| Title |
The Analysis of Localization Problemsby the Meshfree Adaptive Refinement Method |
| Authors |
Han Sang-Eul ; Lee Sang-Joo ; Joo Jung-Sik |
| Keywords |
Meshfree Method ; Radial Basis Function ; Adaptive Refinement ; Radial Point Interpolation Method |
| Abstract |
The Meshfree method is a method used to establish a system of algebraic equations for the whole problem domain without using predefined mesh for the domain discretization. Point interpolation method is based on combination of radial and polynomial basis functions. Introducing of radial basis functions overcomes possible singularity problem. Furthermore, the interpolation function is applicable for all points scattered over in influence domain and thus shape functions are of delta function property, which makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. In this study, an adaptive node generation procedure in the radial point interpolation method is proposed. Since we set the initial configuration of nodes by subdivision of background cell, abrupt changes of inter-nodal distance between higher and lower error regions are unavoidable. This unpreferable nodal spacing induces additional errors. To obtain the smoothy nodal configuration, it's regenerated by local Delaunay triangulation algorithm. This technique was originally developed to generate a set of well-shaped triangles and tetrahedra. In order to evaluate the error estimation technique, cantilever type plate was investigated. To demonstrate the performance of proposed scheme, the results of making optimal nodal configuration with adaptive refinement method are investigated for stress concentration problems. |