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对于工程中的裂纹问题运用二维弹性问题的控制方程和Ｋｅｌｖｉｎ问题的基本解，建立了Ｓｏｍｉｇｌｉａｎａ等式及边界积分方程，并利用常值元及线性元对积分方程离散，从而对裂纹区域进行力学分析．文中所给算例，与文献结果吻合较好．
The Somigliana equation and the boundary integral equations are established for the crack problem in engineering using the control equations of the two-dimensional elastic problem and the Kelvin problem. The Somigliana equations and the boundary integral equations are established. The integral equations are discretized by the constant valued elements and linear elements. analysis. The examples given in the paper are in good agreement with the literature results.