具有任意形状夹杂的弹性力学
Elasticity with Arbitrarily Shaped Inhomogeneity
摘要：
弹性理论中的一个经典问题涉及嵌入在给定应力和剪切模量的材料中的不均匀性。不均匀性是一个任意形状的区域，其应力和剪切模量与周围介质的不同。在本文中，我们提出了一个新的，半解析的方法来寻找应力张量的无限板这样的不均匀性。该解决方案涉及两个共形映射，一个从内部和第二个从单位圆的外部到内部，并分别在外部的不均匀性。该方法通过匹配不均匀体和周围材料之间的边界上的共形映射来提供解决方案。这种匹配仅在单位圆的相对轻微的扭曲下收敛得很好，原因将在文章中讨论。我们提供了一个比较目前的结果，已知的以前的结果。
英文摘要：
A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a new, semi-analytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results.
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