Design and optimization of high stiffness tetrahedral lattice structure

Abstract

As tetrahedra are well known for their stability and excellent load-bearing capabilities, this work proposes a novel method for designing and optimizing high-stiffness tetrahedral lattice structures. First, the tetrahedral lattice cells with periodic boundary conditions are generated within a unit cubic domain based on a specified number and radii of randomly distributed seed points. By analyzing the printability of the lattice cell, several constraints are introduced to restrict both the number of seed points and their radii within each lattice cell. Next, the relationships among the number of seed points, radii, relative density, Young’s modulus, and anisotropy of the lattice cells are analyzed using the homogenization method. For a given design domain, it is discretized into a hexahedral finite element mesh. A topology optimization formulation is then proposed to optimize the number of seed points and their radii across all finite elements. The seed points are randomly sampled within each finite element according to the optimized number and radius. Finally, a strut-shaped tetrahedral lattice with variable radii is generated based on the seed points and their radii. Additionally, a strategy is introduced to eliminate struts in low-density regions to further enhance structural stiffness. Extensive numerical and physical experiments, along with comparisons, have been conducted to demonstrate the effectiveness of the proposed method.