SH波入射时半圆形凸起地形附近浅埋圆形衬砌结构的动应力分析

本文给出了地下圆形衬砌结构与地面上的半圆形凸起地形对垂直于地面入射的SH波散射问题的解答。方法是将求解区域分割成两部分。其一为包含半圆形凸起地形在内的圆形区域Ⅰ，其二为带有一个半圆形凹陷和一个圆形衬砌结构的弹性半空间Ⅱ，半圆形凹陷部分为其公共边界，在区域Ⅰ和Ⅱ中分别构造其位移解，然后再通过移动坐标，使其满足“公共边界”上的条件和地下衬砌的边界条件，建立起求解该问题的无穷代数方程组。最后，本文给出了算例，并讨论了数值结果，给出了圆形衬砌结构周边上的动应力集中系数变化规律。

Dynamic analysis of the scattering of SH-wave by a semi-cylindrical hill above a shallow-embedded cylindrical lining structure in half space

This paper presents a solution to the scattering of SH-wave by a semi-cylindrical hill above a shallow-embedded cylindrical lining structure in half-space by using the methods of complex function and multi-polar coordinate.To solve the problem, the domain of solution is divided into two, the first one is a circulardomain, which includes the boundary of the hill, and all of the rest is considered as the second one.First of all a solution is constructed in the circulardomain, which satisfies the condition that stress is zero at the hill edge and arbitrary at other part. In the second domain three kinds of scattering wave functionsare constructed: one existsin the medium, which satisfies the condition of stress free at the horizontal surface; the other two exist in the lining structure. Then, by using moving coordinate method, the two solutions on the junction interface are conjoined. To satisfythe boundary conditions around the lining structure, the problem to be solved can be reduced to a set of infinite linear algebraic equations. Finally, computationalexamples are provided and discussed.