基于多项式基的径向点插值法及其应用  

A RADIAL POINT INTERPOLATION METHOD BASED ON POLYNOMIAL BASIS AND ITS APPLICATIONS

作　　者：贾延[1] 

机构地区：[1]北方民族大学信息与计算科学学院,宁夏银川750021

出　　处：《计算机应用与软件》2013年第5期184-187,共4页Computer Applications and Software

基　　金：宁夏自然科学基金项目(NZ11138);北方民族大学自主科研基金项目(2011ZQY027)

摘　　要：无单元法的形函数通常不具有插值特性,施加本质边界条件困难。将径向基函数与多项式基函数相耦合,构造新的形函数,不但有效地克服了这一困难,而且发挥了两种基函数各自的优势。将其应用于弹性力学问题Galerkin弱形式中,避免了采用多项式基引起的力矩矩阵的不可逆问题。由于构造出的形函数及其导函数形式简单,具有Kronecker delta插值性质,可直接施加本质边界条件,计算量大幅减小,从而提高了无单元法的计算效率。最后以悬臂梁受均布载荷为例,验证了这种耦合方法不但有效,而且数值结果稳定、计算精度高。Shape function in element-free method does not have interpolation property, and has difficulty in imposing the essential boundary conditions. In the paper we couple the radial basis functions with the polynomial basis functions to have constructed a new shape function, which not just overcomes this difficulty effectively, but also plays the respective advantages of these two kinds of basis function. It is also applied to Galerkin weak-form of elasticity problem, avoids the irreversible problem of moment matrix caused by the adoption of polynomial basis. Since the shape functions constructed and their derivatives are simple in form, and have Kronecker delta interpolation property, the essential boundary conditions can be imposed directly and the computational cost is sharply reduced, thus the computation efficiency of element-free method is improved. Finally, the cantilever beam under uniformly distributed pressure is taken as the example to demonstrate that such coupling method is effective, its numerical results are stable, and the calculation accuracy is high as well.

关 键 词：有限元 多项式函数 径向点插值法 悬臂梁 无单元法 数值模拟 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术] O242[理学—计算数学]