Hk. Stolarski et Yi. Chen, EXTRAPOLATED FIELDS IN THE FORMULATION OF THE ASSUMED STRAIN ELEMENTS.1. 2-DIMENSIONAL PROBLEMS, Computer methods in applied mechanics and engineering, 123(1-4), 1995, pp. 247-262
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.