior.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.25
Output from Nonlinear Cantilever Beam Analysis
Status (.sta) file Summarizes how analysis proceedsshows automatic time
incrementation at work.
You can check the status file while the job is running.
One line written after each successful increment.
SUMMARY OF JOB INFORMATION:STEP INC ATT SEVERE EQUIL TOTAL TOTAL STEP INC OF DOF IF
DISCON ITERS ITERS TIME/ TIME/LPF TIME/LPF MONITOR RIKSITERS FREQ
1 1 1 0 3 3 0.100 0.100 0.1000 1 2 1 0 2 2 0.200 0.200 0.1000 1 3 1 0 2 2 0.350 0.350 0.1500 1 4 1 0 2 2 0.575 0.575 0.2250 1 5 1 0 4 4 0.913 0.913 0.3375 1 6 1 0 2 2 1.00 1.00 0.08750
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.26
Automatic time incrementation Heuristic algorithm (based on many years of experience) controls the
accuracy of time integration. In statics based on number of iterations to converge.
Convergence is easily achieved (considerably less than the maximum number of allowable iterations):
increase increment size Convergence difficult or divergence occurs:
cut back increment size Otherwise:
maintain same increment size Automatic time incrementation works very well. The user should not
change it without good reason.Tip: For highly nonlinear problems, it is recommended that the initial time increment be chosen as a small fraction (e.g., 10%) of the total step time.
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.27
Message (.msg) file Includes:
All convergence controls:
The CONTROLS option overrides defaultsnot usually needed Details about certain model features:
Nondefault model features
Use of NLGEOM
Frequency of restart writes
All iteration details
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.28
Output from Nonlinear Cantilever Beam Analysis
Solver messages:
Numerical singularities: These indicate that so many digits are lost during linear equation solution that the results are not reliable. The most common cause is an unconstrained rigidbody mode in a static stress analysis.
Zero pivots: These occur during linear equation solution when there is a force term but nocorresponding stiffness. Common causesare unconstrained rigid body modes and overconstrained degrees of freedom.
Negative eigenvalues: Negative eigenvalues indicate that the stiffness matrix is not positive definite; for example, a buckling load may have been exceeded.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.29
Output from Nonlinear Cantilever Beam Analysis
Useful troubleshooting information:
Locations of highest residuals
Locations of excessive deformation
Locations of contact changes
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.30
S T E P 1 S T A T I C A N A L Y S I S
APPLY POINT LOADAUTOMATIC TIME CONTROL WITH -
A SUGGESTED INITIAL TIME INCREMENT OF 0.100 AND A TOTAL TIME PERIOD OF 1.00 THE MINIMUM TIME INCREMENT ALLOWED IS 1.000E-03THE MAXIMUM TIME INCREMENT ALLOWED IS 1.00
CONVERGENCE TOLERANCE PARAMETERS FOR FORCE CRITERION FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM 5.000E-03CRITERION FOR DISP. CORRECTION IN A NONLINEAR PROBLEM 1.000E-02INITIAL VALUE OF TIME AVERAGE FORCE 1.000E-02AVERAGE FORCE IS TIME AVERAGE FORCE ALTERNATE CRIT. FOR RESIDUAL FORCE FOR A NONLINEAR PROBLEM 2.000E-02CRITERION FOR ZERO FORCE RELATIVE TO TIME AVRG. FORCE 1.000E-05CRITERION FOR RESIDUAL FORCE WHEN THERE IS ZERO FLUX 1.000E-05CRITERION FOR DISP. CORRECTION WHEN THERE IS ZERO FLUX 1.000E-03CRITERION FOR RESIDUAL FORCE FOR A LINEAR INCREMENT 1.000E-08FIELD CONVERSION RATIO 1.00
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.31
CONVERGENCE TOLERANCE PARAMETERS FOR MOMENT CRITERION FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM 5.000E-03CRITERION FOR ROTATION CORRECTION IN A NONLINEAR PROBLEM 1.000E-02INITIAL VALUE OF TIME AVERAGE MOMENT 1.000E-02AVERAGE MOMENT IS TIME AVERAGE MOMENT ALTERNATE CRIT. FOR RESIDUAL MOMENT FOR A NONLINEAR PROBLEM 2.000E-02CRITERION FOR ZERO MOMENT RELATIVE TO TIME AVRG. MOMENT 1.000E-05CRITERION FOR RESIDUAL MOMENT WHEN THERE IS ZERO FLUX 1.000E-05CRITERION FOR ROTATION CORRECTION WHEN THERE IS ZERO FLUX 1.000E-03CRITERION FOR RESIDUAL MOMENT FOR A LINEAR INCREMENT 1.000E-08FIELD CONVERSION RATIO 1.00
