Automation of finite element formulations for large deformation contact problems
Automation of finite element formulations for large deformation contact problems
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DOI：
10.1002/nme.3009
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发表时间：
2010-08
影响因子：
2.9
通讯作者：
J. Lengiewicz;J. Korelc;S. Stupkiewicz
中科院分区：
文献类型：
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作者：
J. Lengiewicz;J. Korelc;S. Stupkiewicz
本文的目的是提出一种大变形接触问题有限元列式自动化的通用方法。介绍了一种新的基于自动微分的符号，它代表了接触力学的经典数学符号和接触有限元的实际计算机实现之间的桥梁。自动推导所需的公式（例如，元素残差和切线矩阵）与自动代码生成相结合，使有限元实现可能在一个温和的努力。因此，在这项工作中，已经实施了几个3D接触配方，包括惩罚和增广拉格朗日处理的接触约束，和几个接触平滑技术。因此，一个典型的基准问题，可以执行一个客观的方式，导致全面的研究的效率和精度的各种配方的三维接触有限元。版权所有© 2010约翰威利父子有限公司.
The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automatic‐differentiation‐based notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Copyright © 2010 John Wiley & Sons, Ltd.