11b-MechanicalExamples-2010s

11b-MechanicalExamples-2010s - MAE M168/CEE M135C...

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© William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 11b 1-D FEM: Elastic Bar Examples
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© William Klug Summary and Review Weak form Rayleigh- Ritz Potential Energy Galerkin
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© William Klug Summary and Review • Compute element matrices (e.g., 2x2 for linear) • Assemble with code numbers • Add end forces at boundary nodes directly to • Solve
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© William Klug Example 1: Linear Shape Fns. k e = EA B e T B e dx 0 l e = EA l e ( ) 2 1 1 1 1 dx 0 l e k e = 1 L 3 ( ) 2 EA 1 1 1 1 dx 0 l e = EA L 3 1 1 1 1
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© William Klug Consistent Nodal Forces q e = q 0 X j X ( ) l e X X i ( ) l e dX X i X j = q 0 l e x ( ) l e x l e dx 0 l e = q 0 l e 2 q 0 l e 2 = q 0 L 6 1 1
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© William Klug Assemble Global Stiffness
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11b-MechanicalExamples-2010s - MAE M168/CEE M135C...

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