双材料平面中曲线裂纹问题的超奇异积分方程  

HYPER-SINGULAR INTEGRAL EQUATIONS FOR CURVE CRACK IN BI-MATERIAL PLANE

作　　者：杜云海[1] 徐轶洋[1] 刘雯雯[1] 

机构地区：[1]郑州大学力学与工程科学学院,郑州450001

出　　处：《机械强度》2014年第3期445-448,共4页Journal of Mechanical Strength

基　　金：河南省教育厅自然科学基金项目(2009B130004)~~

摘　　要：基于超奇异积分方程法的基本原理,导出了双材料平面中一般曲线裂纹问题以裂纹岸位移间断为基本未知量的超奇异积分方程组,其奇异积分含一类二阶超奇异积分和一类反映裂纹曲率影响的高斯型奇异积分,正常积分项中也含一类可用幂级数表达的曲率影响项。所得结果使超奇异积分方程法对双材料平面中一般曲线裂纹问题的描述更具一般性。该方程组在曲率半径趋于无穷大和取为定值情况下的退化结果也与关于直线裂纹和圆弧裂纹的已有结果有很好的一致性。针对圆弧裂纹的算例表明,所得方程组适用于曲线裂纹问题的数值计算。Based on the basic principles of the hyper-singular integral equation method, the hyper-singular integral equations on the curve crack in bi-material plane were derived, with the crack shore displacement discontinuity being the basic unknown. These singular integrals contained a class of second-order hyper-singular integrals, and Gauss singular integrals, which reflected the influence of crack curvature. The normal integrals also contained a class of items which were affected by the curvature and expressed as power series. The result enabled hyper-singular integral equation method to be more suitable for description of the general crack in bi-material plane. When the curvature radius was taken the value of infinity or constant, the corresponding results were in good agreement with existed result on the straight crack or are crack. The numerical examples show that the derived result is suitable for the numerical calculation for curve cracks.

关 键 词：曲线裂纹 双材料 超奇异积分方程 

分 类 号：O241.83[理学—计算数学] O175.5[理学—数学]