Two-field solid element suiting thin-mesh analysis by admissible matrix formulation

Abstract

An 8-node solid element applicable for thin structures is presented. The element employs eighteen assumed stress modes and the conventional displacement interpolation. The formulation starts with the hybrid stress element proposed by Pian and Tong. The higher order stress modes are first decomposed into the ones which do and do not lead to thin-element locking. The recently established methodology of admissible matrix formulation allows the decoupling of the above two categories of stress modes in the flexibility matrix without triggering element instability or failure of the patch test. The element stiffness can thus be decomposed into a series of matrices. Locking can be eliminated by adjusting the magnitude of the pertinent matrices. Accuracy and convergence rate of the present element are found to be competent to many of the existing plate and shell models.