J F Ramirez, E Mesa, P Boulanger and J W Branch (2011). A Comparison Between Lagrange Multiplier and Penalty Methods for Setting Boundary Conditions in Mesh-free Methods. In VIII Congreso Colombiano de Metodos Numericos, 10 pages, Medellin, Colombia. July 2011. EAFIT Press.
A simulation of a cantilever beam was carried out with the aim of comparing the performance of two mesh-free methods: element-free Galerkin and radial point interpolation methods. In this implementation, we use two different methods to set boundary conditions. The results were compared with the analytical solution of the cantilever problem using Timoshenko formulation [Tim70]. In the paper, we demonstrate that both numerical methods are accurate compared to the analytical solution. However, some consideration must be taken into account when applying these methods to more complex simulations that cannot be well approximated by the boundary conditions scheme.
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