Applicability of Meshfree Method in Computational Solid Mechanics

Meshfree methods are powerful computational tools that offer several advantages over conventional finite element methods. Based on a cloud of points, meshfree methods are easy to construct and provide great adaptivity. Among these methods, the element free Galerkin (EFG) method is widely used for solving solid mechanics problems. In this study, the influence of nodal density on accuracy and computational time is investigated using the EFG method for an axially loaded 1D bar. The method is also applied to a 2D cantilever beam that is subjected to a point load at the free end, and the essential boundary conditions are enforced using Lagrange multipliers. A MATLAB-based program is used to obtain displacement profiles along the length of the bar. The study evaluates the accuracy and computational cost of the EFG method and reports a good agreement between the obtained results and the exact analytical solution.