本文中研究的對象是對於二維全異向性彈性體，處理薄層複材受慣性力之應力，由於在邊界元素法(BEM)在眾所周知問題為當源點非常接近其邊界時，將產生近似奇異積分(nearly singular integration)的問題，就是當薄層體其幾何相對於表面非常靠近或是其中內部點相當靠近邊界時，會產生所謂近似奇異積分的問題。
在本文中，以正規化的邊界積分方程式處理二維異向薄層彈性體，在傳統邊界元素法受自體力效應的問題時有個缺點，在邊界積分式會產生一域積分，在二維異向靜彈力中，已將此域積分轉換成邊界積分，然而此轉換式中含有一項額外線積分，在分析多連通區域時，其會導致運算效率低落，特別是幾何形狀複雜的問題，因此Y.C, Shiah and S.Y, Ye 提出一新方法將域積分轉換成邊界積分，且不需要額外的線積分，本論文即將其邊界積分式在處理薄層板受慣性力作用時，所遇到近似奇異積分的問題，最後再以幾個範例應用與ANSYS進行比對。

As an evident drawback for using the conventional boundary element method, an extra line integral is present in the boundary integral equation when body-force effects are involved. From previous study for two dimension anisotropic elastostatics, it has been transformed the extra domain integral to the boundary integral, and successfully proposed a new approach to validate the transformation, yet without involving extra line integrals. However, this new approach will arise nearly singular integrals when it confronted with thin plates. In this article, applied the approach and treated the nearly singular integrals. By this approach, the BEM’s notion as a boundary solution technique is completely restored. In the end, a few benchmark problems are studied to demonstrate the veracity of formulations as well as our successful implementation in an existing BEM code.

參考文獻
【1】 Cruse, T.A. (1988), Boundary Element Analysis in Computational Fracture Mechanics. Kluwer Academic Publisher, Dordrecht, Netherlands.
【2】 Camp, C.V.; Gipson G.S. (1992): Boundary element analysis of nonhomogeneous biharmonic phenomena, Springer-Verlag, Berlin.
【3】 Deb, A.; Banerjee, P.K. (1990): BEM for general anisotropic 2D elasticity using particular integrals, Commun. Appl.
【4】 Nardini, D.; Brebbia, C. A. (1982): A new approach to free vibration analysis using boundary elements, Boundary Element Methods in Engineering, Computational Mechanics Publications, Southampton.
【5】 Danson, D. (1983): Linear isotropic elasticity with body forces, Progress in Boundary Element Methods, Brebbia, C. A., Ed., Pentech Press, London.
【6】 Y.C, Shiah; Tan, C.L. (1999): Calculation of interior point stresses in two-dimensional boundary element analysis of anisotropic bodies with body forces”, Journal of Strain Analysis for Engineering Design 34, pp.117-128.
【7】 Zhang, J.J.; Tan C.L.; Afagh, F.F. (1996): A general exact transformation of body-force volume integral in BEM for 2D anisotropic elasticity, Computational Mechanics 9 (2):1-10.
【8】 Y.C, Shiah (2014): Analytical transformation of the volume integral for the BEM treating 3D anisotropic elastostatics involving body-force, Computer Methods in Applied Mechanics and Engineering 278, pp 404-422.
【9】 Lekhnitskii, S. G. (1981): Theory of Elasticity of Anisotropic Body, Mir Publishers, Moscow.
【10】 Cruse, T.A. and Swedlow, J.L.(1971): Interactive program for analysis and design problems in advanced composites technology. Report AFML-TR-71-268,US Air Force Materials Laboratory.
【11】 夏育群、陳春來，「邊界元素法之入門介紹」，高立圖書有限公司，中華民國93年12月15日。
【12】 Y.C, Shiah , W.S, Hwang and G.C, Shiah：BEM Stress Analysis for Thin Multilayered Composites Subjected to Inertial Loads.
【13】 Y.C, Shiah , S.Y, Ye ：New treatment of the self-weight and the inertial effects of rotation for the BEM formulation of 2D anisotropic solids
【14】 Y.C, Shiah and Y.J, Lin：BEM’s Inter-Coupled Treatment of the Interfacial Thermal Stresses between Dissimilar Anisotropic Materials, Journal of AIAA, vol. 43, no. 5, pp.1124-1132