4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion

Abstract

SummaryThe unsymmetric finite element method is a promising technique to produce distortion‐immune finite elements. In this work, a simple but robust 4‐node 12‐DOF unsymmetric quadrilateral membrane element is formulated. The test function of this new element is determined by a concise isoparametric‐based displacement field that is enriched by the Allman‐type drilling degrees of freedom. Meanwhile, a rational stress field, instead of the displacement one in the original unsymmetric formulation, is directly adopted to be the element's trial function. This stress field is obtained based on the analytical solutions of the plane stress/strain problem and the quasi‐conforming technique. Thus, it can a priori satisfy related governing equations. Numerical tests show that the presented new unsymmetric element, named as US‐Q4θ, exhibits excellent capabilities in predicting results of both displacement and stress, in most cases, superior to other existing 4‐node element models. In particular, it can still work very well in severely distorted meshes even when the element shape deteriorates into concave quadrangle or degenerated triangle.