# Design and Optimization of Lattice Structures: A Review
## 4 Design and Optimization of Non-Uniform Lattices
### Non-Uniform Lattice Structure Based on Structural Optimization  
The optimization method of non-uniform lattice structure usually includes two main steps: (1) defining an infrastructure in the design domain in advance; (2) optimizing single or multiple parameters of each unit cell according to the results of topology optimization, then the non-uniform lattice structure can be obtained. Structural optimization includes size optimization, shape optimization, and topology optimization [183]. By using the structure optimization method, a large number of scholars have optimized the lattice structure. Scholars optimize the strength of the lattice structures by imposing specific constraints such as stress, strain, or load on the lattice structures. Or the researchers optimize the size and shape of the unit cell structure, and obtain the lattice structures with specific performance by studying the elasticity, heat dissipation, and other properties of the lattice structures [191; 202; 203; 204; 205]. For gradient design of non-uniform lattice structures, [PERSON] and [PERSON] [27] proposed a novel method of designing non-uniform lattice structure based on additive manufacturing technology, namely size  
Figure 19: The gradient lattice structure topologies [190]: (**a**) gradient discrete; (**b**) gradient increasing; (**c**) gradient decreasing. Figure 18: Gradient lattice structure generated by top-down Voronoi-tessellation method [186]. gradient method (SGM). Different from the relative density method, [PERSON] et al. took the distribution of unit cell structure of different size as the optimization objective. The specific way was to locate the unit cells in the area with similar unit Young's modulus, replacing the \"relative density model\" of topology optimization with the distribution of cells of different sizes. Then, by using the young's modulus as the transfer medium instead of the \"relative density,\" the mechanical properties of the lattice structure were closer to the topological optimization results. In addition, in order to ensure that the design domain was completely covered by the unit cell, each cell size needed to be discretized into several gradients, and all the size gradients should be integral times of the minimum gradient. Figure 20 is a non-uniform lattice structure generated based on the SGM. [PERSON] et al. [191] proposed a heuristic method of lattice structure size optimization, i.e., size matching and scaling (SMS) method. In this optimization method, the optimization process was simplified into two variables, i.e., the maximum and minimum diameter of the connecting rod. In this method, first, the stress distribution of the lattice structure with intermediate scale similar to the stress distribution of the solid structure was observed, and then based on the local stress state, the cell structure was selected from the predefined cell library to complete the pre-designed lattice cell structure. Then, by optimizing the element of the support structure, the size of the lattice structure was adjusted to support the stress state. However, the load constraints of the lattice structure prepared by this method were limited, i.e., there was only one load. Figure 21 was the fuselage of the micro air vehicle with high strength, high rigidity and light weight designed by SMS method. [PERSON] and [PERSON] [205] proposed a topology optimization method of variable density non-uniform lattice structure. This method mainly adopted three key technologies: homogenization, optimization,  
Figure 21: Non-uniform lattice structure based on SMS method [191]. Figure 20: Non-uniform lattice structure based on SGM method [27]. and construction (HOC). By introducing the constitutive law of homogenized material, the equivalent continuous solid was used to represent the lattice structure. The constitutive law of homogenized material was a function of the characteristic parameters of the lattice microstructure, such as the relative density and the orientation of the lattice.