A distortion-insensitive four-noded membrane quadrilateral that passes the patch test

Abstract

This chapter discusses the possibility to develop a quadrilateral called Unidirectional Bending-Optimal Quadrilateral Panel (UBOQP) that passes the patch test for any geometry while being bending exact along one direction. This model is directly constructed using the framework of finite element templates by energy fitting arguments. UBOQP is not obtainable by any conventional finite element method (FEM) formulation, which illustrates the customization power of templates. Numerical experiments in a well-known mesh distortion test verify the exact response to bending for any material law, aspect ratio, and skew angles. The four-noded membrane (plane stress) flat quadrilateral is one of the most interesting models from the standpoint of its impact on both theory and practice of the FEM. The rectangular specialization is one of the two multidimensional finite element stiffnesses that is explicitly derived by Turner. It is widely believed that a four-noded flat quadrilateral membrane element that passes the patch test must be sensitive to the mesh distortion response to inplane bending actions.