Question

Which interpolation functions must be used for the primary variables in weak forms of plane elasticity equations?

(a) Hermite family interpolation function

(b) Lagrange family interpolation function

(c) Hierarchical interpolation function

(d) Quadratic interpolation function

This question was addressed to me in a national level competition.

Enquiry is from Plane Elasticity topic in division Plane Elasticity of Finite Element Method

Answer 1

Correct option is (b) Lagrange family interpolation function

To explain I would say: An examination of expanded weak forms of the plane elasticity problems reveals that the variables ux and uy are the primary variables, and only first derivatives of ux and uy with respect to x and y appear, respectively. Therefore, ux and uy must be approximated by the Lagrange family of interpolation functions, and at least bilinear (i.e., linear both in x and y) interpolation is required.