VOLUMETRIC STRAIN COMPATIBILITY TOLERANCE FOR HYBRID SOLIDS 1.000E-05AXIAL STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS 1.000E-05TRANS. SHEAR STRAIN COMPATIBILITY TOLERANCE FOR HYBRID BEAMS 1.000E-05SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P>P0 5.000E-03SOFT CONTACT CONSTRAINT COMPATIBILITY TOLERANCE FOR P=0.0 0.100 DISPLACEMENT COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS 1.000E-05ROTATION COMPATIBILITY TOLERANCE FOR DCOUP ELEMENTS 1.000E-05
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.32
TIME INCREMENTATION CONTROL PARAMETERS:FIRST EQUILIBRIUM ITERATION FOR CONSECUTIVE DIVERGENCE CHECK 4EQUILIBRIUM ITERATION AT WHICH LOG. CONVERGENCE RATE CHECK BEGINS 8EQUILIBRIUM ITERATION AFTER WHICH ALTERNATE RESIDUAL IS USED 9MAXIMUM EQUILIBRIUM ITERATIONS ALLOWED 16EQUILIBRIUM ITERATION COUNT FOR CUT-BACK IN NEXT INCREMENT 10MAXIMUM EQUILIB. ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE 4MAXIMUM ITERATIONS FOR SEVERE DISCONTINUITIES 12MAXIMUM CUT-BACKS ALLOWED IN AN INCREMENT 5MAXIMUM DISCON. ITERS IN TWO INCREMENTS FOR TIME INCREMENT INCREASE 6CUT-BACK FACTOR AFTER DIVERGENCE 0.2500 CUT-BACK FACTOR FOR TOO SLOW CONVERGENCE 0.5000 CUT-BACK FACTOR AFTER TOO MANY EQUILIBRIUM ITERATIONS 0.7500 CUT-BACK FACTOR AFTER TOO MANY SEVERE DISCONTINUITY ITERATIONS 0.2500 CUT-BACK FACTOR AFTER PROBLEMS IN ELEMENT ASSEMBLY 0.2500 INCREASE FACTOR AFTER TWO INCREMENTS THAT CONVERGE QUICKLY 1.500MAX. TIME INCREMENT INCREASE FACTOR ALLOWED 1.500 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED (DYNAMICS) 1.250 MAX. TIME INCREMENT INCREASE FACTOR ALLOWED (DIFFUSION) 2.000 MINIMUM TIME INCREMENT RATIO FOR EXTRAPOLATION TO OCCUR 0.1000 MAX. RATIO OF TIME INCREMENT TO STABILITY LIMIT 1.000 FRACTION OF STABILITY LIMIT FOR NEW TIME INCREMENT 0.9500
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.33
PRINT OF INCREMENT NUMBER, TIME, ETC., EVERY 1 INCREMENTS
RESTART FILE WILL BE WRITTEN EVERY 3 INCREMENTSTHE MAXIMUM NUMBER OF INCREMENTS IN THIS STEP IS 25
LARGE DISPLACEMENT THEORY WILL BE USEDLINEAR EXTRAPOLATION WILL BE USEDCHARACTERISTIC ELEMENT LENGTH 40.0 DETAILED OUTPUT OF DIAGNOSTICS TO DATABASE REQUESTEDPRINT OF INCREMENT NUMBER, TIME, ETC., TO THE MESSAGE FILE EVERY 1 INCREMENTSEQUATIONS ARE BEING REORDERED TO MINIMIZE WAVEFRONTCOLLECTING MODEL CONSTRAINT INFORMATION FOR OVERCONSTRAINT CHECKSCOLLECTING STEP CONSTRAINT INFORMATION FOR OVERCONSTRAINT CHECKS
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.34
Output from Nonlinear Cantilever Beam AnalysisINCREMENT 1 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.100
EQUILIBRIUM ITERATION 1AVERAGE FORCE 1.251E+03 TIME AVG. FORCE 1.251E+03LARGEST RESIDUAL FORCE -4.637E+03 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -1.84 AT NODE 11 DOF 2
FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03LARGEST RESIDUAL MOMENT 28.8 AT NODE 9 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -1.382E-02 AT NODE 11 DOF 6
MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.EQUILIBRIUM ITERATION 2
AVERAGE FORCE 37.8 TIME AVG. FORCE 37.8 LARGEST RESIDUAL FORCE 0.215 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -1.007E-02 AT NODE 11 DOF 1
FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03LARGEST RESIDUAL MOMENT -0.346 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.898E-07 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED
0.005
6.25
0.005
0.2
0.005
36
0.005
36
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.35
EQUILIBRIUM ITERATION 3
AVERAGE FORCE 37.7 TIME AVG. FORCE 37.7 LARGEST RESIDUAL FORCE -2.281E-06 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 3.349E-05 AT NODE 11 DOF 2
THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 7.200E+03 TIME AVG. MOMENT 7.200E+03LARGEST RESIDUAL MOMENT 1.523E-05 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 3.637E-07 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDITERATION SUMMARY FOR THE INCREMENT: 3 TOTAL ITERATIONS, OF WHICH
