On a level set and topological derivative-based strategy for connectivity constraints in topology optimization

Abstract This work addresses a level set-based framework for connectivity constraints in shape and topology optimization, using the concept of topological derivative. By controlling the presence of disconnected material components in optimal designs, the goal is to ensure that optimal solutions are also physically realizable in terms of additive manufacturing and of its final application. The proposed strategy is an extension of the continuous spectral graph approach, originally introduced in Donoso et al. (Struct Multidisc Optim 66(4):71, 2023. https://doi.org/10.1007/s00158-023-03526-8) in the density-based framework, which identifies and enforces connectivity based on the spectrum of a two-phase differential operator. The effectiveness of the strategy is demonstrated through several benchmark problems in structural optimization, in two and three dimensions. Numerical challenges and limitations such as filtering strategies and parameter dependence are illustrated and successful simulations are obtained with either the addition of perimeter penalization or a dilation operator.