工程计算力学中的正交基无网格方法  

Meshless method based on orthogonal basis for engineering computational mechanics

作　　者：苗雨[1] 蒋和洋[2] 王元汉[1] 

机构地区：[1]华中科技大学土木工程与力学学院,湖北武汉430074 [2]北京工业大学建筑工程学院,北京100022

出　　处：《岩土力学》2004年第z2期126-129,共4页Rock and Soil Mechanics

基　　金：北京市自然科学基金资助项目(No.3033012);中国科学院岩土力学重点实验室资助项目(No.Z110202)。

摘　　要：发现并研究了无网格伽辽金法(EFGM)节点不良分布以及采用一般高次多项式基构造形函数时产生数值解振荡的问题。提出工程计算力学的正交基无网格伽辽金法(MLMBOB),并以罚函数法引入强加边界条件,离散化得到偏微分方程的数值解。该方法保留了无网格伽辽金法所拥有的优秀品质,去除了其中的一些缺陷,使得用高次正交基作逼近时有高计算精度,它适合于工程计算中诸多计算问题。并用算例及其误差分析证实了该方法的优越性。The oscillation problems of numerical solution in elemeat-free Galerkin morhod element-free GalerRin method are discovered and researched by using high order polynomial basis. Meshless method based on orthogonal basis (MLMBOB) is presented,in which the penalty function method is applied to the essential boundary conditions. Then the numerical solution of the PDES is got by discretization. This method holds nearly all qualities of EFGM and removes many drawbacks of it. The method has high accuracy by using high order orthogonal basis. It is fit for many problems in engineering computational mechanics. Examples and error analysis are carried out to prove the excellent features of the present method.

关 键 词：无网格 正交基 数值振荡 罚函数法 误差分析 

分 类 号：TB115[理学—数学]