本文中研究的對象是對於三維全異向性彈性體，處理超薄問題以及內部點靠近邊界等問題，由於在邊界元素法(BEM)在社會大眾所周知問題就是，當源點是非常接近其邊界時，將產生的近似奇異積分(nearly singular integration)的問題，就是當超薄體的幾何相對表面是非常靠近彼此以及分析其中內部點相當靠近邊界時，會產生所謂近似奇異積分(nearly singular integration)的問題。
在本文中，自正規化(self-regularization)的邊界積分方程（BIE）之三維等向性彈性體之分析由He and Tan【1】提出，而本文擴展應用於研究超薄幾何問題以及內部點靠近邊界時，與其位置形狀還有跟三維的全異向性材料之間的應力與位移的結果數值。
在本文中，自由項(free term)在三維全異向性彈性的解析解可以得到，在此篇文章將深入解釋此自由項，此外也可以用於自正規化(self-regularization)處理其內部應變/應力的分析。

This research targets investigation of stress concentration in a 3D anisotropic elastic body containing an oblate cavity by the boundary element method (BEM). As is well known in the community of BEM, the problem of nearly singular integration will arise when the source point is very close to the boundary. This situation happens to cases when the opposite surfaces of the oblate cavity are very near to each other or the internal point of analysis is very near the boundary. In this paper, the self-regularized boundary integral equation (BIE) presented by He and Tan [1] for 3D isotropic elastic analysis is applied to investigate how the location and shape of an oblate cavity affect the stress concentration in a 3D anisotropic column. In this paper, the analytical solution of the free term in the BIE for 3D anisotropic elasticity is derived. Also, the self-regularization treatment is taken for the analysis of internal strains/stresses.

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