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Introduction to Finite Element Methods - Lifeng Wang

Chapter 3 Development of Truss

Equations

MEC 539

Instructor: Dr. Lifeng Wang

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Principle of Minimum Potential Energy

Of all the geometrically possible shapes that a body

can assume, the true one, corresponding to the

satisfaction of stable equilibrium of the body, is

identified by a minimum value of the total potential

energy.

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Principle of Minimum Potential Energy

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Principle of Minimum Potential Energy

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Principle of Minimum Potential Energy

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Principle of Minimum Potential Energy

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Example: Example 2.5

Example 2.5

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Example: Problem 2.5

Solution: Example 2.5

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Example: Problem 2.5

Solution: Problem 2.5

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Truss

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Truss

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Truss

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Truss

Derivation of the Stiffness Matrix for a Bar Element

in Local Coordinates

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Truss

differential equation

governing the linear-elastic

bar behavior as

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Truss

Derivation of the Stiffness Matrix

Step 1 Select the Element Type

Step 2 Select a Displacement Function

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Truss

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Truss

Step 3 Define the Strain/Displacement and Stress/Strain

Relationships

-

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Truss

-

-

-

- -

-

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Truss

Step 7 Solve for the Element Forces

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Truss

Examples 3.1

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Truss

Solution

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Truss

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Truss

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Truss

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Truss

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Truss

Break (10 minutes)!

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Truss

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Truss

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Truss

--

-

-

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Truss

-

-

-

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Truss -

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TrussExamples 3.2

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Truss

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Truss

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Truss

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Truss

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Truss

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Truss

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Truss

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TrussExamples 3.3

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Truss

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Truss

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Truss

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Truss

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Truss

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Truss

Local to Global

Global to Local

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Truss

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Truss

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Homework #2

2.22 Solve P2.15 by potential energy approach

3.7, 3.16determine the nodal displacements, the forces in each

element, and the reactions.

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Homework #2