Question

N1, is of the form ____

(a) Co-ordinates

(b) N1=c(1-ξ)(1-η)(1+ξ+η)

(c) N1=(1-ξ)(1-η)

(d) N1=(1-ξ)

I had been asked this question in an online interview.

My question comes from Four Node Quadrilateral for Axis Symmetric Problems in chapter Two Dimensional Isoparametric Elements and Numerical Integration of Finite Element Method

Answer 1

Correct option is (b) N1=c(1-ξ)(1-η)(1+ξ+η)

The explanation: The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions. In this work linear shape functions are used.