A level-set-based topology optimization strategy using radial basis functions and a Hilbertian velocity extension

Abstract

This work addresses the structural compliance minimization problem through a level-set-based strategy that rests upon radial basis functions with compact support combined with Hilbertian velocity extensions. A consistent augmented Lagrangian scheme is adopted to handle the volume constraint. The linear elasticity model and the variational problem associated with the computation of the velocity field are tackled by the finite element method using resources from the FEniCS project. The parameterization mesh constituted by the centers of the radial basis functions may be decoupled from the finite element mesh. A numerical investigation is conducted employing a Python implementation and five benchmark structures. Aimed at isolating the distinct aspects that compose the proposed strategy, the experiments provide grounds to analyze and put into perspective the inherent decisions and the related elements.