Question

Shape function can be written as _____

(a) Nt=(1-ξ)(1-η)

(b) Nt=(1-ξ)

(c) Nt=(1-η)

(d) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)

The question was posed to me in an online quiz.

My query is from Two Dimensional Isoparametric Elements topic in portion Two Dimensional Isoparametric Elements and Numerical Integration of Finite Element Method

Answer 1

Correct choice is (d) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)

To explain: 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.