# 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?

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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

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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.

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