无网格局部Petrov-Galerkin方法的改进及其应用  

On the Improvements and Applications of the Meshless Local Petrov-Galerkin Method

作　　者：姜勇[1] 于宁[1] 李武[2] 

机构地区：[1]同济大学地下建筑与工程系 [2]安徽理工大学土木工程系,安徽淮南232001

出　　处：《同济大学学报（自然科学版）》2006年第5期603-606,共4页Journal of Tongji University:Natural Science

摘　　要：重新审视、研究了无网格局部Petrov-Galerkin方法,在肯定方法优点的同时,指出了它的不足之处,并有针对性地提出了采用蒙特卡罗方法进行数值积分的改进方案.无网格局部Petrov-Galerkin方法的缺点在于刚度矩阵及荷载项的数值积分虽不需要在全局背景网格下进行,却需要在局部支撑域布置更为细致的网格.本文的改进方案摒弃了高斯数值积分,采用不需要背景网格的蒙特卡罗随机积分法.Efforts are made to study the Meshless Local Petrov-Galerkin （MLPG） method in a new viewpoint, pointing out its advantages and disadvantages, and putting forward the Monte-Carlo method to perform the numerical integration. The disadvantage lies in the fact that numerical integration is performed under finer meshes of the support region, that is, integration meshes are still neces- sary. The new method adopts the Monte Carlo method which doesn＇t need background meshes.

关 键 词：无网格Petrov—Galerkin方法 局部对称弱形式 蒙特卡罗方法 数值积分 完全无网格方法 

分 类 号：TU457[建筑科学—岩土工程]