HYBRID PLANE QUADRILATERAL ELEMENT WITH CORNER ROTATIONS

A quadrilateral plane element for analysis of spatial structures is of ten formulated by combining a plane stress (membrane) element with two translational inplane degrees of freedom at each comer to a plate ben ding element with two rotational degrees of freedom and one translatio nal (normal to the plane of element) at each comer. An additional rota tional degree of freedom normal to the plane of the element and a fict itious torsional spring are added at each comer. This brings the total comer nodal degrees of freedom to three rotations and three translati ons and makes the element usable for general spatial structures. A qua drilateral hybrid stress element with two translational and one rotati onal degrees of freedom at each comer is presented in this paper. When used as the membrane constituent of a shell element, the rotational d egree of freedom provides factual torsional stiffness. The element mat rices are derived by minimization of a functional consisting of displa cement and stress fields. Allman's displacement field is used with sev en 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.