8c-Higher-Order-shp-fns-2010s

8c-Higher-Order-shp-fns-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 8c 1-D FEM: Higher Order Shape Functions William Klug Summary & Review Quadratic interpolation Lagrange shape functions ( 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 Higher Order Interpolation in 1-D Linear Interpolation Want Smoother approximation: piecewise quadratic, cubic, etc. Example: can fit a unique parabola (quadratic interpolation) to 3 points ( x 1 , y 1 ) ( x 2 , y 2 ) ( x 3 , y 3 ) William Klug Higher Order Polynomial In general (polynomial of degree n) In Matrix form y ( x ) = 1 x x 2 x n X ( x ) a a 1 a 2 a n a William Klug Want interpolation of point pairs Interpolate n+1 Point Pairs William Klug...
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8c-Higher-Order-shp-fns-2010s - William Klug MAE M168/CEE...

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