A coupled meshless element free Galerkin and radial basis functions method for Level set based topology optimization

This paper presents a meshless element free Galerkin method coupled with the radial basis functions (RBFs) based level set algorithm for topology optimization. The meshless approach provides the struc- tural response and corresponding sensitivities at nodal/grid points, and the solution of RBFs based level set formulation updates the structural geometry accordingly. Thus, this unique and novel approach allows solution of the optimization problems using a single discretization scheme for both the meshless as well as the level set methods. A special technique is proposed for the identification of meshless nodal points within the solid and void regions of the structural geometry. The present method handles the appropriate topological modifications, i.e., hole creation, splitting, merging, etc., affectively. Optimal solutions of the benchmark problems suggest reliability and compatibility of the proposed approach versus the mesh based techniques available within the structural optimization literature.