Meshfree numerical approach based on the Finite Pointset Method for static linear elasticity problems

Abstract In this work a promising meshfree numerical approach is extended and implemented for the first time in the field of linear static elasticity. A real meshfree method, the so called Finite Pointset Method (FPM), is applied and implemented in order to solve the strong/classical form of the governing partial differential equations (PDEs), the well known Navier–Cauchy equations. FPM numerical performance is demonstrated for several classical and well known studied benchmark problems and comparison with other approaches is also reported. Numerical results suggest that FPM method is stable with good convergence behavior for 2D linear static elasticity problems.