各向异性板稳定性分析的局部Petrov-Galerkin方法  

A local Petrov-Galerkin (MLPG) method for the stability analysis of anisotropic thin plate

作　　者：熊渊博[1] 龙述尧[1] 

机构地区：[1]湖南大学工程力学系,湖南长沙410082

出　　处：《暨南大学学报（自然科学与医学版）》2005年第1期74-76,共3页Journal of Jinan University(Natural Science & Medicine Edition)

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：　基于Kircihhoff板理论和对挠度函数采用移动最小二乘近似函数进行插值,进一步研究无网格局部Petrov-Galerkin(MLPG)方法在各向异性板稳定问题中的应用.分析中,本质边界条件采用罚因子法施加,离散的特征值方程由板稳定控制方程的局部积分对称弱形式中得到.通过各向同性板和对称角铺设层合板的数值算例并与其他方法的结果进行比较,表明MLPG法求解各向异性板稳定问题具有收敛性好、精度高等一系列优点.Using the moving least-square (MLS) approximation to interpolate solution variables and Kircihhoff's plate theory, the meshless local Petrov-Galerkin(MLPG) method is extended to solve the stability problems of anisotropic plates. In the analysis, the essential boundary conditions are enforced by a penalty method. The discrete eigenvalue problem is derived using the local integral symmetric weak form of the governing equation of the stability problem. Several examples, isotropic and symmetrically laminated composite plates, are given and compared with results via other methods to show that, the MLPG method has a number of advantages such as the quite good accuracy and high rate of convergence.

关 键 词：各向异性板 局部Petmv-Galerkin方法 等效积分弱形式 移动最小二乘近似 

分 类 号：O343.6[理学—固体力学]