9a-Natural-Coordinates-2010s

# 9a-Natural-Coordinates-2010s - © William Klug MAE M168/CEE...

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Unformatted text preview: © William Klug MAE M168/CEE M135C Introduction to Finite Element Methods Lecture 9a 1-D FEM: Shape Functions in Natural Coordinates © William Klug Summary & Review • Piecewise Linear interpolation • Piecewise Quadratic interpolation • Higher-order… • Global approximation i j N i (x) N j (x) x N(x) ( x 1 , D 1 ) ( x 2 , D 2 ) ( x 3 , D 3 ) ( x 4 , D 4 ) ( x 5 , D 5 ) x x 1 x 2 x 3 x 4 x 5 ( x 1 , D 1 ) ( x 2 , D 2 ) ( x 3 , D 3 ) ( x 4 , D 4 ) ( x 5 , D 5 ) x x 1 x 2 x 3 x 4 x 5 piecewise quadratic segments © William Klug Summary & Review • Piecewise Linear interpolation • Piecewise Quadratic interpolation • Higher-order… • Global approximation i j N i (x) N j (x) x N(x) ( x 1 , D 1 ) ( x 2 , D 2 ) ( x 3 , D 3 ) ( x 4 , D 4 ) ( x 5 , D 5 ) x x 1 x 2 x 3 x 4 x 5 ( x 1 , D 1 ) ( x 2 , D 2 ) ( x 3 , D 3 ) ( x 4 , D 4 ) ( x 5 , D 5 ) x x 1 x 2 x 3 x 4 x 5 piecewise quadratic segments © William Klug • Two-node bar element of length l ....
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9a-Natural-Coordinates-2010s - © William Klug MAE M168/CEE...

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