# What is the function on $\frac{\partial s}{\partial n}$ if S (n, e) denotes the shape function of a linear quadrilateral element?

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What is the function on   $\frac{\partial s}{\partial n}$ if S (n, e) denotes the shape function of a linear quadrilateral element?

(a) Linear in e and constant in n

(b) Constant in e and Linear in n

(c) Linear in both e and n

(d) Constant in both e and n

Asked question is from Plane Elasticity topic in section Plane Elasticity of Finite Element Method

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The correct option is (a) Linear in e and constant in n

Explanation: For a quadrilateral element, the first derivatives of the shape function are not constant. $\frac{\partial s}{\partial n}$ is linear in e and constant in n whereas $\frac{\partial s}{\partial e}$  is linear in n and constant in e. Also, the first derivatives of shape functions for a triangular element are constant element wise, and hence all the strains computed are constant element wise.

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