prob_03_02_01

# prob_03_02_01 - Problem 3.2-1. Given: In Fig. 3.2-2b, let:...

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Problem 3.2-1. Given: In Fig. 3.2-2b, let: x 1 0 := x 2 2 := x 3 3 := Then use this data in the following: Find: a) Verify numerically that shape functions sum to unity b) What should the sum of the x derivatives of the shape function be? Verify the property numerically. Solution: a) N 1 x () x 2 x x 3 x x 2 x 1 x 3 x 1 := N 2 x x 1 x x 3 x x 1 x 2 x 3 x 2 := N 3 x x 1 x x 2 x x 1 x 3 x 2 x 3 := fx N 1 x () N 2 x + N 3 x + := 0 1 2 3 0.999 0.9995 1 1.0005 1.001 x N 1 N 2 + N 3 + x 2 x x 3 x x 2 x 1 x 3 x 1 x 1 x x 3 x x 1 x 2 x 3 x 2 + x 1 x x 2 x x 1 x 3 x 2 x 3 + = x 2 x x 3 x x 2 x 1 x 3 x 1 x 1 x x 3 x x 1 x 2 x 3 x 2 + x 1 x x 2 x x 1 x 3 x 2 x 3 + simplify 1 b) taking derivatives of N 1 , N 2 , and N 3 gives: x N 1 d d x x 2 x x 3 x x 2 x 1 x 3 x 1 d d x 3 5 6 x N 2 d d x x 1 x x 3 x x 1 x 2 x 3 x 2 d d 3 2 x x N 3 d d x x 1 x x 2 x x 1 x 3 x 2 x 3 d d 2x 3 2 3 x N 1 d dx N 2 d d + x N 3 d d + gives 5 6 1 3 x + 3 2 x + 2 3 2 3 x + + 0

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Consider the 3 node bar above. uN 1 u 1 N 2 u 2 + N 3 u 3 + = If the bar undergoes a rigid body movement such that:
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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_03_02_01 - Problem 3.2-1. Given: In Fig. 3.2-2b, let:...

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