超弹性和弹塑性的渐近数值方法:综述

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES
Michel Potier-Ferry
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引用次数: 0

摘要

本文综述了有关渐近数值法(ANM)的文献及其在超弹性和弹塑性中的应用。渐近数值法是一种基于泰勒级数计算的通用延续方法,用于求解非线性偏微分方程。现代的高阶微分技术为计算这些幂级数提供了简单的工具,本文总结了有限应变弹性和弹塑性的相应算法。泰勒级数不仅是一种计算工具,还包含有关所考虑的解曲线结构的有用信息。本文最后简要介绍了这种数值方法的发展历史。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

The literature about the asymptotic numerical method (ANM) is reviewed in this paper as well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation method based on the computation of Taylor series for solving nonlinear partial differential equations. Modern techniques of high-order differentiation provide simple tools for computing these power series, the corresponding algorithms for finite strain elasticity and elastoplasticity being summarized here. Taylor series is not only a computation tool, but it contains also useful information about the structure of the considered solution curve. The paper ends with a short historical account about the development of this numerical method.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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