Based on the growth mechanism of natural biological branching systems and inspiration from the morphology of plant root tips, a bionic design method called Improved Adaptive Growth Method (IAGM) has been proposed in the authors’ previous research and successfully applied to the reinforcement optimization of three-dimensional box structures with respect to natural frequencies. However, as a kind of ground structure methods, the final layout patterns of stiffeners obtained by using the IAGM are highly subjected to their ground structures, which restricts the optimization effect and freedom to further improve the dynamic performance of structures. To solve this problem, a novel post-processing geometry and size optimization approach is proposed in this article. This method takes the former layout optimization result as start, and iteratively finds the optimal layout angles, locations, and lengths of stiffeners with a few design variables by optimizing the positions of some specific node lines called active node lines. At the same time, thicknesses of stiffeners are also optimized to further improve natural frequencies of three-dimensional box structures. Using this method, stiffeners can be successfully separated from their ground structures and further effectively improve natural frequencies of three-dimensional box structures with less material consumption. Typical numerical examples are illustrated to validate the effectiveness and advantages of the suggested method.

Tuned Mass Dampers (TMDs) are often attached to a main structure to reduce vibration, and the TMDs’ positions are important to affect the structural dynamic performance. However, the TMDs’ positions and the material layout of the structure act on each other. This paper suggests a design optimization method by combining the topology optimization of the main structure and the layout of the attached TMDs under harmonic excitations. The main structure with the attached TMDs are modeled by the continuum FEA method to consider the change of TMDs’ locations. Then they are optimized simultaneously by introducing a multi-level optimization frame, which includes the structural topology optimization and the optimal tuning of TMDs. The locations and damping parameters of TMDs are optimized in every step of the SIMP-based topology optimization of the main structure, so as to fully consider the interactions between each other to improve the dynamic performance. Numerical examples of cantilever structures are studied, and the results show that when the main structure and TMDs are optimized simultaneously, the modal strain energy is more concentrated compared with that obtained by the non-simultaneous optimization approach. Therefore, the dynamic compliance of the target mode is dramatically reduced.