耦合多项式基的径向点插值无网格方法  

Meshless Radial Point Interpolation Method with Polynomial Basis

作　　者：贾延[1] 康亚明[2] 

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 [2]北方民族大学化学与化学工程学院,宁夏银川750021

出　　处：《计算机仿真》2013年第11期251-254,共4页Computer Simulation

基　　金：国家自然科学基金项目(50879049);宁夏自然科学基金资助项目(NZ11138);北方民族大学自主科研基金项目(2011ZQY027)

摘　　要：为避免单纯采用多项式基所引起的力矩矩阵的不可逆问题,引入径向基函数,构造新的形函数,使其具有δ函数性质,且可直接施加本质边界条件。无网格法根据变分原理,建立了二维耦合多项式基的径向点插值无网格方法的基本方程,给出了其积分实现方法。最后通过对带孔薄板的数值计算,验证了上述方法的适用性和有效性,仿真结果证明了耦合方法计算效率高,数值结果稳定、易于实现,且解与弹性力学理论解以及有限元解吻合很好。The interpolation functions with the combination of radial and polynomial basis overcomes possible sin- gularity associated with the PIM based on only the polynomial basis. As its shape functions possess the Kronecker del- ta function property, essential boundary conditions can be imposed easily. In this paper, the basic theory was intro- duced, based on the variational principle, the basic equations and numerical integration method were proposed. Nu- merical examples of orifice plate were given to verify the validity and availability. The simulation result shows that the meshless method has high efficiency, high stability, the obtained results agree well with the elasticity analytical solu- tion and with the results obtained with the finite element method.

关 键 词：无网格法 多项式基函数 径向基函数 应力分析 有限元法 

分 类 号：O242[理学—计算数学] O343[理学—数学]