Question

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

I had been asked this question in class test.

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

Answer 1

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.