This paper mainly proposes an alternative way for numerical implementation of thin plates bending based on a new improvement of meshless method, which is combined between the standard element-free Galerkin method and one different shape functions building technique. The moving Kriging (MK) interpolation is applied instead of the traditional moving least-square approximation in order to overcome Kronecker's delta property where the standard method does not satisfy. Obviously, the deflection of the thin plates is approximated via the MK interpolation. To illustrate this approach, numerical analysis is examined in both regular and irregular systems. Three examples with different geometric shapes of thin plates undergoing a simply supported boundary are performed. In addition, two important parameters of the present method are also analyzed. A good agreement can be found among the proposed, analytical and finite element methods. and successfully applied to the analysis of solid problems, fluid flow, heat transfer and so forth that without a mesh of discrete problems is requested [1]. They can also usually be known under different terms, such as meshless or meshfree methods. Beside these new methods, an extended FEM was developed by Belytschko and Black [2] or Moës et al. [3]. One of the pioneering assumed meshless methods is the element-free Galerkin (EFG) method, introduced by Belytschko et al. [4]. It is one of the most viable methods in which the Galerkin weak form and the moving least-square (MLS) approximation are crucially used.Although the EFG method as well as many other meshless methods have been successfully applied to many different areas,inconveniences or disadvantages still remains,which have to be studied and developed [5]. The treatment of essential boundary conditions is one of the most typical issues of such drawbacks. Recently, there are many methods that have been developed to eliminate drawbacks in many different ways, e.g. Lagrange multipliers [4], penalty method [1] or coupling with FEM [6] and so on. Furthermore, in contrast, another approach based on the framework of equilibrium models by a meshless method was also studies by the authors [7].The aim of this paper is a novel combination between Galerkin weak form and moving Kriging (MK) interpolation, which was introduced by Gu for the first time [8]. One of the major good features of the MK is the elimination of the shortcoming of this Kronecker delta function property. Because the essential boundary conditions are automatically satisfied, this is therefore treated very similar to the conventional FEM in the computation. Based on that, this method can be called as meshless Kriging Galerkin method, abbreviated MKG, for the first demonstration of numerical analysis of Kirchhoff plates.On the one side, the Kriging interpolation is a well-known geostatical technique for spatial interpolation in geology and mining, otherwise the application of the MK interpolation in meshless methods is still in its early stages. First, it was successfully introduc...
