含任意裂纹功能梯度材料板的奇异积分方程及其数值解  

Singular Integral Equation and Its Numerical Solution of Infinite FGMs Plane with Arbitrarily Cracks

作　　者：张建勇[1] 马会礼[1] 

机构地区：[1]河海大学常州校区数理教学部,江苏常州213022

出　　处：《河海大学常州分校学报》2007年第2期16-20,共5页Journal of Hohai University Changzhou

基　　金：河海大学常州校区青年科研基金资助项目(06B004-10)

摘　　要：应用平面弹性复变方法,将求解无限各向异性功能梯度材料板中含任意斜裂纹的问题归结为求解一组解析函数的边值问题.通过构造适当的积分变换将边值问题转化为奇异积分方程,进而应用Lobatto-Chebyshev数值求积公式,求出该奇异积分方程的数值解,得到了应力强度因子的近似表达式.结合算例的数值计算结果,分析了裂纹倾角、材料弹性模量、外应力等因素对应力强度因子的影响.The problem of FGMs plane with arbitrarily straight cracks is studied by using the plane elastic complex variable method, and is reduced to solving the boundary value problems for the analytic function. By constructing appropriate integral transformations, the boundary value problems are transformed into singular integral equations. Utilizing Lobatto-Chebyshev quadrature formulas, the singular integral equations are solved numerically. Furthermore, the approximate analytical expressions of stress intensity factors are obtained. At the end, a numerical example is given and the effects of angles, elastic modulusand stress on the SIFs are analyzed.

关 键 词：功能梯度材料 裂纹 奇异积分方程 数值解 应力强度因子 边值问题 

分 类 号：O346.1[理学—固体力学]