Arbitrary Boundary Conditions in Topology Optimization: Applications in Strongly Coupled Viscothermal Multiphysics

Abstract Density based topology optimization has proven to be a powerful framework for designing high-performance structures across a wide range of physical domains. However, a challenge in density based topology optimization is incorporating the influence of boundary dependent conditions such as forces, heat fluxes, and interface conditions in the optimization process, due to the evolving and initially undefined nature of these boundaries. Existing solutions to this problem often rely on physics-specific workarounds, auxiliary fields, or mesh-dependent strategies, limiting their generality and broad applicability. In this work, we introduce a novel approach based on boundary interpolations. This enables the application of arbitrary boundary conditions in density based topology optimization, regardless of mesh structures or underlying physics. The boundary interpolations integrate seamlessly into the density based topology optimization methodology, transforming it straightforwardly into a boundary-aware optimization method. We demonstrate this by designing an optimal acoustic resonator that leverages viscothermal boundary losses to fully absorb an incoming acoustic wave, and we highlight the degradation of the resonator’s absorption performance when physically accurate vibroacoustic multiphysics are taken into account. To recover its performance, we subsequently include a strongly coupled vibroacoustic multiphysics model in the optimization process, along with the associated boundary-dependent coupling conditions. This showcases,to the best of the authors knowledge, the first simultaneous application of multiple interface conditions to a single boundary during a density based topology optimization process. This advancement opens the door not only to the optimal design of complex vibroacoustic systems, encompassing all their physical complexity, but also to other applications that require the incorporation of boundary effects into density based topology optimization.