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

发布时间：2018-03-31 21:45

本文选题：正交异性复合材料板　切入点：共线双半无限裂纹　出处：《应用力学学报》2016年01期

【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。
[Abstract]:By using the generalized complex function method, the plane elasticity problem of orthotropic composite plates with collinear double semi-infinite cracks is studied by constructing appropriate generalized conformal mapping. The analytical solution of the stress field and the stress intensity factor at the tip of two cracks under uniform in-plane loading on some crack surfaces is obtained. The results show that the magnitude of the stress field is not only related to the geometric configuration and external load of the material, but also to the stress intensity factor at the tip of the two cracks. It is also related to the elastic constant of the material, which is a distinct feature of orthotropic composites different from isotropic materials, and the magnitude of the stress intensity factor at the tip of the two cracks is only related to the geometric configuration and external loads of the materials. When the distance between the tip of two cracks tends to infinity, the analytical solution can be reduced to the solution of semi-infinite crack in orthotropic composite plate. The validity of the analytical solution in this paper is verified, and the influence of the loading length on the crack surface, the distance between the two crack tips on the stress intensity factor and the interaction between the two cracks are analyzed by numerical examples.
【作者单位】：内蒙古民族大学数学学院;内蒙古师范大学数学科学学院;
【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)
【分类号】：O346.1

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