功能梯度材料的点插值无网格法

建立了一种新的求解功能梯度材料问题的点插值无网格法，这种无网格方法将径向基函数和多项式基函数耦合构造具有插值特性的近似函数，并将其应用于弹性力学问题Galerkin形式的无网格方法。在计算过程中，取高斯点的材料参数模拟功能梯度材料特性的变化，由于形函数及其导数的构造相对简单，并且满足Delta函数性质，所以该方法具有计算量小、精度高、可以像有限元法一样直接施加边界条件的优点。最后通过数值算例证明了该方法的有效性。

A Meshless Point Interpolation Method for the Functionally Graded Materials.

A Galerkin-based meshless point interpolation method for the functionally graded materials is proposed.in this paper. In this method, the trail function, which is of Delta function property, is constructed by the radial basis functions coupled with the polynomial basis function. In..computational procedures, variations of the material properties are simulated by adopting proper material parameters at Gauss points. The implementation procedure is simpler and the computation cost is much lower because of the simple interpolation, the corresponding derivatives and the Delta function property of the shape functions. In addition, the essential boundary conditions can be implemented easily as in the finite element method. Some numerical results to demonstrate the efficiency of the present method are presented.