双材平面中环形界面环向裂纹问题的超奇异积分方程方法  

HYPERSINGULAR INTEGRAL EQUATION METHOD FOR A CIRCULAR CRACK IN A BIMATERIAL PLANE WITH A CIRCULAR INTERFACE

作　　者：杜云海[1] 吕存景[1] 董栋[1] 柯献辉[1] 

机构地区：[1]郑州大学工程力学系,郑州450001

出　　处：《机械强度》2006年第5期733-738,共6页Journal of Mechanical Strength

摘　　要：从研究环形界面双相材料平面任点处沿径向、环向作用单位力时的弹性力学基本解出发,利用Betti定律、几何关系和虎克定律得到双材料平面环向裂纹问题的位移场和应力场表达式,经代入裂纹岸应力边界条件,导出极坐标下以裂纹岸位移间断为基本未知量的超奇异积分方程组;通过适当的积分变换,用有限部积分原理处理方程组中所包含的两类奇异积分—Cauchy奇异积分和超奇异积分,解决极坐标下环形界面双材料平面环向裂纹问题用超奇异积分方程法的理论描述与数值算法。在嵌入物半径足够大时,计算结果与已发表文献对直线界面情况下平行于界面裂纹问题的计算结果一致。According to the study for the fundamental solution of elasticity on a bi-material plane with the circular interface subjected to the radial and circular unit concentrated forces, the stresses and displacements of the problem about the circular crack are derived by use of Betti＇ s reciprocal theorem, geometric relationship and Hooker＇ s law. Considering the stress boundary conditions of the problem, the equations to describe this crack problem are derived, in which the unknown functions are the displacement discontinuities on the crack surface. Cauchy singular integral and hypersingular integrals contained in the equations are calculated by the finite-port integral principles, then a numerical method is first established to solve the problem of a circular crack contained in the bi-material plane with circular interface in the polar coordinate. Finally, the non-dimensional stress intensity factors of the crack under the uniform pressure are calculated for various parameters, such as the crack position c, the radius r0 of interface, and so on. When r0 is sufficiently large, the calculated results by the present method are consistent with those published in literature for the line crack parallel to the interface.

关 键 词：双相材料 极坐标 环向裂纹 超奇异积分方程 应力强度因子 

分 类 号：O346.1[理学—固体力学] O241.83[理学—力学]