+1 vote
in Finite Element Method by (110k points)
If only the first derivatives of ux and uy appear in the weak forms, then their interpolation must be at least bilinear.

(a) True

(b) False

I have been asked this question in a job interview.

This interesting question is from Plane Elasticity topic in chapter Plane Elasticity of Finite Element Method

1 Answer

+2 votes
by (185k points)
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Best answer
Right choice is (a) True

Best explanation: An examination of the weak form, 0=∫Ωehe\([\frac{\partial w_1}{\partial x}(c_{11}\frac{\partial u_x}{\partial x}+c_{12}\frac{\partial u_y}{\partial y}) + c_{66}\frac{\partial w_1}{\partial y} (\frac{\partial u_x}{\partial y} + \frac{\partial u_y}{\partial x})\)+ρw1ux]dxdy-∫Ωehew1fxdxdy-∮┌dhew1txds reveals that only first derivatives of ux and uy with respect to x and y appear respectively. Therefore, ux and uy must be approximated by the Lagrange family of interpolation functions, and at least a bilinear (i.e., linear both in x and y) interpolation is required.

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