功能梯度材料中的无网格局部径向点插值法  

A Meshless Local Radial Point Interpolation Method for the Analysis of Functionally Graded Materials

作　　者：龙述尧[1] 刘凯远[1] 李光耀[2] 

机构地区：[1]湖南大学力学与航空航天学院,湖南长沙410082 [2]湖南大学汽车车身先进设计制造国家重点实验室,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2007年第3期41-44,共4页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金(10372030)

摘　　要：提出一种新的无网格局部径向点插值法来分析功能梯度材料．这种无网格方法采用径向基函数耦合多项式基函数来近似试函数,采用Heaviside函数作为加权残值法中的权函数．构造成的形函数具有Kronecker Delta性质,不再需要额外的处理来施加本质边界条件．若不考虑体力,则所形成的整体刚度矩阵只包含局部边界积分,而不包含局部域积分和奇异积分．在计算过程中,取局部边界积分中的高斯点的材料参数来模拟问题域材料特性的变化．结果表明,这是一种真正的无网格方法,具有模拟简单,计算精度高等优点．A new meshless local radial point interpolation method for the analysis of functionally graded materials is proposed. Radial basis function （RBF） coupled with a polynomial basis function was used as a trail function, and a Heaviside function was used as a test function of the weighted residual method. The shape function obtained in the trail function had the Kronecker Delta property, and no additional treatment were required to impose essential boundary conditions. The method did not involve sub-domain and singularity integration in generating the global stiffness matrix except for the body force integration. It only involves local boundary integrations. In computational procedures, variations of the material properties of the considered domain were simulated by adopting proper material parameters at Gauss points in local boundary integrations. The results have showed that the proposed method is a truly meshless method and has the advantage of easy implementation and high accuracy.

关 键 词：功能梯度材料 无网格局部径向点插值法 径向基函数 Heaviside函数 

分 类 号：O343[理学—固体力学]