prob_03_11_02 - Problem 3.11-2 If load q is constant, the...

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Problem 3.11-2 If load q is constant, the integrand in Eq. 3.11-6 becomes [N] T q d x . Using the integral, verify that the total force F on a straight side with a midside node is allocated F /6, 2 F /3, and F /6. Solution: The nodal coordinates are: x 4 a = y 4 b = x 7 0 = y 7 b = x 3 a = y 3 b = x 6 a = y 6 0 = x 2 a = y 2 b = Fig. 3.2-2 on page 85 lists 2nd order polynomials for a bar element. We will generate a Q4 Lagrange Polynomial N 3 as the product of the polynomials in the X and Y directions. N 3 x 4 x () x 7 x x 4 x 3 x 7 x 3 y 2 y y 6 y y 2 y 3 y 6 y 3 = N 3 a x x a a a b y y b b b = simplify N 3 xy ax + by + 4a 2 b 2 = Inserting known values For evaluating a distributed load along the top edge, y=b at all points of interest. Thus: N 3 xa x + 2a 2 = Simliarily: N 4 x 3 x x 7 x x 3 x 4 x 7 x 4 y 1 y y 8 y y 1 y 4 y 8 y 4 = x aa + a b y y b b b = xx a 2 = N 7 x 4 x x 3 x x 4 x 7 x 3 x 7 1 = a x a x a a = a 2 x 2 a 2 = Thus: N 4 N 7 N 3 1 2 2 a 2 x 2 +
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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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