Kirchhoff板弯曲问题的改进的复变量无单元Galerkin方法

发布时间：2018-11-26 13:38

【摘要】：基于改进的复变量移动最小二乘法,建立了Kirchhoff板弯曲问题的改进的复变量无单元Galerkin方法.相对于移动最小二乘法,改进的复变量移动最小二乘法采用一维基函数建立二维问题的逼近函数,提高了形函数计算效率.由改进的复变量移动最小二乘法建立Kirchhoff板的挠度逼近函数,根据Kirchhoff板弯曲问题的Galerkin弱形式建立离散方程,并应用罚函数法施加本质边界条件,推导了Kirchhoff板弯曲问题的改进的复变量无单元Galerkin法的公式.通过对4个典型算例进行计算和分析,说明了本文建立的Kirchhoff板弯曲问题的改进的复变量无单元Galerkin方法的有效性,并通过分析数值解的精度对本文方法中如何选取合适的基函数、权函数、影响域比例参数、节点分布和罚因子进行了讨论.数值算例说明了本文方法具有较好的收敛性和较高的计算精度.
[Abstract]:Based on the improved moving least square method of complex variables, an improved Galerkin method with complex variables without elements for bending of Kirchhoff plates is established. Compared with the moving least square method, the improved moving least square method uses a wiki function to establish the approximation function of the two-dimensional problem, which improves the efficiency of the shape function calculation. The deflection approximation function of Kirchhoff plate is established by the improved moving least square method of complex variables. The discrete equation is established according to the Galerkin weak form of the Kirchhoff plate bending problem, and the essential boundary conditions are applied by the penalty function method. The improved complex variable element free Galerkin method for bending of Kirchhoff plates is derived. Through the calculation and analysis of four typical numerical examples, the effectiveness of the improved complex variable element free Galerkin method for the bending problem of Kirchhoff plates established in this paper is illustrated, and the accuracy of the numerical solution is analyzed for how to select the appropriate basis function in this method. The weight function, the proportional parameter, the node distribution and the penalty factor are discussed. Numerical examples show that the proposed method has good convergence and high accuracy.
【作者单位】：上海大学上海市应用数学和力学研究所;上海大学力学系;
【基金】：国家自然科学基金(编号:11571223,U1433104)资助项目
【分类号】：O241.8

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