弹性地基板分析的局部Petrov-Galerkin方法

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。

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

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 verning equation and a moving least-square 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.