15b-2D-Elasticity

15b-2D-Elasticity - © William Klug MAE M168/CEE M135C...

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Unformatted text preview: © William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 15b 2D FEA: Elasticity © William Klug • Simple 2-D elements • Pascal’s Triangle Summary and Review T x , y ( ) = a + bx + cy = T 1 N 1 + T 2 N 2 + T 3 N 3 Linear Triangle Bi-linear rectangle © William Klug Summary and Review C-conforming interpolation T x , y ( ) = T N i x , y ( ) i = 1 3 ∑ 1 B T DB tdA ( ) A e ∫ k e e ∑ T = N T Qt dA A e ∫ − N T hdS S q ∫ Q e e ∑ T x , y ( ) = a const . T + bx + cy const . ∇ T Conformity + Completeness → Convergence Linear completeness © William Klug Displacement Vector 2-D 3-D © William Klug Strain ε = ε x ε y γ xy = ∂ u ∂ x ∂ v ∂ y ∂ u ∂ y + ∂ v ∂ x = ∂ ∂ x ∂ ∂ y ∂ ∂ y ∂ ∂ x ∂ u v u = ∂ u Differential operator © William Klug Hooke’s Law...
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This note was uploaded on 08/09/2011 for the course MAE 168 taught by Professor Klug during the Spring '11 term at UCLA.

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15b-2D-Elasticity - © William Klug MAE M168/CEE M135C...

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