Top3DFVT: Topology optimization algorithm for three-dimensional continuum elastic structures applying the finite-volume theory

Resumo

Topology optimization is a powerful computational tool for determining optimal material layouts within a design domain, aiming to minimize structural compliance under a prescribed volume constraint. Conventional density-based approaches, such as the solid isotropic material with penalization (SIMP) and the rational approximation of material properties (RAMP), are widely employed to interpolate material properties and drive the solution toward discrete "black-and-white" topologies. Although most topology optimization frameworks rely on the finite element method (FEM), alternative discretization strategies, such as the finite-volume theory (FVT), have demonstrated promising capabilities, particularly in addressing numerical issues like checkerboard patterns in the absence of filtering techniques. The proposed formulation employs compatibility and continuity conditions in the surface-averaged sense at the subvolume faces and locally satisfies the equilibrium equations at the subvolume level, providing a physically consistent basis for structural analysis. This work presents an extension of a density-based topology optimization algorithm grounded in the zeroth-order finite-volume theory for three-dimensional linear elastic structures. The numerical formulation adopts structured meshes and an artificial interpolation scheme to enhance solution discreteness and stability. In addition, an adaptation of the optimality criteria (OC) method is adopted, aimed at suppressing gray-scales, employing a linear relationship between material stiffness and density (Voigt model of micromechanics) instead of a penalization of intermediate densities approach. The formulation's effectiveness is demonstrated through numerical examples, establishing it as a promising alternative for 3D topology optimization.