数值流形法局部网格加密算法  

Local Mesh Refinement Algorithm of Numerical Manifold Method

作　　者：伍书重 莫思阳 张友良 张亚军 WU Shu-zhong;MO Si-yang;ZHANG You-liang;ZHANG Ya-jun(School of Civil and Architectural Engineering,Hainan University,Haikou 570228,China)

机构地区：[1]海南大学土木建筑工程学院,海口570228

出　　处：《科学技术与工程》2021年第7期2850-2856,共7页Science Technology and Engineering

基　　金：海南省重大科技计划(ZDKJ201803);国家自然科学基金地区科学基金(51868017);国家重点基础研究发展计划(2014CB047100)。

摘　　要：数值流形方法中网格加密是提高精度的方法之一,全局加密会严重导致计算效率低下,因此需要研究在数值流形法中覆盖系统网格局部加密。提出了数值流形法一到四级局部网格加密,可以根据实际情况需求自主选择网格加密等级进行计算分析。在数值流形法覆盖系统生成的算法基础上,采用C++面向对象编程技术开发程序。最后绘制裂纹分析数值算例计算后的位移图。结果表明:按照一到四级加密顺序对需加密区进行网格加密后,应力强度因子(stress intensity factor, SIF)与解析解误差均在5%以内,且符合加密越精细、计算结果精度越高的规律。可见此局部加密算法有效。In the numerical manifold method,mesh refinement is one of the methods to improve the accuracy,and the global refinement will lead to low computational efficiency.Therefore,it is necessary to study the local mesh refinement of the covering system in the numerical manifold method.The numerical manifold method with one-to-four level of local mesh refinement was proposed then.It was used to select the mesh refinement level according to the actual situation.On the basis of numerical manifold method covering system generation algorithm,C++object-oriented programming technology was used to develop the program.Finally,the displacement plot of numerical examples of crack analysis was drawn.The following results are got from the research.According to the refined order of one-to-four level,the error rate between stress intensity factor(SIF)and analytical solution of SIF is less than 5%after the refining region is local mesh refined.The result is in line with the rule.The denser the refined mesh is,the more accurate the result is.It can be concluded that the local refinement algorithm is effective.

关 键 词：数值流形法 局部加密算法 数值模拟 裂纹分析 

分 类 号：TU441.4[建筑科学—岩土工程]