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.

中文翻译：

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将非对称 8 节点六面体实体单元 US-ATFH8 扩展到几何非线性分析

目的

本文的目的是将最近的一个具有高畸变容限的非对称 8 节点、24-DOF 六面体实体单元 US-ATFH8 扩展，它使用线性弹性控制方程的解析解作为试函数（解析试函数）到几何非线性分析。

设计/方法/方法

基于这些分析试验函数在非线性分析过程中仍然可以在每个增量步中正常工作的假设，目前的工作重点是通过两种不同的方式构建非对称单元 US-ATFH8 的增量非线性公式：一般更新拉格朗日函数（ UL) 方法和增量共旋转 (CR) 方法。关键创新是如何更新包含线性分析试验函数的应力。

发现

3D 结构的几个数值例子表明，得到的非线性单元，US-ATFH8-UL 和 US-ATFH8-CR，无论是使用规则还是扭曲的粗网格，都表现得很好，并且表现出比传统对称非线性单元更好的性能固体元素。

原创性/价值

将单元 US-ATFH8 扩展到几何非线性分析的成功再次显示了具有解析试验函数的非对称有限元方法的优点，尽管这些函数是线性弹性控制方程的解析解。