A parameterized level set topology optimization strategy using FEniCS and radial basis functions with compact support

Resumo

This work addresses level-set based methods for structural topology optimization. Compact support C2-
Wendland radial-based functions are employed to parameterize the level sets. Structures are assumed to be in static
equilibrium, under plane stress state and built with isotropic linear elastic materials, and the classical compliance
minimization problem is considered. Aiming to save the computational effort of the potentially large number of
linear systems to be solved, the computational linear algebra of the resulting sparse interpolation matrix is explored
in contrast with the use of classic multiquadric radial basis functions, with dense matrices in the related systems.
Implementation is made in Python using the FEniCS project for the resolution of the equilibrium system and

the sensitivity analysis, based on a recent work of Laurain, that uses direct numerical resolution of the Hamilton-
Jacobi equation for the level set update. Both strategies are, therefore, compared. Additionally, our approach is

put into perspective with the radial basis function parameterization Matlab code of Wei et al. Numerical results
of experiments with classical benchmark problems are presented.