用局部Petrov-Galerkin法分析薄板自由振动  

An Analysis of Free Vibration Problem for a Thin Plate by Local Petrov-Galerkin Method

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：《力学季刊》2004年第4期577-582,共6页Chinese Quarterly of 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：利用薄板振型方程的等效积分弱形式和对振型函数采用移动最小二乘近似函数进行插值,本文进一步研究了无网格局部PetrovGalerkin方法在薄板自由振动问题中的应用。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。在插值近似时,采用虚拟实际节点值变换方法直接引入本质边界条件。通过数值算例和与其他方法的结果进行比较,表明无网格局部PetrovGalerkin法求解弹性薄板自由振动问题具有收敛性好、精度高等一系列优点。The Meshless local Petrov Galerkin(MLPG) method is extended to solve the free vibration problem of thin square plates using moving least square approximation to interpolate solution variables, and the equivalent integral weak form to the governing equation. The present method is an effective truly meshless one as it doesnt need any meshgrids, and all integrals can be easily evaluated over regularly shaped domains and their boundaries. In the analysis, the essential boundary conditions can directly be imposed using a transformation from the fictitious nodal value to the actual nodal values. Several examples were given and compared with other methods to show that in solving free vibration problems, the meshless local Petrov Galerkin method has a number of advantages such as the quite good accuracy and the high rate of convergence.

关 键 词：无网格局部PETROV-GALERKIN方法 薄板 自由振动 移动最小二乘近似 

分 类 号：O326[理学—一般力学与力学基础]