不同复合材料界面问题的另一形式自相似解

Another type of self-similar solutions to interface problems concerning dissimilar composite materials

针对不同复合材料界面问题的另一形式自相似解进行研究,利用复变函数理论的方法推导出另一形式自相似解的表达式。根据正交异性体弹性动力学反平面问题运动方程和不同复合材料界面问题的相应关系,应用自相似函数的方法可以很容易地将所讨论的问题转化为Riemann-Hilbert问题,而后一问题可以用通常的Muskhel-ishvili方法求解,并且可以相当简单地得到问题的闭合解。这些解在断裂动力学以及弹性动力学、静力学问题当中具有重要的应用价值和理论意义。

Another type of self-similar solutions to interface problems concerning dissimilar composite materials were researched exclusively. A representation of self-similar solutions of other modality is deducted by the methods of the theory of complex functions. According to elastodynamics equation of motion of the anti-plane problem for an orthotropic anisotropic body and relevant relationship of interface problems on dissimilar composite materials, the problems considered can be very facilely transformed into Riemann-Hilbert problem by application of the approaches of self-similar functions which is resolved by Muskhelishvili＇s measure and their closed solutions are obtained rather straightforward. Those solutions have an important applied value and theoretical meaning in fracture dynamics, ealstodynamics as well as elastostatics.