Finite Element Analysis - Theory to Practice;Building a Solid Foundation

Dr. John J. WoodPresentation 2007-47

United States Air Force Academy

Finite Element Analysis - Theory to Practice; Building a Solid Foundation

AbstractOver the past five years the Introduction to Finite Element Analysis course at the United States Air Force Academy (USAFA) has evolved into a learning experience deep in foundational knowledge and understanding to empower the students with an ability to discern “correctness” of both approach and solution versus unsubstantiated results. The course is rich in simple but practical applications which reinforce the foundational underlying assumptions and limitations in the methods while sparking the interest of the students. The course content has seen continuous development driven both by feedback from our graduates and also by assessment of the curriculum mapped against the needs and expectations of engineers in the Air Force. The course employs scaffolding learning theory that begins with a solid theoretical foundation in each topical area followed by an investigation and reinforcement using MSC Software computer modeling. Extensive use of software tutorials developed at USAFA substantially reduces the time required to achieve proficiency using basic modeling skills. A multi-phase course project was recently added to the curriculum to enhance experiential learning in a more open-ended design environment. The incrementally tasked project requires increasingly complex modeling strategies to solve the same problem of a statically indeterminate beam, of which the analytical solution can readily be obtained. The project successfully builds upon previously learned and practiced analysis methods while providing a basis for comparison against a mechanics of materials solution. The three-pronged approach of theoretical background, instructional tutorials and a multi-phased course project provides a successful framework for a solid foundation in the finite element method.

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Finite Element Analysis - Theory to Practice; Building a Solid Foundation

Our Customers:

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Our Mission:Introduce Cadets to Structural Analysis using the FE Method

Course Information:EM431 – Introduction to Finite Element Analysis

Text: A First Course in the Finite Element Method, Logan, 4th Ed.

Fall Elective Course, 30 Students per Semester

40 1-Hour Lessons

Senior Mechanical, Aeronautical & Astronautical Engineering Cadets

Finite Element Analysis - Theory to Practice; Building a Solid Foundation

TheoreticalFoundation

Visual Mechanics of Materials (Vis-MoM)

Instruction Based Patran/Nastran Tutorials

ProjectApplication

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Theoretical Foundation

Theory Visual Mechanics

Tutorials Application

- Direct Stiffness Method Introduced to Link New Concepts to Existing Knowledge

Model Dimen #dof Coord SysSprings 1D #nodes LocalBeams 1D 2x #nodes LocalTrusses 2D 2x #nodes GlobalFrames 2D 3x #nodes Global

- Minimum Potential Energy Approach Introduced-- Preferred method for analysis of structural systems-- Pedagogical alignment with text-- 1D, 2D (incl axisymmetric) & 3D element analysis-- Heat transfer and vibrations special topics

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Visual Mechanics of Materials (Vis-MoM)

A Combined Effort Between USAFA and MSC Software

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Theory Visual Mechanics

Tutorials Application

- Bridge Gap Between Mechanics of Materials and FEA- Introduce Students to FEA as a Viable Analysis Tool

- Courseware Designed to Motivate Students to Study/Learn Mechanics of Materials

-- Extensive interactivity integrated with multimedia-- Modules focus on specific mechanics topics-- Example, workout and design problems

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Instruction Based Patran/Nastran Tutorials

- Computer Labs at Strategic Points-- Students experiment with Patran/Nastran

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Theory Visual Mechanics

Tutorials Application

-- Analytical verification required for all FEA solutions

- Guided Learning through Instructional Tutorials-- Compliment/reinforce theoretical concepts-- Scaffolding learning theory applied

--- Gradual increase in model complexity--- Gradual decrease in direction

Instruction Based Patran/Nastran Tutorials

- Explicit Instructions Provided for each Step- Mechanics of Materials Verification Provides Exact Solution

Builds Confidence in Value of Method

Tutorial 1 Double-Cantilevered Bar

Tutorial 2Truss

Y 100 lbs

X

Step 4. Apply Loads

b

cf

eh

i

jl

k

a

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Theory Visual Mechanics

Tutorials Application

9000 N

Instruction Based Patran/Nastran Tutorials

- Higher-Level Instructions Provided- Mechanics of Materials Verification Provides Approximate Solution

Engineering Judgment Req’d –-- Simply supported assumption – upper deflection bound-- Fixed support assumption – lower deflection bound

Tutorial 3 Indeterminate Beam

Tutorial 4Wt Bench

P

Step 4. Create Displacement Constraints

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Theory Visual Mechanics

Tutorials Application

Instruction Based Patran/Nastran Tutorials

- Mechanics of Materials Verification Analysis Required- Heat Transfer and Vibrational Verification Required

Tutorial 5 RocketNozzle

Tutorial 7 EngineCoolingFin

Tutorial 63D BearingSupport

Tutorial 8 BeamVibration

Special Topics:- Axisymmetry- Heat transfer- Dynamics-- Nat Freq-- Normal Modes

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Theory Visual Mechanics

Tutorials Application

Application – Course Project

Course Project1

(adapted from Jolley, Rencis, and Grandin “A Module for Teaching Fundamentals of Finite Element Theory and Practice using Elementary Mechanics of Materials,” Proceedings of the 2003 ASEE

Annual Conference & Exposition)12

Theory Visual Mechanics

Tutorials Application

Application – Course Project

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Theory Visual Mechanics

Tutorials Application

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2)(

dxvdEIxM =

⎥⎥⎦

⎤

⎢⎢⎣

⎡+−−=

2412241 4322 wxwLxxwLEI

v

Phase 1 – Analytical Solution

-No Geometric Discontinuities- Comparison with Analytical

Solution- Convergence Studies

Phase 2 – 1D Beam Model

-No Geometric Discontinuities- Comparison with Analytical &

1D Solution- Convergence Studies

Phase 3 – 2D Quad Model

-Geometric Discontinuities Modeled

- Comparison with Analytical, 1D & 2D Solutions

- Convergence Studies- Stress Concentrations

Included in Analytical Model

Phase 4 – 3D Tet Model Phase 5 – Redesign to Prevent Failure

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Dr. John J. WoodEmail: john.wood@usafa.edu Tel. (719) 333 1927

References

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(1) Jolley, Rencis, and Grandin “A Module for Teaching Fundamentals of Finite Element Theory and Practice using Elementary Mechanics of Materials,” Proceedings of the 2003 ASEE Annual Conference & Exposition, 2003