Four-node generalized conforming membrane elements with drilling DOFs using quadrilateral area coordinate methods

Abstract

Two 4-node generalized conforming quadrilateral membrane elements with drilling DOF, named QAC4 θ and QAC4 θ M, were successfully developed. Two kinds of quadrilateral area coordinates are used together in the assumed displacement fields of the new elements, so that the related formulations are quite straightforward and will keep the order of the Cartesian coordinates unchangeable while the mesh is distorted. The drilling DOF is defined as the additional rigid rotation at the element nodes to avoid improper constraint. Both elements can pass the strict patch test and exhibit better performance than other similar models. In particular, they are both free of trapezoidal locking in MacNeal's beam test and insensitive to various mesh distortions.