Question

For a four noded element while implementing a computer program, the compact representation of shape function is ____

(a) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)

(b) Nt=(1-ξ)(1-η)

(c) Nt=\(\frac{1}{4}\)(1+ξξi)(1+ηηi)

(d) Undefined

The question was asked in an interview for job.

My question is based upon Two Dimensional Isoparametric Elements in chapter Two Dimensional Isoparametric Elements and Numerical Integration of Finite Element Method

Answer 1

Correct answer is (c) Nt=\(\frac{1}{4}\)(1+ξξi)(1+ηηi)

To elaborate: FourNodeQuad is a four-node plane-strain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium. Each element node has 3 degrees-of-freedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p).