Analysis of a method to compute mixed-mode stress intensity factors for non-planar cracks in three-dimensions

IF 1.9 3区 数学 Q2 Mathematics
Benjamin E. Grossman‐Ponemon, M. Negri, A. Lew
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引用次数: 0

Abstract

In this work, we present and prove results underlying a method which uses functionals derived from the interaction integral to approximate the stress intensity factors along a three-dimensional crack front. We first prove that the functionals possess a pair of important properties. The functionals are well-defined and continuous for square-integrable tensor fields, such as the gradient of a finite element solution. Furthermore, the stress intensity factors are representatives of such functionals in a space of functions over the crack front. Our second result is an error estimate for the numerical stress intensity factors computed via our method. The latter property of the functionals provides a recipe for numerical stress intensity factors; we apply the functionals to the gradient of a finite element approximation for a specific set of crack front variations, and we calculate the stress intensity factors by inverting the mass matrix for those variations.
三维非平面裂纹混合模态应力强度因子计算方法分析
在这项工作中,我们提出并证明了一种方法的结果,该方法使用从相互作用积分中导出的泛函来近似三维裂缝前缘的应力强度因子。我们首先证明泛函具有一对重要的性质。对于平方可积张量场,如有限元解的梯度,泛函是定义良好且连续的。此外,应力强度因子是这些泛函在裂缝前缘的函数空间中的代表。我们的第二个结果是通过我们的方法计算的数值应力强度因子的误差估计。泛函的后一种性质为计算应力强度因子提供了一种方法;我们将函数应用于一组特定裂纹前缘变化的有限元近似梯度,并通过对这些变化的质量矩阵进行反求来计算应力强度因子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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