+1 vote
in Finite Element Method by (110k points)
For a linear triangular element, what is the order of matrix B in the strain-displacement relation ε=BD, where D denotes the displacement matrix?

(a) 6×3

(b) 3×6

(c) 3×8

(d) 8×3

I got this question in an international level competition.

I would like to ask this question from Plane Elasticity in section Plane Elasticity of Finite Element Method

1 Answer

+2 votes
by (185k points)
selected by
Best answer
Right answer is (b) 3×6

To explain I would say: For plane elasticity problems the strain-displacement relation is given by ε=BD, where ε=[εxxεyyεxy]^T, B=\(\begin{pmatrix}\frac{\partial \psi_1}{\partial x}&0&\frac{\partial \psi_2}{\partial y}&0&…&\frac{\partial \psi_n}{\partial y}&0\\0&\frac{\partial \psi_1}{\partial y}&0&\frac{\partial \psi_2}{\partial y}&…&0&\frac{\partial \psi_n}{\partial y}\\\frac{\partial \psi_1}{\partial y}&\frac{\partial \psi_1}{\partial x}&\frac{\partial \psi_2}{\partial y}&\frac{\partial \psi_2}{\partial x}&…&\frac{\partial \psi_n}{\partial y}&\frac{\partial \psi_n}{\partial x}\end{pmatrix}\) and D=\(\begin{bmatrix}u_x^1&u_y^1&u_x^2&u_y^2&u_x^3&u_y^3\end{bmatrix}\)^T. The order of matrix B is 3x2n, where n is the number of nodes in the element. A linear triangular element has three nodes, thus n=3.

Order of B is 3×2*3


Related questions

We welcome you to Carrieradda QnA with open heart. Our small community of enthusiastic learners are very helpful and supportive. Here on this platform you can ask questions and receive answers from other members of the community. We also monitor posted questions and answers periodically to maintain the quality and integrity of the platform. Hope you will join our beautiful community