0 ARE SEVERE DISCONTINUITY ITERATIONS AND 3 ARE EQUILIBRIUM ITERATIONS.TIME INCREMENT COMPLETED 0.100 , FRACTION OF STEP COMPLETED 0.100 STEP TIME COMPLETED 0.100 , TOTAL TIME COMPLETED 0.100
Output from Nonlinear Cantilever Beam Analysis
4 or fewer iterations (do this again and t can increase)
0.005
0.2
0.005
36
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.36
INCREMENT 2 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.100EQUILIBRIUM ITERATION 1
AVERAGE FORCE 75.6 TIME AVG. FORCE 56.7 LARGEST RESIDUAL FORCE 0.861 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -2.013E-02 AT NODE 11 DOF 1
FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.440E+04 TIME AVG. MOMENT 1.080E+04LARGEST RESIDUAL MOMENT -1.38 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 3.914E-06 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED
Output from Nonlinear Cantilever Beam Analysis
no increase
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.37
EQUILIBRIUM ITERATION 2AVERAGE FORCE 144. TIME AVG. FORCE 90.9 LARGEST RESIDUAL FORCE -6.928E-05 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -1.84 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 1.701E-04 AT NODE 11 DOF 2
THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 1.600E+04 TIME AVG. MOMENT 1.160E+04LARGEST RESIDUAL MOMENT 1.218E-04 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -1.382E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.804E-06 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDTIME INCREMENT MAY NOW INCREASE TO 0.150
ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS.
TIME INCREMENT COMPLETED 0.100 , FRACTION OF STEP COMPLETED 0.200 STEP TIME COMPLETED 0.200 , TOTAL TIME COMPLETED 0.200
Output from Nonlinear Cantilever Beam Analysis
4 consecutive increments with 4 or fewer iterations: t = 1.5told
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.38
INCREMENT 3 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.150EQUILIBRIUM ITERATION 1
AVERAGE FORCE 133. TIME AVG. FORCE 105. LARGEST RESIDUAL FORCE 3.02 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -2.75 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -3.764E-02 AT NODE 11 DOF 1
FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 2.518E+04 TIME AVG. MOMENT 1.613E+04LARGEST RESIDUAL MOMENT -4.47 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -2.071E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.722E-05 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED
Output from Nonlinear Cantilever Beam Analysis
t = 1.5told
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.39
EQUILIBRIUM ITERATION 2
AVERAGE FORCE 252. TIME AVG. FORCE 145. LARGEST RESIDUAL FORCE -7.965E-04 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -2.75 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 5.629E-04 AT NODE 11 DOF 2
THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 2.798E+04 TIME AVG. MOMENT 1.706E+04LARGEST RESIDUAL MOMENT 7.461E-04 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -2.070E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.967E-06 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDTIME INCREMENT MAY NOW INCREASE TO 0.225
ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS.
TIME INCREMENT COMPLETED 0.150 , FRACTION OF STEP COMPLETED 0.350 STEP TIME COMPLETED 0.350 , TOTAL TIME COMPLETED 0.350
RESTART INFORMATION WRITTEN IN STEP 1 AFTER INCREMENT 3
Output from Nonlinear Cantilever Beam Analysis
4 or fewer
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.40
INCREMENT 4 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.225 EQUILIBRIUM ITERATION 1
AVERAGE FORCE 1.528E+03 TIME AVG. FORCE 490. LARGEST RESIDUAL FORCE -4.550E+03 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -5.95 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -1.82 AT NODE 11 DOF 2
FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 4.853E+04 TIME AVG. MOMENT 2.493E+04LARGEST RESIDUAL MOMENT -344. AT NODE 9 DOF 6LARGEST INCREMENT OF ROTATION -4.477E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -1.371E-02 AT NODE 11 DOF 6
MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.
