Question

Which option is correct for the first derivative of the shape function S in the study of plane elasticity problems?

(a) It is element-wise constant for triangular element whereas not a constant for quadrilateral element

(b) It is element-wise constant for both the triangular element as well as a quadrilateral element

(c) It is not a constant for triangular element whereas element-wise constant for quadrilateral element

(d) It is a combination of a linear function and constant for both the triangular element and a quadrilateral element

The question was posed to me by my school teacher while I was bunking the class.

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

Answer 1

Correct answer is (a) It is element-wise constant for triangular element whereas not a constant for quadrilateral element

The best explanation: In the study of plane elasticity problems, the first derivatives of the shape function S for a triangular element are element-wise constant, whereas, for a quadrilateral element, they are not constant. Notably,   \(\frac{\partial s (n, e)}{\partial n}\) is linear in e and constant in n whereas \(\frac{\partial s (n, e)}{\partial e}\) is linear in n and constant in e.