反平面弹性力学反问题的自守函数法
Method of automorphic functions for an inverse problem of antiplane elasticity
摘要：
研究了多连通区域反平面弹性力学的非线性反问题。当周围无限体在无穷远处受反平面均匀剪切时，需要确定$n$均匀应力夹杂的轮廓。本文采用多连通圆形区域的共形映射方法。通过求解分段解析对称自守函数的两个Riemann-Hilbert问题，得到了保角映射。对于与第一类Schottky群相关联的域，发现了一个（$3n-4$）参数族共形映射的级数形式表示，从而解决了这个问题。两个和三个均匀应力夹杂的数值结果的报告和讨论。
英文摘要：
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane uniform shear at infinity. A method of conformal mappings of circular multiply connected domains is employed. The conformal map is recovered by solving consequently two Riemann-Hilbert problems for piecewise analytic symmetric automorphic functions. For domains associated with the first class Schottky groups a series-form representation of a ($3n-4$) parametric family of conformal maps solving the problem is discovered. Numerical results for two and three uniformly stressed inclusions are reported and discussed.
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