Smooth topological design of material microstructures based on floating projection

Topology optimization stands as a pivotal technique in realizing periodic microstructure design. A novel approach is proposed, integrating the energy-based homogenization method with the Floating Projection Topology Optimization (FPTO) method to achieve smooth topology design. The objective is to optimize the periodic microstructure to maximize the properties of specific materials, such as bulk modulus and shear modulus, or to achieve negative Poisson’s ratio. Linear material interpolation is used to eliminate the nonlinear challenges and design dependence caused by material penalty. Furthermore, the three-field density representation technique is applied to augment length scales and solid/void characteristics. Through systematic analysis and numerical simulations, the impacts of various initial designs and optimization parameters on the optimization outcomes are investigated. The results demonstrate that the optimized periodic microstructures exhibit extreme performance with clear boundaries. The identification of appropriate optimization parameters is crucial for enhancing the extreme mechanical properties of material microstructures. It can provide valuable guidance for aerospace component design involving material microstructures and metamaterials.