Influence of Weight-Functions on the Performance of  Element-Free Galerkin Method

The influence of the weight functions on the performance of the element-free Galerkin method has been studied. The convergence and computational cost using various functions for 1D and 2D structural models are examined. Acceptable ranges, as well as the best scaling parameters for each weight function, are pointed out. Mesh-free methods are completely independent of mesh and approximate the governing partial differential equations based on the only set of nodes. We have discussed the analysis of six different weight functions using the physical nature of field problems and show that the continuity of mesh-free shape function i.e., moving least square shape function depends on weight function. It is observed that the so-called weight function which is showing a minimum error is not always true. The convergence & computational cost (computation time) are also important factors. The manuscript contains the solution of 1D and 2D elastostatic problems with ten different weight functions. Paper represents the comparative study of different weight functions to predict the best field behavior with systematic analysis of each case.