On invariance of isoparametric hybrid/mixed elements

Abstract

In this paper the issue of invariance for various hybrid/mixed models with and without incompatible displacement modes is addressed. Special emphasis is directed to assumed spaces of the primary variables which are based on the natural co-ordinates. It is found that if the assumed spaces of all primary variables are invariant to orthogonal transformations, any derived models would automatically be invariant. In contrast to the traditional concept of choosing the starting stress/strain interpolants based on either global or local co-ordinate systems, it is shown that it is not necessary to employ either complete or balanced polynomial expansions of natural co-ordinates in order to preserve the element invariance. Based on one of the newly proposed classes of stress/strain interpolants, 8-node invariant-assumed stress brick elements are proposed which are close to Loikkanen and Irons' assumed stress counterpart of Wilson's Q6 brick element.