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 引用本文: 肖洪天 岳中琦. 梯度材料中矩形裂纹的对偶边界元方法分析[J]. 力学学报, 2008, 40(6): 840-848.
Hongtian Xiao, Zhongqi Yue. Dual boundary element analysis of rectangular-shaped cracks in graded materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(6): 840-848.
 Citation: Hongtian Xiao, Zhongqi Yue. Dual boundary element analysis of rectangular-shaped cracks in graded materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(6): 840-848.

## Dual boundary element analysis of rectangular-shaped cracks in graded materials

• 摘要: 采用对偶边界元方法分析了梯度材料中的矩形裂纹. 该方法基于层状材料基本解，以非裂纹边界的位移和面力以及裂纹面的间断位移作为未知量. 位移边界积分方程的源点配置在非裂纹边界上，面力边界积分方程的源点配置在裂纹面上. 发展了边界积分方程中不同类型奇异积分的数值方法. 借助层状材料基本解，采用分层方法逼近梯度材料夹层沿厚度方向力学参数的变化. 与均匀介质中矩形裂纹的数值解对比，建议方法可以获得高精度的计算结果. 最后，分析了梯度材料中均匀张应力作用下矩形裂纹的应力强度因子，讨论了梯度材料非均匀参数、夹层厚度和裂纹与夹层之间相对位置对应力强度因子的影响.

Abstract: This paper analyzes the rectangular-shaped crack in the graded materials byusing the dual boundary element method. The method is based on thefundamental solutions for multilayered solids and uses a pair of boundaryintegral equations, namely, the displacement and traction boundary integralequations. The former is collocated exclusively on the uncracked boundary,and the latter on one side of the crack surface. The displacement and/ortraction are used as unknown variables on the uncracked boundary and therelative crack opening displacement (i.e., displacement discontinuity) istreated as an unknown quantity on the crack surface. The layered techniqueis used to analyze the variation of parameters of the graded interlayer.Numerical examples of stress intensity factors (SIFs) calculation are givenfor the rectangular-shaped crack parallel to the graded interlayer. Theresults show that the SIFs obtained with the present formulation are in verygood agreement with existing numerical results. The nonhomogeneous parameterand the distance of the crack from the interlayer exert an obvious influenceon the SIFs of the rectangular-shaped crack in the graded material.Furthermore, it may be shown that the proposed method can be used to analyzedifferent cracks subject to complex loads in graded materials and to modelthe non-homogeneous solids with multiple interacting cracks.

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