Application of the 2-D constant strain assumption to FEM elements consisting of an arbitrary number of nodes

The formulation for the constant strain element is revisited to develop multi-noded elements that can be used as transition elements in a finite element mesh. Although the constant strain approach is computationally attractive, spurious force-free displacement modes arise for elements consisting of more than three nodes. These unstable mode shapes are typified by "hourglassing" which develops in quadrilateral elements when constant strain is assumed within the element. The means for stabilizing spurious mode shapes for quadrilateral elements is well documented in the literature, however, in this paper, a general formulation for stabilizing forces is presented for elements having an arbitrary number of nodes and therefore is not restricted to quadrilateral elements. This paper examines the use of meshes consisting of constant strain elements created from polygons having differing numbers of element nodes. The effectiveness of the stabilization procedure is illustrated along with "patch test" examples to assess the consistency of the approximation. The elements are shown to be surprisingly robust, yielding reasonable results even when poorly designed mesh transitions are used.