A New Local Perimeter Control Approach to Minimum Length Scale in Topology Optimization

ABSTRACT This work presents a novel framework for enforcing minimum length‐scale constraints in topology optimization, a fundamental challenge for ensuring manufacturable designs. Two complementary methodologies are proposed. The first, and primary, approach is based on local perimeter control, which regulates the amount of perimeter within localized regions of the design domain. Although the geometric interpretation may not be immediately intuitive, the formulation remains purely geometric and can be implemented by repeating standard filtering operations for a contour‐related variable. The second methodology introduces a differentiable skeleton representation of the structure. Building upon recent advances in skeleton‐based techniques, this approach avoids the definition of an auxiliary problem and instead leverages conventional filtering and projection tools widely used in topology optimization. Together, these two methodologies provide robust and computationally efficient mechanisms for imposing minimum member size constraints while maintaining consistency with the optimization framework. Their effectiveness is demonstrated through numerical experiments in linear elasticity and heat conduction, which highlight the robustness of the proposed methods across varying mesh densities and design complexities.