Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis

Abstract

Purpose

The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis.

Design/methodology/approach

Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions.

Findings

Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements.

Originality/value

The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

Citation

Li, Z., Cen, S. and Li, C. (2021), "Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis", Engineering Computations, Vol. 38 No. 8, pp. 3219-3253. https://doi.org/10.1108/EC-04-2020-0203