Microstructural Topology Optimization for Periodic Beam-Like Structures Using Homogenization Method

As primary load-bearing components extensively utilized in engineering applications, beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements. Combining topology optimization with fully coupled homogenization beam theory, we provide a highly efficient design tool to access desirable periodic microstructures for beams. The present optimization framework comprehensively takes into account for key deformation modes, including tension, bending, torsion, and shear deformation, all within a unified formulation. Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures, e.g., extreme tension (compression)–torsion stiffness, maximization of minimum critical buckling load, and minimization of structural compliance. When optimizing microstructures for macroscopic performance, we emphasize investigating the influence of shear stiffness on the optimized results. The novel chiral beam-like structures are fabricated and tested. The experimental results indicate that the optimized tension (compression)–torsion structure has excellent buffer characteristics, as compared with the traditional square tube. This proposed optimization framework can be further extended to other physical problems of Timoshenko beams.