Extension of unsymmetric finite elements US‐QUAD8 and US‐HEXA20 for geometric nonlinear analyses

Abstract

Purpose

This paper aims to present an extension of two recently published elements (which are based on Petrov‐Galerkin formulation) to geometric nonlinear (GNL) problems.

Design/methodology/approach

Two different sets of shape functions, namely isoparametric and metric, suitably chosen to satisfy the necessary compatibility and completeness conditions, are used as test and trial functions, respectively. Total Lagrangian formulation is used for the implementation of the element.

Findings

In implementing the unsymmetric formulation for nonlinear problems, the deformation gradient tensor can be evaluated invariably using either isoparametric or metric shape functions. The developed elements are found to exhibit improved performance in the presence of mesh distortions.

Research limitations/implications

The numerical problems in this paper involve linear elastic materials.

Originality/value

Extension of US‐QUAD8 and US‐HEXA20 for GNL problems is new.

Citation

Tat Ooi, E., Rajendran, S. and Hock Yeo, J. (2007), "Extension of unsymmetric finite elements US‐QUAD8 and US‐HEXA20 for geometric nonlinear analyses", Engineering Computations, Vol. 24 No. 4, pp. 407-431. https://doi.org/10.1108/02644400710748715