三维无限接合体双材料多界面裂纹的超奇异微积分方程法  

Analysis of Multiple Interfacial Cracks in Three Dimensional Bimaterials Using Hypersingular Integral-Differential Equation Method

作　　者：徐春晖[1] 秦太验[1] 袁丽[1] 野田尚昭[2] 

机构地区：[1]中国农业大学理学院,北京100083 [2]九州工业大学工学部,日本北九州市804-8550

出　　处：《应用数学和力学》2009年第3期282-290,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10872213)

摘　　要：利用有限部积分的概念,导出了三维无限接合体中多个界面裂纹,在任意载荷作用下的超奇异微积分方程组.数值分析中,未知的位移间断采用基本分布函数和多项式乘积的形式来近似,其中基本分布函数是根据界面裂纹应力的振荡奇异性来选取的.作为典型算例,研究了存在两个矩形界面裂纹时,裂纹之间距离、裂纹形状及双材料弹性常数对应力强度因子的影响.计算表明,应力强度因子随裂纹间的距离的增大而减小.Using the finite-part integral concepts, a set of hypersingular integral-differential equations for multiple interfacial cracks in a three-dimensional infinite bimaterial subjected to arbitrary loads was derived. In the numerical analysis, unknown displacement discontinuities were approximated by the products of the fundamental density functions and power series, where the fundamental functions were chosen to express a two-dimensional interface crack exactly. As illustrative examples, the stress intensity factors for two rectangular interface cracks were calculated for various spacing, crack shape and elastic constants. It is shown that the stress intensity factors decrease with the increasing of crack spacing.

关 键 词：应力强度因子 奇异积分方程 界面裂纹 有限部积分 边界元法 

分 类 号：O346.1[理学—固体力学]