It could be shown that the shape function matrix for this tetrahedron element is of the...
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It could be shown that the shape function matrix for this tetrahedron element is of the following form of a (12x3) matrix: N₁ 0 0 0 0 N3 0 0 N₁ 00N3 0 N₁0 N₂ 0 and the S matrix for a three-dimensional finite element is: N = B = b₁ 0 0 0 0 N₂ N₂ N₁ 0 0 N₂ 0 0 д/ду 0 0 a/əz 0 д/дz д/ду д/дх 0 a/az a/ay a/ax 0 Given that B = SN, write down, in terms of N, (i=1,2,3,4) and the partial differential operators (i.e. a/ax, a/ay and a/az), the mathematical form of the matrix elements b₁, C₁, d3 and d4 in the following B matrix: 0 0 b₂ 0 0 C1 0 \d₁ S = /a/ax 0 C1 0 d₁ 0 b₁ 0 C2 d₁ C₁ 0 0b₁d₂ 0 C2 0 d₂ 0 0 C3 0 0 0 0 N₁ 0 N3 0 0 N₁ 0 b3 0 0 0 C3 0 b₂ d₂ C₂ 0 b₂ d3 0 0 0 0 0 b4 0 0 0 0 0 C4 d3 0 0 b3 0 C4 b4 d3 C3 0 d4 0 b3 d4 0 d4 0 C4 b4 It could be shown that the shape function matrix for this tetrahedron element is of the following form of a (12x3) matrix: N₁ 0 0 0 0 N3 0 0 N₁ 00N3 0 N₁0 N₂ 0 and the S matrix for a three-dimensional finite element is: N = B = b₁ 0 0 0 0 N₂ N₂ N₁ 0 0 N₂ 0 0 д/ду 0 0 a/əz 0 д/дz д/ду д/дх 0 a/az a/ay a/ax 0 Given that B = SN, write down, in terms of N, (i=1,2,3,4) and the partial differential operators (i.e. a/ax, a/ay and a/az), the mathematical form of the matrix elements b₁, C₁, d3 and d4 in the following B matrix: 0 0 b₂ 0 0 C1 0 \d₁ S = /a/ax 0 C1 0 d₁ 0 b₁ 0 C2 d₁ C₁ 0 0b₁d₂ 0 C2 0 d₂ 0 0 C3 0 0 0 0 N₁ 0 N3 0 0 N₁ 0 b3 0 0 0 C3 0 b₂ d₂ C₂ 0 b₂ d3 0 0 0 0 0 b4 0 0 0 0 0 C4 d3 0 0 b3 0 C4 b4 d3 C3 0 d4 0 b3 d4 0 d4 0 C4 b4
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Horngrens Accounting
ISBN: 978-0133855388
10th Canadian edition Volume 2
Authors: Tracie L. Miller-Nobles, Brenda L. Mattison, Ella Mae Matsumura, Carol A. Meissner, Jo-Ann L. Johnston, Peter R. Norwood
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