An Efficient Filter Implementation Method and Its Applications in Topology Optimization Utilizing k-d Tree Data Structure

Topology optimization (TO) with the variable density concept has made significant advancements in academic research and engineering applications; yet it still encounters obstacles associated with computer inefficiencies in the filtering process. This work introduces a novel filter implementation method that significantly enhances the optimization process by adapting the k-d tree data structure. The proposed method converts traditional neighborhood search operations into extremely efficient spatial searches while preserving solution accuracy. This method inherently accommodates a comprehensive array of manufacturability constraints, including symmetry, local volume control, periodic patterning, stamping-oriented overhang control, and more, without compromising computational duration. Extensive numerical examples validate the proposed method’s efficiency yielding precise, scalable designs, achieving substantial acceleration relative to conventional methods The method demonstrates specific advantage in large scale optimization challenges and intricate complex geometric restrictions, encompassing unstructured meshes. This study explores a new paradigm for effective constraint integration in topology optimization through advanced data structures, providing extensive applicability in engineering design.