An adaptive node regeneration technique for the efficient solution of elasticity problems using MDLSM method

An efficient adaptive node regeneration method is proposed in this paper for solving elasticity problems using the mixed discrete least squares meshless (MDLSM) method. The method starts with a point-wise error estimation of the solution produced on an arbitrary initial configuration defined by the user using the MDLSM method. The point-wise error estimate is associated with the support domain of the nodal points and used to calculate the required nodal spacing at each support domain and subsequently generate new nodes at support domain level. A node-removing process is then used to remove some of the nodes created at the overlapping regions of the support domains. To improve the quality of the final configuration, a node-moving procedure based on interpolation of the errors on the original configuration is used to create the final nodal configuration. The proposed method is a single step refinement procedure and is capable of producing nodal configurations of desired accuracy for different problems. The proposed method is used to simulate three benchmark examples from the literature and the results are produced and compared with those of the conventional multi-stage node enrichment method. The results indicate the superior efficiency and effectiveness of the proposed method compared to the available methods.