改进的无单元Galerkin法分析薄板小挠度弯曲  

Analysis of Thin Plate Bending with the Improved Element-free Galerkin Method

作　　者：王伟[1,2] 姚林泉[2] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006 [2]苏州大学城市轨道交通学院,江苏苏州215137

出　　处：《江苏第二师范学院学报》2015年第9期1-4,共4页Journal of Jiangsu Second Normal University

基　　金：国家自然科学基金项目"热机电耦合压电层合曲壳结构的动力学特征及控制机理研究"(项目编号:11172192)

摘　　要：无单元伽辽金(EFG)法采用移动最小二乘近似构造形函数,从能量泛函的变分形式出发得到控制方程,并用罚函数法施加本质边界条件,从而得到偏微分边值问题的数值解.改进的广义移动最小二乘近似(IGMLS)在构造函数时要求近似函数在所有节点处误差的平方和与近似函数导数仅在导数边界附近各节点处误差的平方和之和最小.同时,为了节省计算时间,基函数采用加权正交多项式.将IGMLS与EFG相结合,对板弯曲离散建立了相应的代数方程.通过数值算例证实了IGMLS比改进的移动最小二乘近似(IMLS)具有更高的精度,所需的运算时间要小于广义移动最小二乘近似(GMLS).The Element-free Galerkin( EFG) method uses the moving least square approximation to construct the shape functions,uses variational form of the energy functional to obtain the governing equations,uses the penalty function method to impose the essential boundary conditions,and finally obtains the numerical solution to the boundary value problem of the partial differential equations. When it is used to construct functions,the improved generalized moving least squares approximation( IGMLS) requires that the sum reach the smallest value,where the sum is the summation of the error square sum of the approximation function at all nodes and the error square sum of the approximation derivative function only at those nodes near the derivative boundary. At the same time,to save the computing time,the weighted orthogonal polynomial is taken as the basis function. Combining IGMLS with EFG,we establish the corresponding algebraic equation for the plate bending discrete. By the numerical examples,we confirm that IGMLS has higher accuracy than the improved moving least squares approximation( IMLS),and the required computing time is less than the generalized moving least squares approximation( GMLS).

关 键 词：无单元伽辽金(EFG) 改进广义移动最小二乘近似(IGMLS) 加权正交基函数 薄板弯曲 

分 类 号：O175.2[理学—数学]