Kriging插值无网格法形函数性质

Shape functions in meshless Kriging interpolation method

针对以往无网格法中本征边界条件处理困难的问题,采用滑动Kriging插值技术代替以往无网格法中滑动最小二乘法构造无网格形函数。结果表明:与其他无网格法不同,由此方法所构造的无网格法形函数具有Kronecker δ-函数属性,从而使得本征边界条件处理非常容易。数值算例结果证明该法构造的形函数具备过点插值性质并且具有很好的曲线拟合特性,是一种非常好的无网格法形函数。

In view of overcome the difficulties in implementing essential boundary conditions tor traditional meshless method, a moving Kriging interpolation procedure is proposed to replace the moving least square method in constructing shape function. The proposed new method has the property of Kronecker δ function and makes the essential boundary conditions implementation much ease. The case study shows that the shape functions and their derivatives of the meshless Kriging interpolation method have the properties of Kronecker delta function. Also the shape functions have high accuracy in curve fitting and can pass the patch test. The shape function constructed by the proposed method is a valid function for meshless method.