自然邻接点局部Petrov-Galerkin法求解中厚板弯曲问题

Natural Neighbor Petrov-Galerkin Method for Moderately Thick Plates

将基于自然邻接点插值的无网格局部Petrov-Galerkin方法应用于分析中厚板弯曲问题.自然邻接点插值创建的形函数具有Kronecker Delta函数性质,故能够准确地直接施加本质边界条件.在板中面上的局部多边形子域上采用局部Petrov-Galerkin方法建立系统平衡方程,这些子域由Delaunay三角形创建,采用高斯积分法进行域积分和边界积分.该方法集合了自然元法和无网格局部Petrov-Galerkin法的优点,易于施加本质边界条件,无需刚度矩阵的整合,得到的刚度矩阵是带状稀疏矩阵.通过算例分析,表明该方法计算简便,求解精度高,数值解稳定.

This paper presented a meshless local Petrov-Galerkin method based on the natural neigh- bour interpolation for a plate described by the Reissner-Mindlin theory. The natural neighbour interpola- tion shape functions have Kronecker Delta function property, which facilitates the imposition of essential boundary conditions. The local weak forms of the equilibrium equations and the boundary conditions are satisfied in local polygonal sub-domains in the mean surface of the plate. These sub-domains were con- structed with Delaunay tessellations and domain integrals were evaluated over included Delaunay triangles by using the Gaussian quadrature scheme. The present method combines the advantage of easy imposition of essential boundary conditions of NEM with some prominent features of the MLPG. The numerical re- sults have shown that the proposed method is easy to implement and very effective for these problems.