含共线双半无限裂纹的正交异性复合材料板平面弹性问题的解析解  

Analytical solutions for the plane elasticity problem of orthotropic composite plate with two semi-infinite collinear cracks

作　　者：高健[1] 刘官厅[2] 

机构地区：[1]内蒙古民族大学数学学院,通辽028043 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《应用力学学报》2016年第1期1-6,175,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11262017);内蒙古民族大学科学研究基金(NMDYB15001)

摘　　要：运用广义复变函数方法,通过构造适当的广义保角映射研究了含有共线双半无限裂纹的正交异性复合材料板的平面弹性问题,得出了部分裂纹面上受均匀面内载荷时应力场与两裂纹尖端处应力强度因子的解析解。结果表明:应力场的大小不仅与材料的几何构型及外载荷有关,还与材料的弹性常数有关,这是正交异性复合材料不同于各向同性材料的显著特征;两裂纹尖端处应力强度因子的大小只与材料的几何构型及外载荷有关;当两裂纹尖端的距离趋于无穷大时,所得到的解析解可退化为已有的正交异性复合材料板中半无限裂纹问题的解,通过将其与已有文献中的结果进行对比,验证了本文解析解的正确性。并通过数值算例分析了裂纹面上的受载长度、两裂纹尖端的距离对应力强度因子的影响规律以及两裂纹之间的相互作用。By using the generalized complex variable function method and constructing an appropriate generalized conformal mapping, the plane elasticity problem of two semi-infinite collinear cracks in orthotropic composite plate is investigated. The analytical solutions of the stress field and the stress intensity factors under the action of uniform in-plane load on partial crack surface are derived. It is shown that the stress field not only changes by the geometric configuration of the material and the external load, but also relates to the elastic constants of the material, which is the significant characteristic of the orthotropic composite materials different from the isotropic materials. Moreover, the stress intensity factors only change with the geometric configuration of the material and the external load. When the distance between the two crack tips tends to infinity, the present results can be reduced to the well-known solutions of the plane elasticity problem of orthotropic composite plate with a semi-infinite crack. Finally, numerical examples are given to analyze the influences of loaded crack length and the distance between the two crack tips on the stress intensity factors and the interactions between the two cracks.

关 键 词：正交异性复合材料板 共线双半无限裂纹 广义保角映射 应力场 应力强度因子 

分 类 号：O346.1[理学—固体力学]