A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional pro...A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional problems is proposed.The exact formula for the hypersingular integral over the non-con- forming crack tip element is given next.By virtue of Green's-function-library strategy,a series of stress in- tensity factors(SIF)of different crack orientations,locations and/or sizes in a complicated structure can be obtained easily and efficiently.Finally,several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed.展开更多
构造了一种适合边界元分析裂纹问题的三角形单元,该单元中的形函数包含两部分,主要部分用于捕捉裂纹尖端上位移分布的陡峭特性(性质),另一部分为常规的拟合函数,体现裂纹尖端位置附近的物理量在其他方向上的连续分布。形函数主要部分的...构造了一种适合边界元分析裂纹问题的三角形单元,该单元中的形函数包含两部分,主要部分用于捕捉裂纹尖端上位移分布的陡峭特性(性质),另一部分为常规的拟合函数,体现裂纹尖端位置附近的物理量在其他方向上的连续分布。形函数主要部分的构造充分利用了已有理论研究获得的结论,在裂纹表面,随着距离远离尖端,位移分布与 r 函数保持同阶变化。在传统形函数的基础上,通过先乘以一项同阶于 r 的变量项,再在系数中将其在形函数所在点上的值除去,便得到新型的用于拟合裂纹尖端附近位移和面力分布的形函数。新的形函数能够满足形函数的delta性质,但归一性不再满足,因此,新的形函数只用于物理量的拟合,而几何量的拟合依然采用传统方案。通过对偶边界元方法计算裂纹尖端的张开位移后,利用一种位移外插方法计算获得应力强度因子。数值算例关注了一种无限域内的圆盘裂纹,应用新构造的三角形单元于对偶边界元中计算结构在受到斜拉力时裂纹尖端的三种应力强度因子。通过与参考解进行对比,验证了该插值方案用于对偶边界元分析裂纹问题时的正确性和高精度。展开更多
Because exact analytic solution is not available, we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. T...Because exact analytic solution is not available, we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. The integral equations by this procedure are reduced to infinite algebraic equations. The accuracy of the solution lies in the boundary collocation technique. The application of which for some complicated initialboundary value problems in solid mechanics indicates the method is powerful.展开更多
基金the Aeronautical Science Foundation of China (No.99C53026).
文摘A new type of dual boundary integral equations(DBIE)is presented first,through which,a smaller system of equations needs to be solved in fracture analysis.Then a non-conforming crack tip element in two-dimensional problems is proposed.The exact formula for the hypersingular integral over the non-con- forming crack tip element is given next.By virtue of Green's-function-library strategy,a series of stress in- tensity factors(SIF)of different crack orientations,locations and/or sizes in a complicated structure can be obtained easily and efficiently.Finally,several examples of fracture analysis in two dimensions are given to demonstrate the accuracy and efficiency of the method proposed.
文摘构造了一种适合边界元分析裂纹问题的三角形单元,该单元中的形函数包含两部分,主要部分用于捕捉裂纹尖端上位移分布的陡峭特性(性质),另一部分为常规的拟合函数,体现裂纹尖端位置附近的物理量在其他方向上的连续分布。形函数主要部分的构造充分利用了已有理论研究获得的结论,在裂纹表面,随着距离远离尖端,位移分布与 r 函数保持同阶变化。在传统形函数的基础上,通过先乘以一项同阶于 r 的变量项,再在系数中将其在形函数所在点上的值除去,便得到新型的用于拟合裂纹尖端附近位移和面力分布的形函数。新的形函数能够满足形函数的delta性质,但归一性不再满足,因此,新的形函数只用于物理量的拟合,而几何量的拟合依然采用传统方案。通过对偶边界元方法计算裂纹尖端的张开位移后,利用一种位移外插方法计算获得应力强度因子。数值算例关注了一种无限域内的圆盘裂纹,应用新构造的三角形单元于对偶边界元中计算结构在受到斜拉力时裂纹尖端的三种应力强度因子。通过与参考解进行对比,验证了该插值方案用于对偶边界元分析裂纹问题时的正确性和高精度。
基金Project supported by the National Natural Science Foundation of China(No.K19672007)
文摘Because exact analytic solution is not available, we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics. The integral equations by this procedure are reduced to infinite algebraic equations. The accuracy of the solution lies in the boundary collocation technique. The application of which for some complicated initialboundary value problems in solid mechanics indicates the method is powerful.
