Question

Which option is not correct about the four-noded rectangular plane stress element used in FEM?

(a) It has eight degrees of freedom

(b) Shape functions N1, N2, N3 and N4 are bilinear functions of x and y

(c) The displacement field is continuous across elements

(d) Its Delaunay triangulation is unique

The question was posed to me in an internship interview.

My doubt stems from Library of Elements and Interpolation Functions in division Interpolation Functions, Numerical Integration and Modelling Considerations of Finite Element Method

Answer 1

Right answer is (d) Its Delaunay triangulation is unique

To elaborate: The four-node quadrilateral element with linear displacements for a plane stress problem has two degrees of freedom at each node. The total degrees of freedom of the element is eight. The displacement field is continuous across elements connected at nodes and the shape functions N1, N2, N3 and N4 are bilinear functions of x and y. Its Delaunay triangulationis not unique, but it has two solutions.