Hole Seeding in Level Set Topology Optimization via Density Fields

Abstract: Two approaches that use a density field for seeding holes in level set topology optimization are proposed. In these approaches, the level set field describes the material-void interface while the density field describes the material distribution within the material phase. Both fields are optimized simultaneously by coupling them through either a single abstract design variable field or a penalty term introduced into the objective function. These approaches eliminate drawbacks of level set topology optimization methods that rely on seeding the initial design domain with a large number of holes. Instead, the proposed approaches insert holes during the optimization process where beneficial. The dependency of the optimization results on the initial hole pattern is reduced, and the computational costs are lowered by keeping the number of elements intersected by the material interface at a minimum. In comparison to level set methods that use topological derivatives to seed small holes at distinct steps in the optimization process, the proposed approaches introduce holes continuously during the optimization process, with the hole size and shape being optimized for the particular design problem. The proposed approaches are studied using the extended finite element method for spatial discretization, and the solid isotropic material with penalization for material interpolation using fictitious densities. Their robustness with respect to algorithmic parameters, dependency on the density penalization, and performance are examined through 2D and 3D benchmark linear elastic numerical examples, and a geometrically complex mass minimization with stress constraint design problem.