Question

If N3 is dependent shape function, It is represented as ____

(a) N3=ξ

(b) N3=1-ξ

(c) N3=1-η

(d) N3=1-ξ-η

I had been asked this question in my homework.

This interesting question is from Two Dimensional Problems topic in chapter Two Dimensional Problems using Constant Strain Triangles of Finite Element Method

Answer 1

The correct option is (d) N3=1-ξ-η

Easy explanation: The shape function is a function which interpolates the solution between the discrete values obtained at the mesh nodes. N1, N2, N3 are not linearly independent only one of two of these are independent.