基于球面波势函数基本解方法的弹性波三维散射与动应力求解  

Method of fundamental solution based on complete spherical wave potential solutions to 3-D elastic wave scattering and dynamic stress

作　　者：刘中宪[1,2] 王治坤 梁建文 王楚楚[1] LIU Zhong-xian;WANG Zhi-kun;LIANG Jian-wen;WANG Chu-chu(Tianjin Key Laboratory of Civil Structure Protection and Reinforcing, Tianjin Chengjian University, Tianjin 300384, China;Tianjin Institute of Earthquake Engineering, Tianjin 300384, China;Department of Civil Engineering, Tianjin University, Tianjin 300072, China)

机构地区：[1]天津城建大学天津市土木建筑结构防护与加固重点实验室,天津300384 [2]天津市地震工程研究所,天津300384 [3]天津大学土木工程系,天津300072

出　　处：《岩土力学》2019年第7期2730-2738,共9页Rock and Soil Mechanics

基　　金：国家自然科学基金项目(No.51678390);天津市自然科学基金重点项目(No.18JCZDJC39200);天津市科技支撑计划项目(No.17YFZCSF01140)~~

摘　　要：针对弹性波三维散射和动应力集中问题,提出一种基于球面波势函数的基本解方法(SWP-MFS)。方法基于单层位势理论,采用膨胀波和矢量剪切波球面波势函数构造散射波场,根据边界条件建立边界积分方程并配点求解。精度检验表明,该方法具有良好的数值精度及稳定性。以无限空间中三维夹杂体及空洞对平面P、SV波的散射为例,进行方法展示,并揭示了三维夹杂体周围弹性波散射的一些重要规律。结果表明:三维夹杂体随其内部介质刚度降低,位移谱曲线震荡越加强烈。三维球形空洞在P波和SV波水平入射下应力集中规律不同,前者在顶部和底部及附近更明显,后者在纵截面两45°角线附近更明显。与以往的集中力源函数相比,新的波场构造基本解更为简洁易用,为三维弹性波动分析提供了一种新型无网格数值方法。A new method of fundamental solution based on complete spherical wave potential(SWP-MFS) is proposed to solve 3-D elastic-wave scattering and dynamic stress concentration. The method established the boundary integral equation according to the boundary condition. The solution was solved by placing the spherical wave sources of compressional wave and shear wave on a virtual boundary based on the single layer potential theory. Through comparing with other available results, the excellent numerical accuracy and stability of the SWP-MFS are validated. The method was demonstrated in an example of the 3-D scattering of P or SV waves around an inclusion and a cavity in elastic full-space. Several important conclusions about scattering of 3-D elastic waves around an inclusion were obtained. As the modulus ratio decreases(the inclusion becomes softer), the displacement amplitude spectrums oscillate more rapidly with large amplitude. For horizontal incident P waves, it seems that the dynamic stress concentration effect is more pronounced near the top and bottom of the spherical cavity, while it is more obvious near the two 45-degree angles of the longitudinal section for horizontal incident SV waves. Compared with employing the Green’s functions of concentrated force, the fundamental solution of SWP-MFS is more concise and easy to use, and provides a new meshless boundary-type method for elastic waves analysis.

关 键 词：基本解方法 球面波势函数 三维弹性波散射 动应力集中 

分 类 号：P315.3[天文地球—地震学]