Topological design optimization of lattice structures to maximize shear stiffness

Abstract To improve the poor shear performance of periodic lattice structure consisting of hexagonal unit cells, this study develops a new computational design method to apply topology optimization to search the best topological layout for lattice structures with enhanced shear stiffness. The design optimization problem of micro-cellular material is formulated based on the properties of macrostructure to maximize the shear modulus under a prescribed volume constraint using the energy-based homogenization method. The aim is to determine the optimal distribution of material phase within the periodic unit cell of lattice structure. The proposed energy-based homogenization procedure utilizes the sensitivity filter technique, especially, a modified optimal algorithm is proposed to evolve the microstructure of lattice materials with distinct topological boundaries. A high shear stiffness structure is obtained by solving the optimization model. Then, the mechanical equivalent properties are obtained and compared with those of the hexagonal honeycomb sandwich structure using a theoretical approach and the finite element method (FEM) according to the optimized structure. It demonstrates the effectiveness of the proposed method in this paper. Finally, the structure is manufactured, and then the properties are tested. Results show that the shear stiffness and bearing properties of the optimized lattice structure is better than that of the traditional honeycomb sandwich structure. In general, the proposed method can be effectively applied to the design of periodic lattice structures with high shear resistance and super bearing property.

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