Implementation of Meshless Method: Application to Composite Materials

Although the standard Finite Element Method (FEM) has a very wide range of applications, it still has limitations where it does not give acceptable results. Indeed, it cannot sufficiently capture defects that involve strong and weak discontinuities: i.e. a jump in the displacement or in the stress field. In this context, the element Free Galerkin (EFG) method is capable of resolving these problems. This paper presents a comparative simulation based on the FEM and the meshless EFG method on a mechanical structure. We demonstrate the effectiveness of the meshless EFG method for characterizing the static behavior of the plate subjected to tensile loading in plane stress, by comparing the performance of this method (via the MATLAB code) with that of the classical finite element method (in Abaqus). The results obtained by this method are coherent and closer to analytical results than those obtained by the finites elements method.