Extrapolated fields in the formulation of the assumed strain elements Part 1: Two-dimensional problems

A new assumed strain quadrilateral element with accurate in-plane bending behavior is presented. The basic idea consists in introduction of a parallelogram domain associated with the given quadrilateral element, development of the related assumed strain field for the parallelogram, and subsequent extrapolation of this field to the domain of the original quadrilateral. The assumed strain field for the parallelogram is constructed by identification of various modes of its deformation and then by proper modification of the strain field in some of these modes. In particular, the strain operator with respect to the so-called in-plane bending modes is modified so as to simulate the strain field resulting from the assumptions usually made in structural mechanics. The modification of the strain fields leads to the assumed strain operator. The proposed new assumed strain quadrilateral element exhibits remarkably accurate performance for both membrane and bending dominated problems even when severely distorted and high aspect ratio meshes are considered and when materials are nearly incompressible.