正交各向异性复合材料板Ⅱ型三裂纹尖端应力场分析

摘要

This paper mainly studies the plane problems of the three crack of orthotropic compos-ite plate.By fracture mechanics model,plane fracture problems of composite materials can be converted to a class of boundary value problems of partial differential equation.By introducing the appropriate conformal mapping,mapping will be evenly distributed crack for parallel cycle on the complex plane crack.By introducing the westergaard stress function and using the complex variable function method and the method of undetermined coefficients,the analytical expressions of stress field and displacement field can be obtained.The results of the study can provide a meaningful reference for the strength design of structure and material.%研究了正交各向异性复合材料板三裂纹平面问题。通过复合材料断裂中的力学模型，将复合材料平面断裂问题转化为一类偏微分方程的边值问题；引入合适的保角映射，将均匀分布的三裂纹映射为复平面上的平行周期裂纹；通过引入合适的 westergaard应力函数，采用复变函数法和待定系数法得到了应力场和位移场的解析表达式。研究结果为结构和材料的强度设计提供了参考。