060000 0034919 0007621 0 0 0 0007621 0034919 0060000

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Unformatted text preview: tegrals associated with element matrices [ N ]T , [ N ]T [ N ], [ B ]T [ D][ B] Here we numerically evaluate for a quadratic element 1 L [ N ]T [ N ]d ξ ∫ 2 −1 Chapter 27 Page 17 G. Subbarayan [N]T[N] contains fourth order terms (ξ4) since N1 (ξ ) = ξ (ξ − 1) 2 N 2 (ξ ) = −(ξ 2 − 1) N 3 (ξ ) = ξ 2 (ξ + 1) (2n-1)=4 requires n=5/2 or 3 integration points Chapter 27 Page 18 G. Subbarayan 3-point quadrature: 1 L L3 [ N ]T [ N ]dξ = ∑ [ N (ξi )]T [ N (ξi )]Wi ∫ 2 −1 2 i =1 From Table 27.1 ξ1 = −0.774597, ξ 2 = 0.0, ξ3 = 0.774597 5 8 5 W1 = ,W2 = , W3 = 9 9 9 Chapter 27 Page 19 G. Subbarayan Let g (ξ ) = [ N (ξ )]T [ N (ξ )] ⎡ 0.472380 0.274920 −0.060000 ⎤ ⎡0 0 0⎤ g (ξ1 ) = ⎢ 0.274920 0.160000 −0.034919 ⎥ g (ξ 2 ) = ⎢ 0 1 0 ⎥...
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This document was uploaded on 01/29/2014.

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