prob_06_08_02 - Problem 6.8-2 If element thickness can vary...

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Problem 6.8-2 If element thickness can vary and is computed as t = Σ N i t i from nodal values t i , what order Gauss quadrature is needed to compute the exact volume of (a) a four-node plane element, and (b) an eight-node plane element? Solution: Volume 1 1 η 1 1 ξ Jt d d = t 1 n i N i t i () = = J Σ N i ξ , x i Σ N i η , x i Σ N i ξ , y i Σ N i η , y i = (a) For a 4-node element, each of the shape functions are 1st order in ξ and η . Thus the determinate of [J] is a polynomial with ξ and η at most 1st power. Each of the N i are at most 1st order in ξ and η Thus Jt f ξ 2 η 2 , = The order of polynomial integrated exactly is:
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.

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