A four-node hybrids stress finite element with penalized functions

Abstract

A penalized stress condition for multi-variable finite elements is applied to develop a simple four-node Reissner-Mindlin plate element. Introducing a penalty factor in the modified Hellinger-Reissner energy functional and adopting the bilinear transverse and rotation displacement interpolations as well as a assumed linear stress field, the paper formulates a simple 15-/3 hybrid stress element. The elimination of stress parameters is made on the element level. Numerical studies demonstrate that the presented element is of high accuracy, not sensitive to mesh distortion and free of shear locking in the limit of thin plate and therefore the present element can apply to thin and moderately thick plates.