EXTRAPOLATED FIELDS IN THE FORMULATION OF THE ASSUMED STRAIN ELEMENTS.1. 2-DIMENSIONAL PROBLEMS

A new assumed strain quadrilateral element with accurate in-plane bend ing 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 parallelogra m, and subsequent extrapolation of this field to the domain of the ori ginal 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 mode s. In particular, the strain operator with respect to the so-called in -plane bending modes is modified so as to simulate the strain field re sulting from the assumptions usually made in structural mechanics. The modification of the strain fields leads to the assumed strain operato r. The proposed new assumed strain quadrilateral element exhibits rema rkably accurate performance for both membrane and bending dominated pr oblems even when severely distorted and high aspect ratio meshes are c onsidered and when materials are nearly incompressible.