正交异性体反平面问题另一形式自相似解的推导

正交异性体的反平面运动方程有几种表达方式，而以自相似解表达方式尤为简单。由于在弹性动力学问题的计算中可以获得解析解，使得考虑的问题相应地简化，并具有一定的普遍性，因此对自相似形式的解的推导具有重要的意义。本文针对这一问题进行研究，利用复变函数论的方法导出另一形式自相似解的一般表达式。应用该法可以很容易地将所讨论的问题转化为Riemann—Hilbert问题，而后一问题可以用同通常的Muskhelishvili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问题当中具有重要的应用价值。

Deduction of Self-similar Solutions in Other Form on Anti-plane Problem for an Orthotropic Anisotropic Body

The anti-plane equation of motion for an orthotropic anisotropic body has several expressive manners, moreover the presentations of self-similar solutions are particularly simple. Because the analytical solutions can be obtained in computations of elastodynamics problems, the considered problems become considerably simple and possess an evident generality, hence the deduction of self-similar solutions in other form has significance. Ageneral representation of self-similar solutions in other form was deduced by the methods of complex variables theory. Applying this method, it can be transformed into Riemann-Hil-bert problem. By using Muskhelishvili method, their closed solutions were obtained rather simple. Those solutions have an important applied value in fracture dynamics as well as elastodynamics problems.