An efficient quadrilateral plane element with drilling degrees of freedom using orthogonal stress modes

Abstract

In this paper, a mixed quadrilateral plane element with drilling degrees of freedom using Allman's interpolation scheme is developed. The assumed stress space includes three constant stress modes and four quasi-linear stress modes which are equilibrating for regular element geometry. Owing to the intrinsic orthogonality of the constant and higher order stress modes, the element is particularly efficient. Only a 4 × 4 symmetry matrix is required to be inverted while no incompatible displacement modes are involved. The element has two spurious kinematic modes which, however, can effectively be suppressed by using two very simple stabilization matrices. A number of popular benchmark problems are examined and the accuracy achieved is very satisfactory. © 1992.