Topological design of multi-cell hexagonal tubes under axial and lateral loading cases using a modified particle swarm algorithm

Multi-cell structures have widely been studied due to their excellent energy absorption ability. However, few systematic studies have been conducted on the topological design of cross-sectional configurations of thin-walled tubes. To make full use of the material, topology optimization of multi-cell hexagonal tubes was conducted under both axial compression and lateral bending loadings. A binary particle swarm optimization (PSO) was enhanced by introducing the mass constraint factor to guide the movement of particles, which could improve the success rate of obtaining the global optimum. It was found that the optimum designs under the axial load placed the material outward to strengthen the interaction between the outer and inner walls and created more partitions between the inside rib walls. While under the lateral load, all the optimum designs have diagonally-connected elements to resist local deformation, and the material was also placed outward to increase the moment of inertia and thus to resist the global deformation. For the multiple loading cases, the final optimal designs are similar to the compression designs or combined designs from the two loading cases.