弹性地基板分析的局部Petrov-Galerkin方法  

A LOCAL PETROV-GALERKIN METHOD FOR ANALYSIS OF PLATES ON ELASTIC FOUNDATION

作　　者：熊渊博[1] 龙述尧[1] 李光耀[1] 

机构地区：[1]湖南大学,湖南长沙410082

出　　处：《土木工程学报》2005年第11期79-83,共5页China Civil Engineering Journal

基　　金：国家自然科学基金(10372030);国家973项目(2004CB719402)

摘　　要：利用弹性地基板控制微分方程的等效积分对称弱形式和对解变量(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(MLPG)方法在弹性地基板弯曲问题中的应用。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,MLPG方法不但能够求解弹性静力学问题,而且在求解弹性地基板问题时仍具有收敛快,精度高的特点。The meshless local Petrov-Galerkin （MLPG） method is extended to solve bending problems of a thin plate on elastic foundation. The method employs a weak symmetric equivalent integral form of the go vetoing equation and a moving leastsquare approximation to interpolate the primary variables. The present method is a true meshless method as it doesn＇t need any grids, and all integrals can be easily evaluated over regularly shaped domains （in general, spheres in three-dimensional problems）. The essential boundary conditions are enforced by a penalty method. Several examples show that in solving the bending problems of thin plates on elastic foundation, the meshless local Petrov-Galerkin method, just like in solving static problems of elasticity, can have good stability, high accuracy and rate of convergence.

关 键 词：薄板 双参数弹性地基 局部PETROV-GALERKIN方法 移动最小二乘近似 

分 类 号：TU470[建筑科学—结构工程] O302[建筑科学—土工工程]