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Null-field integral equations for stress field around circular holes under antiplane shear

机译：反平面剪切作用下圆孔周围应力场的零场积分方程

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摘要

In this paper, we derive the null-field integral equation for a medium containing circular cavities with arbitrary radii and positions under uniformly remote shear. To fully capture the circular geometries, separate expressions of fundamental solutions in the polar coordinate and Fourier series for boundary densities are adopted. By moving the null-field point to the boundary, singular integrals are transformed to series sums after introducing the concept of degenerate kernels. The solution is formulated in a manner of a semi-analytical form since error purely attributes to the truncation of Fourier series. The two-hole problems are revisited to demonstrate the validity of our method. The bounded-domain approaches using either displacement or stress approaches are also employed. The proposed formulation has been generalized to multiple cavities in a straightforward way without any difficulty. (c) 2005 Elsevier Ltd. All rights reserved.
机译：在本文中，我们推导了含有圆腔的介质的零场积分方程，该圆腔具有任意半径并且在均匀的远程剪切力作用下处于一定位置。为了完全捕获圆形几何形状，采用了极坐标和傅里叶级数的基本解的边界密度的单独表达式。通过将零场点移至边界，在引入简并核的概念后，奇异积分被转换为级数和。由于误差纯粹归因于傅立叶级数的截断，因此该解决方案以半分析形式制定。再次讨论了两孔问题，以证明我们方法的有效性。还采用了使用位移或应力方法的有界域方法。所提出的配方已经以一种简单的方式被毫不费力地推广到了多个腔体。 （c）2005 Elsevier Ltd.保留所有权利。

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