三维间断位移法及强奇异和超奇异积分的处理方法  

THREE-DIMENSIONAL DISCONTINUOUS DISPLACEMENTMETHOD AND THE STRONGLY SINGULAR ANDHYPERSINGULAR INTEGRALS

作　　者：周维垣[1] 吴劲松[1] 肖洪天[2] 

机构地区：[1]清华大学水利水电工程系,北京100084 [2]山东科技大学工程力学系,泰安271019

出　　处：《力学学报》2002年第4期645-651,共7页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：从积分方程Somigliana等式出发,导出三维状态下单位位错集度的基本解.在此基础上,建立了边界积分方程,并给出了其离散形式.对强奇异和超奇异积分,采用了Hadamard定义的有限部分积分来处理.最后,给出了计算裂纹应力强度因子的算例,并与解析解进行了比较,证实了该方法的有效性.Based on Somigliana's identity of integral equations, the fundamental solutions of unit dislocation intensity are obtained. Using the solutions, boundary integral equations and the BEM are presented. In dealing with strongly singular and hypersingular integrals, the methods of finite part integrals by Hadamard are employed. For evaluating stress intensity factors, the relationship of stress intensity factors and discontinuous displacements is presented. The SIF values of penny-shaped and elliptical cracks in infinite domains are evaluated by using the present method. The numerical results show that the present method is effective and can be used to exactly calculate the crack problems in an infinite domain. The present method may be coupled with the traditional displacement boundary integral equations for analysis of crack problems in finite domains.

关 键 词：处理方法 三维间断位移法 强奇异积分 超奇异积分 裂纹 应力强度因子 

分 类 号：O346.1[理学—固体力学]