三维断裂问题中的位移不连续方法  

Displacement Discontinuity Method in 3D Problems of Fracture Mechanics

作　　者：Zvyaguin AV Smirnov NN Luzhin AA Shamina AA Zvyaguin AV;Smirnov NN;Luzhin AA;Shamina AA(Moscow M.V.Lomonosov State University,Russia,Moscow,119992,Leninskie Gory 1;Federal Science Center Scientific Research Institute for System Analysis of the Russian Academy of Sciences,Russia,Moscow,117218,36-1 Nakhimovskiy pr.)

机构地区：[1]国立莫斯科罗蒙诺索夫大学,俄罗斯莫斯科119992 [2]俄罗斯科学院联邦科学中心系统分析科学研究所,俄罗斯莫斯科117218

出　　处：《湘潭大学学报（自然科学版）》2020年第4期69-93,共25页Journal of Xiangtan University(Natural Science Edition)

基　　金：俄罗斯基础研究基金项目(16-29-15076)。

摘　　要：该研究将位移不连续方法引入三维空间中对边界元数值方法进行改进,旨在有效地减少计算过程中三维空间单元数.该方法通过对裂缝表面进行基础单元划分来表征弹性介质的非连续特征,并有效地降低了计算规模.此外,该文还给出了一个基于双层位势的新基本解.与此同时,可认为该方法能有效地模拟水力裂缝扩展及其与天然断层之间的相互作用效应.The present paper suggests a modification of boundary elements numerical method,which uses displacement discontinuity method in 3D space.The current method can effectively decrease the computational elements number in 3D space because final elements are placed only on the surface of a fracture simulating the discontinuity of elastic medium.Thus the dimension of the problem is decreased.The new fundamental solutions were developed based on double layer potentials.The method proved to be effective for hydraulic fractures modeling and their interaction with natural faults in host rock formations.

关 键 词：三维空间 弹性介质 裂缝 边界单元法 位移不连续方法 

分 类 号：O174[理学—数学]