“分区”与“契合”思想求解半空间含凸起地形对SH波散射问题的研究进展  

Research Progress of“Partition”and“Conjunction”Ideas in Solving the Scattering of SH Waves by Hill in Half Space

作　　者：屈恩相 齐辉[2] 郭晶[2] 杨杰[3] 郑易 Qu Enxiang;Qi Hui;Guo Jing;Yang Jie;Zheng Yi(School of Architecture and Civil Engineering,Qiqihar University,Qiqihar,Heilongjiang 161006,China;School of Aerospace and Civil Engineering,Harbin Engineering University,Harbin,Heilongjiang 150001,China;School of Mechanical Engineering,Shanghai Dianji University,Shanghai 201306,China)

机构地区：[1]齐齐哈尔大学建筑与土木工程学院,黑龙江齐齐哈尔161006 [2]哈尔滨工程大学航天与建筑工程学院,黑龙江哈尔滨150001 [3]上海电机学院机械学院,上海201306

出　　处：《黑龙江工业学院学报（综合版）》2022年第4期74-82,共9页Journal of Heilongjiang University of Technology(Comprehensive Edition)

基　　金：国家自然科学青年基金项目(项目编号:12002198);齐齐哈尔大学教育科学研究项目(项目编号:GJQTYB202118)。

摘　　要：地震波中的横波SH波对含凸起地形的散射问题一直都是地震工程学研究的热点课题之一,解析法求解含凸起地形问题时要比凹陷地形问题困难很多。波函数展开法、复变函数法、多极坐标法等常常被用来研究SH波对有凸起地形的散射问题。“分区”思想是将求解的理论模型分成若干个区域,然后构造若干个区域所满足各自的辅助问题。“契合”思想是将分成的若干区域在公共边界上进行“契合”,满足公共边界的位移和应力连续的条件,然后建立该问题的无穷代数方程组并截取有限项给出算例和讨论数值结果。“分区”与“契合”技术的应用使得求解含凸起地形的复杂问题变得更为简单。The scattering of SH waves by a hill in seismic waves is always one of the hot topics in seismic engineering.It is more difficult to solve the problem by analytic method than by using a concave topography.The wave function expansion method,the complex function method and the multipolar coordinate method are often used to study the scattering of SH waves on hill.The"partition"technique is to divide the solved theoretical model into several regions and then constructs several regions that satisfy the respective ancillary problems.The idea of“conjunction”is the“conjunction”of the multi-divided regions on the common boundary,which satisfies the condition of continuous displacement and stress on the common boundary,then the infinite algebraic equations of the problem are established and the finite terms are truncated to give numerical examples and discuss the numerical results.The application of“partition”and“conjunction”technology makes it easier to solve complex problems with hill,and effectively promotes the development of seismic engineering.

关 键 词：SH波 凸起地形 分区 契合 

分 类 号：TU435[建筑科学—岩土工程]