A radial point interpolation method (RPIM)[l-3] is developed for analyses of three-dimensional solids. The RPIM has been developed and successfully applied to one-dimensional and two-dimensional problems of computational mechanics [1-5]. In this paper, the RPIM formulation for a three-dimensional (3-D) domain is developed to construct 3-D meshfree shape functions. It is found that the RPIM using the radial basis function (RBF) is stable and very easy to extend to three-dimensional domains. Importantly, the RPIM shape functions so-constructed have the delta function property. It makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least-squares (MLS) approximation. The system equations are then obtained using RPIM shape functions and the Galerkin weak form of the governing equations for 3-D solids. Several numerical examples are presented to verify the accuracy and efficiency of this present meshfree method. Some important parameters in this method are also investigated using numerical examples. It is concluded that the present meshfree RPIM is very efficient for analyses of 3-D solids.
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