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 引用本文: 牛忠荣 程长征 胡宗军 叶建乔. V形切口应力强度因子的一种边界元分析方法[J]. 力学学报, 2008, 40(6): 849-857.
Zhongrong Niu, Changzheng Cheng, Zongjun Hu, Jianqiao Ye. Boundary element analysis of the stress intensity factors for the v-notched structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(6): 849-857.
 Citation: Zhongrong Niu, Changzheng Cheng, Zongjun Hu, Jianqiao Ye. Boundary element analysis of the stress intensity factors for the v-notched structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(6): 849-857.

## Boundary element analysis of the stress intensity factors for the v-notched structures

• 摘要: 将V形切口结构分成围绕切口尖端的小扇形和剩余结构两部分. 尖端处扇形域应力场表示成关于尖端距离\rho的渐近级数展开式，从线弹性理论方程推导出了一组分析平面V形切口奇异性的常微分方程特征值问题，通过求解特征方程，得到前若干个奇性指数和相应的特征向量. 再将切口尖端的位移和应力表示为有限个奇性阶和特征向量的组合. 然后用边界元法分析挖去小扇形后的剩余结构. 将位移和应力的线性组合与边界积分方程联立，求解获得切口根部区域的应力场、应力幅值系数和整体结构的位移和应力. 从而准确计算出平面V形切口的奇异应力场和应力强度因子.

Abstract: In this paper a new way is proposed to determine thegeneralized stress intensity factors of the plane V-notch structures byboundary element method. Firstly, a small sector around the V-notch tip isdug out from the V-notch structure. Based on the assumption of an asymptoticstress field in the V-notch tip region, evaluation of stress singularitiesof the sector zone are transformed into an eigenvalue problem of theordinary differential equations. Then the solutions of the eigenvalueproblem provide the singularity orders and associated eigenvectors of theV-notch. Hence the displacements and tractions on the arc of the abovesector are expressed as the linear combination of the finite terms of theseries expansion with different singular orders. Secondly, the boundaryelement method is used to model the V-notch structure removed the smallsector, in which the boundary conditions along the arc edge from cutting thesector are expressed by the above linear combination. Consequently, thegeneralized stress intensity factors and the stress field of the V-notchedstructure are obtained through the boundary element analysis. Finally, twonumerical examples are given to show the effectiveness of the presentmethod.

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