prob_06_08_03 - Problem 6.8-3 Show that the volume of an...

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Problem 6.8-3 Show that the volume of an eight-node solid element is computed exactly by an order two Gauss rule. Solution: J Σ N i ξ x i Σ N i η x i Σ N i ζ x i Σ N i ξ y i Σ N i η y i Σ N i ζ y i Σ N i ξ z i Σ N i η z i Σ N i ζ z i = Volume 1 1 ζ 1 1 η 1 1 ξ J d d d = For an 8-node solid element, each of the shape functions are 1st order in   and . J f 1 η ζ ( ) f 4 ξ ζ ( ) f 7 ξ η ( ) f 2 η ζ ( ) f 5 ξ ζ ( ) f 8 ξ η ( ) f 3 η ζ ( ) f 6 ξ ζ ( ) f 9 ξ η ( )
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