Question

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

Answer 1

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.