中厚板弯曲分析的无网格弱-强式法(MWS)

Meshfree weak-strong(MWS) form method for moderately thick plates bending problems

基于局部弱式和强式配点相结合的无网格弱-强式法(meshfree weak-strong method,MWS)求解中厚板问题。MWS法对问题域使用整体离散节点表征和强形式配点法进行计算,在自然边界条件上或靠近自然边界条件的区域采用局部弱形式Petrov-Galerkin法计算,用移动最小二乘法或径向点插值法来构造形函数,是一种理想的真正无网格法。采取MWS法,文中计算了中厚板的弯曲问题和能量误差。算例结果和对比分析表明,无网格弱-强式法(MWS)可以自然协调处理两类边界条件,计算效率高、数值结果稳定;对计算域采用规则节点布置,其解与弹性力学理论解以及有限元解都吻合很好。

This paper formulates the meshfree weak-strong(MWS) form method for moderately thick plates bending analysis.In this paper,the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries;the local Petrov-Galerkin weak form is applied only to the nodes on natural boundaries of the problem domain.With the moving least squares method constructing the shape function,the MWS method is a true ideal meshfree method.Examples show that the presented method performs well with the natural and essential boundaries.Besides the MWS method has very good efficiency and accuracy for moderately thick plates bending problems;results obtained with regular nodes are found to agree well with the elasticity analytical solution and with the results obtained by the finite element method.