中文摘要：

利用薄板控制微分方程的等效积分对称弱形式和对变量（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方法在薄板屈曲问题中的应用。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，无网格局部Petrov-Galerkin法不但能够求解弹性静力学问题，而且在求解弹性稳定性问题时仍具有收敛快，稳定性好，精度高的特点。

英文摘要：

Meshless local Petrov-Galerkin （MLPG） method is extended to solve buckling problems of a thin plate. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a local symmetric weak form. The present method is a truly meshless one as it does not need any meshgrids, and all integrals can be easily evaluated over regularly shaped domains （in general, spheres in the three-dimensional problem） and their boundaries. The essential boundary conditions are enforced by a penalty method. Several examples are given to show that in solving buckling problems, the meshless local Petrov-Galerkin method still possesses some advantages such as good stability, high accuracy and high rate of convergence, just as in solving elastic static problems.