高阶板理论的无网格弱-强式法(MWS)

Meshfree Weak-strong(MWS) Form Method for Moderately Thick Plates Based on the Third Order Shear Deformation Theory

基于局部弱式和强式配点相结合的无网格弱-强式法(meshfree weak-strongmethod,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.采用中厚板的高阶理论对弯曲问题和能量误差进行计算.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 formulated the meshfree weak-strong（MWS） form method for moderately thick plates based on the third order shear deformation theory（TSDT）. The meshfree collocation method based on strong form equations was applied to the interior nodes and the nodes on the essential boundaries; the local Petrov- Galerkin weak form was applied only to the nodes on natural boundaries of the problem domain. Using the moving least squares method to construct the shape function, the MWS method is a truly ideal meshfree method. Examples have shown that the proposed method performs well with natural and essential boundaries. Besides, the MWS method has 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 in the finite element method.