邊界元素法的奇異性一直為眾多學者所關心，至今已有許多相關文獻探討。近期文獻所提之非對稱複材疊層板之伸張-彎矩偶合問題的邊界積分方程式亦含有奇異積分，本論文即針對此問題提出改進方案。作法上是將整個邊界分為兩個區間：奇異區間以科西主值的方式求出奇異積分的明式解；正規區間則以標準高斯積分處理，然後使用Matlab軟體撰寫邊界元素相關程式碼。自由項係數與相關論文比對後，不論是在平滑邊界或是轉角處，數值解與理論解吻合；最後以平面問題為範例，將邊界元素程式與Ansys有限元素軟體作互相驗證。

Many researchers focus on the singular integral of boundary element method. The boundary integral equation for the coupled stretching-bending analysis of unsymmetric laminates derived recently in the literature also contains singular integral. To avoid this problem, the modified boundary integral equations is separated into two parts. One is the singular part in which the singular integral is taken in the sense of Cauchy principal value, and the other is the regular part which is calculated through the use of Gaussian quadrature rule. To perform the numerical computation, the computer program is coded by MATLAB. No matter in smooth boundary or corner, the results show that the present calculations are well agreed with the analytical solutions. Finally, comparison between the present boundary element method and finite element method (through ANSYS) are presented by the reduced cases－plane problems.

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