含曲线裂纹的各向异性板断裂问题  

Fracture Problem in Anisotropic Composite Plate Including Curve Crack

作　　者：程海霞[1] 李俊林[1] 

机构地区：[1]太原科技大学应用科学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2012年第5期503-508,529,共7页Journal of North University of China(Natural Science Edition)

基　　金：山西省自然科学基金资助项目(2011011021-3)

摘　　要：对各向异性板中抛物线裂纹的断裂问题进行了研究.根据各向异性板的有关理论,设出了应力函数的复变函数表达式.运用保角映射方法和待定系数法,通过构造恰当的保角映射函数,把带有抛物线几何形状裂纹的物理平面映射为带有单位圆的无限域.在该无限域上借助应力边界条件把复合材料断裂问题转化为一类求解方程边值问题,推导出了应力函数的表达式.得到了无穷远处受斜对称载荷时抛物线曲线裂纹尖端附近的应力强度因子、应力场和位移场的解析解.The expression of stress function was set up according to the relevant theory of the anisotropic plate,as well as after research of fracture problems about anisotropic composite plate of parabolic crack.Using the conformal mapping method and method of undetermined coefficients,the physical plane with complex geometric crack shapes was mapped into the infinite domain with a unit circle by the appropriate conformal mapping function.Based on the stress boundary conditions,the problems of fracture in composite materials were transformed into the solving boundary value problems of equations and the expression of stress function was determined in the infinite domain.The expressions for stress field and the stress intensity factor are obtained near the parabolic crack tip as well.

关 键 词：保角映射 各向异性板 曲线裂纹 断裂分析 应力强度因子 

分 类 号：O346.1[理学—固体力学]