16a-2D-Quadrature

16a-2D-Quadrature - © 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 16a 2-D Quadrature © William Klug Summary and Review p u Γ u Γ e e T A dA ∫ = k B EB 1 v 1 u 2 v 2 u 3 v 3 u 2 1 3 u v u = N 1 N 2 N 3 N 1 N 2 N 3 N u 1 v 1 u 2 v 2 u 3 v 3 d © William Klug Quadrature in 1-D • Review ( ) ( ) ( ) ( ) 1 1 1 1 2 2 1 n n n i i i I d w w w w φ ξ φ ξ φ ξ φ ξ φ ξ − = ∑ ∫ = ≈ + + + = … n = selected order of numerical integration ξ i = quadrature points w i = quadrature weights 1 − 1 1 − 1 1 − 1 © William Klug 1-D: Quadrature Weights and Quadrature Points 2 -0.57735027 0.57735027 1.0 1.0 3 3 -0.77459667 0.0 0.77459667 0.55555555 0.88888889 0.55555555 5 4 -0.86113631 -0.33998104 0.33998104 0.86113631 0.34785485 0.65214515 0.65214515 0.34785485 7 5 -0.90617975 -0.53846931 0.0 0.53846931 0.90617975 0.23692689 0.47862867 0.56888889 0.47862867 0.23692689 9 n 1 ξ 1 w 2 1 n − © William Klug...
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16a-2D-Quadrature - © William Klug MAE M168/CEE M135C...

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