Prob_14_02_02a - Problem 14.2-2(a Given The sketch represents three nodes on a z=constant face of an axisymmetirc quadratic element Nodes shown are

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Problem 14.2-2(a) Given: The sketch represents three nodes on a z=constant face of an axisymmetirc quadratic element. Nodes shown are uniformly spaced. Determine the consistent nodal load vector if z-direction traction z is applied to the face as follows: a) z has a constant value p over the face. b) z has a parabolic variation based on nodeal values p 4 , p 7 , and p 3 . Solution: rS N T Φ d = along edge 3, 7, 4 η 1 = N 1 N 2 = N 5 = N 6 = N 8 = 0 = N 0 0 0 0 0 0 0 0 N 3 0 0 N 3 N 4 0 0 N 4 0 0 0 0 0 0 0 0 N 7 0 0 N 7 0 0 0 0 = Φ 0 p = N 3 1 4 1 ξ () 1 η 1 4 1 ξ 1 η 2  1 4 1 ξ 2 1 η = applying η 1 = N 3 ξ 2 ξ 2 = similarily N 4 ξ 2 ξ 2 = N 7 1 ξ 2 = rN 3 r 3 N 4 r 4 N 7 r 7 = since node 7 is at the middle: r 7 r 3 r 4 2 = r ξ 2 ξ 2 r 3 ξ 2 ξ 2 r 4 1 ξ 2 r 3 r 4 2 = simplify r r 3 2 r 4 2 ξ r 3 2 ξ r 4 2 = r 1 2 r 3 r 4 ξ r 3 r 4
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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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Prob_14_02_02a - Problem 14.2-2(a Given The sketch represents three nodes on a z=constant face of an axisymmetirc quadratic element Nodes shown are

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