Output from Nonlinear Cantilever Beam Analysis
t = 1.5told
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.41
EQUILIBRIUM ITERATION 2AVERAGE FORCE 281. TIME AVG. FORCE 179. LARGEST RESIDUAL FORCE 0.349 AT NODE 11 DOF 2LARGEST INCREMENT OF DISP. -5.94 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -9.348E-03 AT NODE 11 DOF 1
THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 4.847E+04 TIME AVG. MOMENT 2.491E+04LARGEST RESIDUAL MOMENT -2.26 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -4.471E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.353E-05 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDTIME INCREMENT MAY NOW INCREASE TO 0.338
ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS.
TIME INCREMENT COMPLETED 0.225 , FRACTION OF STEP COMPLETED 0.575 STEP TIME COMPLETED 0.575 , TOTAL TIME COMPLETED 0.575
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.42
INCREMENT 5 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 0.338EQUILIBRIUM ITERATION 1
AVERAGE FORCE 1.248E+04 TIME AVG. FORCE 2.638E+03LARGEST RESIDUAL FORCE -3.911E+04 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -14.2 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -5.31 AT NODE 11 DOF 2FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.049E+05 TIME AVG. MOMENT 4.090E+04LARGEST RESIDUAL MOMENT -4.323E+03 AT NODE 9 DOF 6LARGEST INCREMENT OF ROTATION -0.107 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -4.037E-02 AT NODE 11 DOF 6MOMENT EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.
EQUILIBRIUM ITERATION 2AVERAGE FORCE 556. TIME AVG. FORCE 254. LARGEST RESIDUAL FORCE 16.6 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -14.2 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -8.119E-02 AT NODE 11 DOF 1FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.044E+05 TIME AVG. MOMENT 4.080E+04LARGEST RESIDUAL MOMENT -42.5 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -0.107 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.095E-04 AT NODE 11 DOF 6THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED
Output from Nonlinear Cantilever Beam Analysis
t = 1.5told
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.43
EQUILIBRIUM ITERATION 3AVERAGE FORCE 559. TIME AVG. FORCE 255. LARGEST RESIDUAL FORCE -28.9 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -14.1 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 0.130 AT NODE 11 DOF 2FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.
AVERAGE MOMENT 1.153E+05 TIME AVG. MOMENT 4.299E+04LARGEST RESIDUAL MOMENT 3.833E-02 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -0.106 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.112E-03 AT NODE 11 DOF 6ESTIMATE OF ROTATION CORRECTION -1.004E-06MOMENT EQUILIB. ACCEPTED BASED ON SMALL RESIDUAL AND ESTIMATED CORRECTIONEQUILIBRIUM ITERATION 4
AVERAGE FORCE 1.053E+03 TIME AVG. FORCE 354. LARGEST RESIDUAL FORCE 1.092E-03 AT NODE 11 DOF 2LARGEST INCREMENT OF DISP. -14.1 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -2.092E-04 AT NODE 11 DOF 2THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 1.153E+05 TIME AVG. MOMENT 4.299E+04LARGEST RESIDUAL MOMENT -2.910E-02 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -0.106 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION -1.875E-06 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGEDITERATION SUMMARY FOR THE INCREMENT: 3 TOTAL ITERATIONS, OF WHICH
0 ARE SEVERE DISCONTINUITY ITERATIONS AND 3 ARE EQUILIBRIUM ITERATIONS.TIME INCREMENT COMPLETED 0.338 , FRACTION OF STEP COMPLETED 0.913 STEP TIME COMPLETED 0.913 , TOTAL TIME COMPLETED 0.913
Output from Nonlinear Cantilever Beam Analysis
