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15b-2D-Elasticity

15b-2D-Elasticity - MAE M168/CEE M135C Introduction to...

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© William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 15b 2D FEA: Elasticity
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© 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
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© William Klug Summary and Review C 0 -conforming interpolation T x , y ( ) = T 0 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
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© William Klug Displacement Vector 2-D 3-D
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© William Klug Strain ε = ε x ε y γ xy = u x v y u y + v x = x 0 0 y y x u v u  = u Differential operator
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© William Klug Hooke’s Law σ = σ x σ y τ xy = E 11 E 12 E 13 E 11
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