Structure eigenfrequency adjusting using topology optimization with granular material model

Topology optimization has emerged as a significant focus in structural design, renowned for its capacity to meet the demands for high strength, increased stiffness, and minimized weight. The structure of granular materials often displays tension and compression asymmetry similar to biological structures, providing a compelling explanation for the mechanical properties observed in certain biological systems. Optimizing the micro-scale constitutive structure through topology optimization facilitates the attainment of structures exhibiting biological anisotropy. This paper employs the parametric level set method to refine the eigenfrequencies and specific gaps between eigenfrequencies of granular material stru ctures, thereby eliminating the issue of zigzag boundaries in final topologies and ensuring the creation of optimal structures with smooth boundaries. The constitutive relationship of granular materials is formulated by correlating the forces and displacements among spherical granules. A mathematical framework for topology optimization is developed using radial basis function-based parametric level sets. The robustness of this method is substantiated through benchmark problems in topology optimization, exam ining the influence of the tension-compression asymmetry factor on eigenfrequency adjustments. Analysis of the final topologies confirms the reliability and s of the mathematical approach for topology optimization.