A new enriched 4-node 2D solid finite element free from the linear dependence problem

In this paper, we propose a new 4-node 2D solid finite element enriched by interpolation cover functions. Instead of using the bilinear shape functions of the standard 4-node finite elements, piecewise linear shape functions are adopted as the partition of unity functions to resolve the linear dependence problem; thus, rank deficiency of the stiffness matrix is not observed. Higher order cover functions can be arbitrarily employed to increase solution accuracy without mesh refinements or introduction of additional nodes. The new enriched 4-node element also shows good convergence behavior, even when distorted meshes are used. Herein, we investigate the linear dependence problem of the new enriched element. Its convergence, effectiveness, and usefulness are demonstrated through the solution of four plane stress problems: an ad hoc problem, a tool jig problem, a slender beam problem, and an automotive wheel problem.