6-5 - 310 Finite Element Analysis and Design 5. A structure...

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310 Finite Element Analysis and Design 5. A structure shown in the figure is approximated with one triangular element. Plane strain assumption is used. (a) Calculate the strain displacement matrix [ B ]. (b) When nodal displacements are given by { u 1 , v 1 , u 2 , v 2 , u 3 , v 3 } = {0, 0, 2, 0, 0, 1}, calculate the element strain vector. Solution: (a) From nodal coordinates: x 1 = 0, y 1 = 0, x 2 = 10, y 2 = 10, x 3 = 0, y 3 = 20, the following coefficients are calculated: 1 2 3 2 3 1 3 1 2 1 3 2 2 1 3 3 2 1 10 20 10 10 0 10 b y y b y y b y y c x x c x x c x x       Also area A = 20 10/2 = 100. Thus, the strain-displacement matrix becomes 1 2 3 1 2 3 1 1 2 2 3 3 0 0 0 10 0 20 0 10 0 11 0 0 0 0 10 0 0 0 10 2 200 10 10 0 20 10 10 b b b c c c A c b c b c b   
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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