Topology Optimization Sensitivity Dynamic Filtering Method With Density Penalization

ABSTRACT To tackle the challenge of structural boundary blurring in density‐based topology optimization, a sensitivity dynamic filtering method incorporating density penalization is proposed. By enhancing the traditional sensitivity filtering framework, element relative densities are penalized to rapidly drive them toward binary states (0 or 1). Concurrently, during the topology iteration, the filtering radius is adaptively reduced according to structural discreteness, thereby minimizing the sensitivity influence of surrounding elements within the shrunk radius on the central element. The proposed method is integrated with the Solid Isotropic Material with Penalization (SIMP) method and validated through numerical examples. Results demonstrate that the proposed method can effectively suppress intermediate‐density elements, generate structures with sharp boundaries, and support topological optimization that accounts for element stress while circumventing numerical instabilities like checkerboard patterns—ultimately achieving substantial improvements in topology optimization efficiency.