A continuous topology optimization framework using an explicit binarization constraint

Achieving crisp, manufacturable black-and-white (0/1) designs from element-based topology optimization methods is a critical and long-standing challenge. This paper introduces a novel continuous framework, termed Explicit Binarization Topology Optimization (EBTO), that addresses this challenge by treating binarization not as an implicit byproduct but as a direct mathematical constraint. The proposed method achieves this by introducing an explicit constraint formulated using a tunable function that directly measures and controls the global “greyness” of the design. This approach fundamentally decouples the binarization mechanism from the material model, allowing for the use of a linear material interpolation scheme that simplifies sensitivity analysis and provides a clearer physical interpretation for optimization problems. The versatility and robustness of the EBTO framework are demonstrated through a comprehensive set of 2D and 3D numerical examples, including compliance minimization, compliant mechanism design, and challenging stress-based optimization problems. The results consistently show that the proposed method generates clear 0/1 solutions with excellent structural performance, demonstrating superior results in benchmark cases compared to established methods. Furthermore, a set of guiding principles for formulating such explicit constraints is established, providing a foundation for future advancements in this class of topology optimization methods.