An efficient 3D topology optimization method integrating multi-root adaptive octree and scaled boundary finite element method

This paper presents a 3D adaptive topology optimization framework that integrates a Multi-Root Adaptive Octree (MRAO) mesh organization with the Scaled Boundary Finite Element Method (SBFEM). The method targets non-cubic and irregular domains for which a single power-of-two octree root can create substantial transient background mesh overhead. Independent roots are combined with hash-based element keys, SBFEM treatment of hanging node polyhedra, and a shared library of 144 precomputed master element stiffness matrices. SBFEM accuracy and analytical sensitivities are verified separately, and the data structure contribution is assessed with a controlled OCT-SBFEM/MRAO-SBFEM cantilever series. Across benchmark Cases 1–3, same-density reanalysis on uniform grids of eight-node hexahedral finite elements gave relative displacement and compliance differences no greater than 1.313 % and 2.759 %, respectively. At the 160 × 32 × 64 target resolution, MRAO-SBFEM was 3.47 times faster and reduced the working set memory by 30.7 %. In a separate end-to-end GE bracket comparison with different initial mesh paths but identical minimum cell size (1 mm) and number of prescribed iterations, MRAO-SBFEM required 27,862 s, while OCT-SBFEM required 143,267 s, corresponding to an observed time ratio of approximately 5.14.