弹性静力问题的无网格弱-强形式结合法

基于改进的移动最小二乘(MLS)二阶导数近似,建立了一种求解弹性静力问题的无网格弱-强形式结合法(MLS-MWS)。该方法采用节点离散求解域,通过MLS构造形函数,将求解域划分为边界域和内部域,并分别使用控制方程的局部弱形式和强形式来建立离散系统方程。对强形式中涉及的近似函数二阶导数计算,提出了一种将其转化为求两次一阶导数的方法,与传统方法相比,该方法计算简单、精度高。MLS-MWS法结合了弱、强形式无网格法的优点,Neumann边界条件容易满足,并且只需在边界区域进行积分。文中应用该方法分析了两个弹性力学平面问题,分析结果表明本文方法具有良好的精度和收敛性。

A meshless weak-strong form method for elasto-static problems

A meshless weak-strong form method based on an improved moving least square approximation of second order derivatives (MLS-MWS) is developed for solving elasto-static problems. It uses a set of nodes to discretize the problem domain and the MLS method to construct shape functions. The problem domain in this method is divided into two regions, boundary region and interior region. The local weak-form and strong-form of the governing equations are applied for the nodes in these two regions, respectively, when establishing the discrete system equations. Due to the strong-form involves evaluating the second order derivatives of approximation function, a sequence of two first order differentiation scheme is proposed, which provides more simple calculation and better accuracy than the traditional methods. The MLS-MWS method combines advantages of both weak- and strong-form meshless methods, which satisfies Neumann boundary conditions naturally and only requires numerical integration in the boundary region. With the presented method, two numerical examples of the elasticity plane problem are studied. The numerical results show that it can give good computational accuracy and rate of convergence.