CHAP 6 Finite Elements for Plane Solids 311 6. Calculate the shape function matrix [N] and strain-displacement matrix [B] of the triangular element shown in the figure Solution: Since the element has three nodes, start with 123( , )u x yxy. By substituting nodal values, we have 1111212221313331uuuuuuuuThus, the approximate solution becomes 12131123( , )()()(1)u x yuuu xuu yxy uxuyuFrom the above approximation scheme, we can obtain three shape functions, as 123( , )1( , )( , )N x yxyN x yxN x yyThen, the matrix of shape functions can be written as 10000100xyxyxyxyNThe strain displacement matrix can be obtained from the definition of strain as
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