+1 vote
in Finite Element Method by (110k points)
In Finite Element Analysis, what is the correct load vector for the linear quadrilateral element with area Ae, thickness he and uniform body force vector f?

(a) \(\frac{A_e h_e}{4} \)f

(b) \(\frac{A_e h_e}{3}\)f

(c) \(\frac{h_e}{3A_e}\)f

(d) \(\frac{h_e}{4A_e}\)f

This question was addressed to me in an online interview.

My enquiry is from Plane Elasticity topic in division Plane Elasticity of Finite Element Method

1 Answer

+2 votes
by (185k points)
selected by
Best answer
Correct choice is (a) \(\frac{A_e h_e}{4} \)f

The best I can explain: For a linear quadrilateral element,for the case in which the body force is uniform and thus the body force components are element-wise constant (say, equal to, \(f_{x0}^e\) and \(f_{y0}^e\) respectively), the load vector F has the form F=\(\int_{\Omega_c}h_e(\psi^e)^T f_0^edx\)

=\(\frac{A_e h_e}{4}\begin{bmatrix}f_{x0}^e\\f_{y0}^e\\f_{x0}^e\\f_{y0}^e\\f_{x0}^e\\f_{y0}^e\\f_{x0}^e\\f_{y0}^e\end{bmatrix}\). The internal load vector Q is computed only when the element falls on the boundary of the domain on which tractions are specified.

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