壳结构的无网格局部Petrov-Galerkin方法  

Meshless local Petrov-Galerkin analyses of shell structure

作　　者：李迪[1,2] 林忠钦[1] 李淑惠[1] 陈关龙[1] 

机构地区：[1]上海交通大学机械学院,上海200030 [2]山东理工大学,淄博255049

出　　处：《计算力学学报》2009年第4期505-509,517,共6页Chinese Journal of Computational Mechanics

基　　金：山东省自然科学基金(2003ZX01);山东理工大学科技基金(2006KJM33)资助项目

摘　　要：无网格近似函数具有高度光滑性,能够很好的逼近曲壳表面及其位移场。无网格局部Petrov-Galerkin方法不论插值还是离散都不需要单元,是一种真正的无网格方法。本文基于无网格局部Petrov-Galerkin方法的基本原理,采用移动最小二乘插值,利用控制微分方程弱形式,建立了Mindlin壳结构的无网格局部Petrov-Galerkin分析方法,用屋顶壳、受夹圆柱壳、几何非线性圆柱壳作为计算实例分析了求解精度、收敛性和稳定性,并与精确解和有限元计算结果进行了对比,表明该方法计算精度高及收敛性好。Because of the high order of continuity of approximation functions, Meshless method could express the surface and displacement of a shell very well. The meshless local Petrov-Galerkin method （MLPG） was a truly meshless one as it did not need any finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. MLPG method for solving Mindlin shell structure was represented and discussed. The present method used the moving leastsquares approximation to interpolate the solution variables, and employed a local weak form. The numerical examples presented on barrel vault roof, pinched cylinder and geometrically non-linear analysis of shell structure, show that high accuracy, the stablility and the quick convergence of the present method, comparing with those obtained by finite element method and theoretical computation.

关 键 词：无网格法 无网格局部Petrov-Galerkin法 壳结构 微分方程弱形式 移动最小二乘 

分 类 号：O34[理学—固体力学]