A 4‐node quadrilateral membrane element with in‐plane vertex rotations and modified reduced quadrature

Abstract

An assessment is made of a 4‐node quadrilateral membrane element with one rotational and two translational degrees of freedom per node, as formulated by Taylor and Simo. The element, QC9, is formed by degeneration of the 9‐node Lagrange element and condensation of the centre degrees of freedom. An 8‐point, modified reduced integration scheme is implemented in this element, QC9(8), to improve on the 3 × 3 quadrature performance, yet avoid the additional rank deficiency due to reduced integration (2 × 2). QC9(8) performs as good or better than all elements surveyed. It is shown that a similar degeneration of the 16‐node Lagrangian element can be carried out, but that the resulting element fails the patch test.

Citation

Stander, N. and Wilson, E.L. (1989), "A 4‐node quadrilateral membrane element with in‐plane vertex rotations and modified reduced quadrature", Engineering Computations, Vol. 6 No. 4, pp. 266-271. https://doi.org/10.1108/eb023781