The residual is within tolerance, but the rotation correction is too large. The estimate of the rotation correction of the next iteration is acceptably small.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.44
INCREMENT 6 STARTS. ATTEMPT NUMBER 1, TIME INCREMENT 8.750E-02EQUILIBRIUM ITERATION 1
AVERAGE FORCE 641. TIME AVG. FORCE 402. LARGEST RESIDUAL FORCE 74.0 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -3.55 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. -0.180 AT NODE 11 DOF 1
FORCE EQUILIBRIUM NOT ACHIEVED WITHIN TOLERANCE.AVERAGE MOMENT 1.179E+05 TIME AVG. MOMENT 5.547E+04LARGEST RESIDUAL MOMENT -99.4 AT NODE 5 DOF 6LARGEST INCREMENT OF ROTATION -2.702E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 5.186E-04 AT NODE 11 DOF 6ESTIMATE OF ROTATION CORRECTION -1.594E-05MOMENT EQUILIB. ACCEPTED BASED ON SMALL RESIDUAL AND ESTIMATED CORRECTION
EQUILIBRIUM ITERATION 2AVERAGE FORCE 695. TIME AVG. FORCE 411. LARGEST RESIDUAL FORCE -0.505 AT NODE 11 DOF 1LARGEST INCREMENT OF DISP. -3.53 AT NODE 11 DOF 2LARGEST CORRECTION TO DISP. 1.386E-02 AT NODE 11 DOF 2
THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGEDAVERAGE MOMENT 1.309E+05 TIME AVG. MOMENT 5.764E+04LARGEST RESIDUAL MOMENT 8.716E-02 AT NODE 7 DOF 6LARGEST INCREMENT OF ROTATION -2.687E-02 AT NODE 11 DOF 6LARGEST CORRECTION TO ROTATION 1.493E-04 AT NODE 11 DOF 6
THE MOMENT EQUILIBRIUM EQUATIONS HAVE CONVERGED
Output from Nonlinear Cantilever Beam Analysis
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.45
ITERATION SUMMARY FOR THE INCREMENT: 2 TOTAL ITERATIONS, OF WHICH0 ARE SEVERE DISCONTINUITY ITERATIONS AND 2 ARE EQUILIBRIUM ITERATIONS.
TIME INCREMENT COMPLETED 8.750E-02, FRACTION OF STEP COMPLETED 1.00 STEP TIME COMPLETED 1.00 , TOTAL TIME COMPLETED 1.00
RESTART INFORMATION WRITTEN IN STEP 1 AFTER INCREMENT 6
THE ANALYSIS HAS BEEN COMPLETED
ANALYSIS SUMMARY:TOTAL OF 6 INCREMENTS
0 CUTBACKS IN AUTOMATIC INCREMENTATION15 ITERATIONS INCLUDING CONTACT ITERATIONS IF PRESENT15 PASSES THROUGH THE EQUATION SOLVER OF WHICH 15 INVOLVE MATRIX DECOMPOSITION, INCLUDING0 DECOMPOSITION(S) OF THE MASS MATRIX1 REORDERING OF EQUATIONS TO MINIMIZE WAVEFRONT0 ADDITIONAL RESIDUAL EVALUATIONS FOR LINE SEARCHES0 ADDITIONAL OPERATOR EVALUATIONS FOR LINE SEARCHES3 WARNING MESSAGES DURING USER INPUT PROCESSING0 WARNING MESSAGES DURING ANALYSIS0 ANALYSIS WARNINGS ARE NUMERICAL PROBLEM MESSAGES0 ANALYSIS WARNINGS ARE NEGATIVE EIGENVALUE MESSAGES0 ERROR MESSAGES
Output from Nonlinear Cantilever Beam Analysis
Look here for warning and error messages. Search the message file and data file to determine the causes of these messages.
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.46
Output from Nonlinear Cantilever Beam Analysis
Visual diagnostics in ABAQUS/Viewer
Toggle on to see the locations in the model where the largest residuals and displacement increments and corrections occur.
A similar display is given for rotational degrees of freedom
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Workshop 3: Nonlinear Statics
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L3.48
Workshop 3: Nonlinear Statics
Workshop tasks1. Define alternate material
directions correspondingto the skew angle of the plate.
2. Analyze the deformation of the skew plate with and without considering nonlinear geometric effects.
3. Include plasticity in the material definition.
4. View the results using ABAQUS/Viewer.
Video Clip
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Multistep Analysis in ABAQUS
Lecture 4
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L4.2
Overview
Multistep Analyses Restart Analysis in ABAQUS
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit
Multistep Analyses
Copyright 2004 ABAQUS, Inc.
Introduction to ABAQUS/Standard and ABAQUS/Explicit L4.4
Multistep Analyses
It is often convenient to divid