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A boundary element analysis for stress intensity factors of multiple circular arc cracks in a plane elasticity plate

机译：平面弹性板中多个圆弧裂纹应力强度因子的边界元分析

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摘要

In this paper, a numerical approach for analyzing interacting multiple cracks in infinite linear elastic media is presented. By extending Bueckner's principle suited for a crack to a general system containing multiple interacting cracks, the original problem is divided into a homogeneous problem (the one without cracks) subjected to remote loads and a multiple crack problem in an unloaded body with applied tractions on the crack surfaces. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements proposed recently by the author. Test examples are given to illustrate that the numerical approach is very accurate for analyzing interacting multiple cracks in an infinite linear elastic media under remote uniform stresses. In addition, the displacement discontinuity method with crack-tip elements is used to analyze a multiple crack problem in a finite plate. It is found that the boundary element method is also very accurate for investigating interacting multiple cracks in a finite plate. Specially, a generalization of Bueckner's principle and the displacement discontinuity method with crack-tip elements are used to analyze multiple circular arc crack problems in infinite plate in tension (including: Two Collinear Circular Arc Cracks, Three Collinear Circular Arc Cracks, Two Parallel Circular Arc Cracks, Three Parallel Circular Arc Cracks and Two Circular Arc Cracks) in a plane elasticity plate. Many results are given.
机译：本文提出了一种用于分析无限线性弹性介质中多个裂纹相互作用的数值方法。通过将适用于裂纹的Bueckner原理扩展到包含多个相互作用的裂纹的一般系统，将原始问题分为承受远程载荷的均质问题（无裂纹的均匀问题）和在施加载荷的情况下在无载体中的多个裂纹问题。裂纹表面。因此，可以通过考虑后一个问题来获得有关应力强度因子（SIF）的结果，该问题可以通过作者最近提出的带有裂纹尖端元素的位移不连续性方法轻松进行分析。给出了测试例子，说明了数值方法对于分析均匀应力作用下的无限线性弹性介质中相互作用的多个裂纹非常准确。另外，利用裂纹尖端单元的位移不连续性方法来分析有限板中的多重裂纹问题。发现边界元法对于研究有限板中的多个裂纹的相互作用也非常准确。特别地，采用Bueckner原理的推广和带裂纹尖端单元的位移不连续性方法来分析无限大板在张力下的多个圆弧裂纹问题（包括：两个共线圆弧裂纹，三个共线圆弧裂纹，两个平行圆弧）平面弹性板上的裂纹，三个平行的圆弧裂纹和两个圆弧裂纹）。给出了许多结果。

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