Hybrid plane quadrilateral element with corner rotations

Abstract

A quadrilateral plane element for analysis of spatial structures is often formulated by combining a plane stress (membrane ) element with two translational inplane degrees of freedom at each corner to a plate bending element with two rotational degrees of freedom and one translational (normal to the plane of element) at each corner. An additional rotational degree of freedom normal to the plane of the element and a fictitious torsional spring are added at each corner. This brings the total corner nodal degrees of freedom to three rotations and three translations and makes the element usable for general spatial structures. A quadrilateral hybrid stress element with two translational and one rotational degrees of freedom at each corner is presented in this paper. When used as the membrane constituent of a shell element, the rotational degree of freedom provides factual torsional stiffness. The element matrices are derived by minimization of a functional consisting of displacement and stress fields. Allman's displacement field is used with seven stress modes. The element passes the patch test and is invariant to orientation of axes and node numbering. Results of commonly employed benchmark tests are presented to show that the element is accurate and robust.