数值流形方法接触检索算法的改进  

An improvement of contact detection algorithm of numerical manifold method

作　　者：刘泉声[1,2] 何军[1,2] 吴月秀[1,2] 

机构地区：[1]武汉大学土木建筑工程学院,湖北武汉430072 [2]武汉大学岩土与结构工程安全湖北省重点实验室,湖北武汉430072

出　　处：《岩石力学与工程学报》2016年第1期40-49,共10页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家重点基础研究发展计划(973)项目(2014CB046904);国家自然科学基金重点项目(41130742);湖北省自然科学基金重点项目(2011CDA119)~~

摘　　要：数值流形方法(NMM)的接触理论是其一大特色,然而也是NMM在计算中耗时最多的计算部分,有必要提高NMM接触算法的效率。首先介绍NMM的覆盖系统和接触判断方法,着重分析NMM接触检索算法的效率及其所存在的缺陷。然后,根据NMM接触判断方法特点,定义接触阈值、接触线段以及每个接触线段的接触覆盖区,并提出求接触覆盖区x轴极值和y轴极值的方法。最后基于DESS(double-ended spatial sorting)接触检索算法对所求得的接触覆盖区极值进行空间排序,建立了新的NMM接触检索算法。改进后的接触检索算法,可以直接判断出具体的接触点–边对,以及具体的接触形式(角角接触或角边接触),且提升NMM接触检索算法的效率。The contact theory of numerical manifold method（NMM） is not only an important attribute of NMM but also the most time consuming part of NMM algorithm. Thus,it′s necessary to improve the efficiency of contact algorithm of NMM. Cover system and contact judgment method of NMM are introduced first in this paper. The efficiency of contact detection algorithm of NMM and its defects are analyzed in detail as well. After that,contact threshold as well as contact segments and the corresponding contact zones is defined based on the characteristic of contact algorithm. And the extremums of x and y coordinates of the contact zones are calculated. Then,spatial sorting is carried out by referring to double-ended spatial sorting（DESS） algorithm and the new contact detection algorithm of NMM is proposed. The new contact detection algorithm can detect the specific contact pair（vertexedge or vertex-angle） thus have higher efficiency compared with the original contact detection algorithm in NMM.

关 键 词：数值分析 数值流形方法 接触检索 空间排序 效率提升 

分 类 号：O242[理学—计算数学]