14b-Quadratic-Tris-Quads

14b-Quadratic-Tris-Quads - 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 14b Quadratic Triangles and Quadralaterals William Klug r s 2 1 3 1 1 X Y Standard Domain (Natural) Actual Domain (Physical) Summary and Review Build shape functions and do integrals in natural coordinates. Compute derivatives using chain rule u r , s ( ) v r , s ( ) 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 X r , s ( ) Y r , s ( ) X = N 1 N 2 N 3 N 1 N 2 N 3 N X 1 Y 1 X 2 Y 2 X 3 Y 3 C William Klug Higher Order Isoparametric Elements 5 6 7 8 1 2 3 4 X Y r 1 s 5 4 3 2 6 X Y 1 4 2 3 5 6 1 4 2 3 5 6 7 8 William Klug...
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14b-Quadratic-Tris-Quads - William Klug MAE M168/CEE M135C...

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