A node enrichment adaptive refinement in Discrete Least Squares Meshless method for solution of elasticity problems M.H. Afshar Associate professor, University of Science and Technology, School of Civil Engineering, Tehran, Iran Email: mhafshar@iust.ac.ir M. Naisipour M.Sc. Student, University of Science and Technology, School of Civil Engineering, Tehran, Iran Email: m_naisipour@civileng.iust.ac.ir J. Amani Ph.D. Student, University of Science and Technology, School of Civil Engineering Tehran, Iran Email: jamani@iust.ac.ir Abstract In this paper, an adaptive refinement procedure is proposed to be used with Discrete Least Squares Meshless (DLSM) method to obtain accurate solution of planar elasticity problems. DLSM method is a newly introduced meshless method based on the least squares concept. The method leads the solution to a given problem that minimizes a least squares functional defined as the weighted summation of the squared residual of the governing differential equation and its boundary conditions. A moving least square is also used to construct the shape function making the approach a fully least squares based approach. An error estimate and adaptive refinement strategy is proposed in this paper to further increase the efficiency of DLSM method. For this, a residual based error estimator is introduced and used to discover the region of higher errors. The proposed error estimator has the advantages of being available at the end of each analysis adaptive configuration contributing to the efficiency of the proposed process. An enrichment method is then used by adding more nodes in the vicinity of nodes with higher errors. A Voronoi diagram is used to locate the position of the nodes to be added to the current nodal configuration. Efficiency and effectiveness of the proposed procedure is examined by adaptively solving two benchmark problems. The results show the ability of the proposed strategy for accurate simulation of elasticity problems. Keywords: DLSM method, Error estimate, Voronoi diagram, Adaptive refinement, Planar Elasticity. 1. Introduction