Ch_27

# Subbarayan at 1 1 22 n1 n 2 n 3 n 4 1 1

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Unformatted text preview: ⎢ ⎥ ⎢ ⎥ ⎢ −0.060000 −0.034919 0.007621 ⎥ ⎢0 0 0⎥ ⎣ ⎦ ⎣ ⎦ ⎡ 0.007621 −0.034919 −0.060000 ⎤ g (ξ3 ) = ⎢ −0.034919 0.160000 0.274920 ⎥ ⎢ ⎥ ⎢ −0.060000 0.274920 0.472380 ⎥ ⎣ ⎦ Chapter 27 Page 20 G. Subbarayan 1 L L T ∫1[ N ] [ N ]dξ = 2 {W1 [ g (ξ1 ) + g (ξ3 )] + W2 g (ξ2 )} 2− ⎧ ⎡ 0.480 0.240 −0.120 ⎤ ⎡0 0 0⎤ ⎫ L ⎪5 ⎢ ⎥ + 8 ⎢0 1 0⎥ ⎪ = ⎨ ⎢ 0.240 0.320 0.240 ⎥ ⎢ ⎥⎬ 2 ⎪9 9 ⎢ −0.120 0.240 0.480 ⎥ ⎢0 0 0⎥ ⎪ ⎦ ⎣ ⎦⎭ ⎩⎣ Chapter 27 Page 21 G. Subbarayan Spatial Derivative Example Determine derivative of shape functions with respect to x and y at given point Chapter 27 Page 22 G. Subbarayan N1 = (1 − ξ )(1 − η ) 1 4 N 2 = 1 (1 + ξ )(1 − η ) 4 N 3 = 1 (1 + ξ )(1 + η ) 4 N 4 = 1 (1 − ξ )(1 + η ) 4 ∂N1 = − 1 (1 − η ) 4 ∂ξ ∂N...
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## This document was uploaded on 01/29/2014.

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