prob_06_08_01 - Problem 6.8-1 In a 3 node bar element, let...

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Problem 6.8-1 In a 3 node bar element, let x 3 - x 2 = L/3 and x 2 - x 1 = 2L/3. Use one-point Gauss Quadrature to determine the 3 by 3 stiffness matrix of an element with uniform A and E. Solution: N 1 2 ξ ξ 2 + () 1 ξ 2 1 2 ξξ 2 + = Eq. 6.1-4 B 1 J 1 2 1 2 ξ + 2 ξ 1 2 12 ξ + = Eq. 6.1-7 J 1 2 1 2 ξ + 2 ξ 1 2 ξ + x 1 x 2 x 3 = 1 2 1 2 ξ + 2 ξ 1 2 ξ + x 1 x 1 2 L 3 + x 1 L + = 1 3 ξ L 1 2 L + = B 1 1 3 ξ L 1 2 L + 1 2 1 2 ξ + 2 ξ 1 2 ξ + = k 1 1 ξ B T E B A J d = EA 1 1 ξ 1 1 3 ξ L 1 2 L + 1 2 1 2 ξ + 2 ξ 1 2 ξ + 1 2 1 2 ξ + 2 ξ 1 2 ξ +
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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_06_08_01 - Problem 6.8-1 In a 3 node bar element, let...

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