薄板屈曲分析的局部Petrov-Galerkin方法  

LOCAL PETROV-GALERKIN METHOD FOR BUCKLING ANALYSIS OF A THIN PLATE

作　　者：熊渊博[1] 龙述尧[1] 胡德安[1] 

机构地区：[1]湖南大学工程力学系,湖南长沙410082

出　　处：《工程力学》2006年第1期23-27,共5页Engineering Mechanics

基　　金：国家自然科学基金(10372030);湖南省自然科学基金(02JJY4071)资助项目

摘　　要：利用薄板控制微分方程的等效积分对称弱形式和对变量(挠度)采用移动最小二乘近似函数进行插值,研究了无网格局部Petrov-Galerkin方法在薄板屈曲问题中的应用。它不需要任何形式的网格划分,所有的积分都在规则形状的子域及其边界上进行,并用罚因子法施加本质边界条件。数值算例表明,无网格局部Petrov-Galerkin法不但能够求解弹性静力学问题,而且在求解弹性稳定性问题时仍具有收敛快,稳定性好,精度高的特点。Meshless local Petrov-Galerkin （MLPG） method is extended to solve buckling problems of a thin plate. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a local symmetric weak form. The present method is a truly meshless one as it does not need any meshgrids, and all integrals can be easily evaluated over regularly shaped domains （in general, spheres in the three-dimensional problem） and their boundaries. The essential boundary conditions are enforced by a penalty method. Several examples are given to show that in solving buckling problems, the meshless local Petrov-Galerkin method still possesses some advantages such as good stability, high accuracy and high rate of convergence, just as in solving elastic static problems.

关 键 词：薄板 屈曲 无网格局部PETROV-GALERKIN方法 移动最小二乘近似 特征值 

分 类 号：O34[理学—固体力学]