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A Total Lagrangian based method for recovering the un-deformed configuration in finite elasticity

机译：基于全拉格朗日法的有限弹性恢复未变形构型的方法

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摘要

The problem of finding the un-deformed configuration of an elastic body, when the deformed configuration and the loads are known, occurs in many engineering applications. Standard solution methods for such problems include conservation laws based on Eshelby's energy-momentum tensor and re-parameterization of the standard equilibrium equations. In this paper we present a different method for solving such problems, based on a re-parameterization of the nodal forces using the Total Lagrangian formulation. The obtained nonlinear system of equations describing equilibrium can be solved using either Newton-Raphson or an explicit dynamic relaxation algorithm. The solution method requires only minor modifications to similar algorithms designed for forward motion calculations. Several examples involving large deformations and different boundary conditions and loads are presented.
机译：当已知变形的构型和载荷时，寻找弹性体的未变形的构型的问题在许多工程应用中都会出现。解决此类问题的标准方法包括基于Eshelby能量动量张量的守恒定律和标准平衡方程的重新参数化。在本文中，我们基于使用总拉格朗日公式对节点力进行重新参数化，提出了解决此类问题的另一种方法。可以使用Newton-Raphson或显式动态松弛算法求解获得的描述平衡的非线性方程组。该解决方案方法只需要对为前进运动计算而设计的类似算法进行少量修改。给出了一些涉及大变形以及不同边界条件和载荷的例子。

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  • 来源
    《Applied Mathematical Modelling》 |2015年第14期|3913-3923|共11页
  • 作者

    Grand Roman Joldes; Adam Wittek; Karol Miller;

  • 作者单位

    Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, 35 Stirling Highway, Crawley/Perth, WA 6009, Australia;

    Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, 35 Stirling Highway, Crawley/Perth, WA 6009, Australia;

    Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, The University of Western Australia, 35 Stirling Highway, Crawley/Perth, WA 6009, Australia;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Un-deformed configuration; Total Lagrangian formulation; Explicit time integration; Dynamic relaxation; Newton-Raphson iterations;

    机译：不变的配置;拉格朗日方程式明确的时间整合;动态放松;牛顿-拉夫森迭代;

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