Comparison between lagrange multiplier and penalty methods to enforce essential boundary conditions in meshfree methods

Abstract

A simulation of a cantilever beam was carried out with the aim of compared the performance of two Meshfree methods, Element Free Galerkin Method and Radial Point Interpolation Method, using two different methods to impose the Essential Boundary Conditions. The results were validated with the analytical solution of the problem, obtained by Timoshenko in [Tim70]. It was possible to conclude that both methods show a good performance for the solution of the simulated problem. However, some consideration must be taken into account when these are applied to other types of approximation that cannot easily satisfy essential boundary conditions.