A boundary strip indicator for material distribution-based topology optimization

Abstract This article proposes a boundary strip indicator for density-based topology optimization that can be used to estimate the design’s surface area (perimeter in 2D) or identify a coating layer. We investigate the theoretical properties of the proposed boundary strip indicator and propose a differentiable approximation that preserves key properties, such as non-negativity. Finally, we use the boundary strip indicator in a heat conduction design optimization problem for a coated structure. The resulting designs show a strong dependence on the properties of the coating.