Improvement of the Extended-Enriched MLPG Meshless Method by Using Optimal Nodal Points Distribution to Find 3D-SIFs

Using appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique based on Voronoi diagram and Delaunay triangulation is used to distribute nodal points in the sub-domain of analysis. Therefore, with this technique, the nodal points used in the MLS approximation to apply the MLPG method with enriched polynomial base functions are optimally increased in different steps. By doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the Mono-objective PSO algorithm to find the penalty factor the coefficient, convergence, arrangement of nodal points during the three stages of Voronoi diagram implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns=7 andto estimation of 3D-SIFs in computational fracture mechanics.