# Design and Optimization of Lattice Structures: A Review
## 2 Lattice Structures  
### The Definition and Classification of Lattice Structure  
As for the definition of lattice structures, [PERSON] and [PERSON] defined early the structures in which the cell walls have a common generator as two-dimensional cellular structures like honeycombs, and defined the structures in which cell walls have random orientations in space as three-dimensional cellular structures like foams [2]. However, there is still no unified concept about the definition of lattice structures, because the topology structures of lattices are not limited to only changing size of struts and connection mode of cells. Many scholars have their own understanding of lattice structures based on [PERSON] and [PERSON]'s definition of lattice structures. Generally speaking, lattice structures are defined as the three-dimensional structures composed of consecutively and repeatedly arranged interconnected cells, which can also be understood as a porous material structure composed of interconnected struts and nodes in three-dimensional space [69; 70; 71; 72]. [PERSON] et al. defined lattice structure as an architecture formed by an array of spatial periodic unit cells with edges and faces [7]. [PERSON] et al. defined lattice structure as the truss-like structure with interconnected struts and nodes in three-dimensional space [23]. [PERSON] et al. defined lattice structure as the porous and hollow structure formed by arranging unit cells in three-dimensional space [73]. [PERSON] et al. defined lattice structure as the space-filling unit cell that is able to be tessellated along any axis with no gaps between the cells [74]. There is a common point in the above definitions of lattice structure, that is, lattice structure is a three-dimensional space structure. For all that, there are still shortcomings in the above definition of lattice structure. For example, [PERSON]'s definition of lattice structure [7] only emphasizes the periodic unit cells arrangement but ignores the aperiodic unit cells. Moreover, the gradient lattice structure appears in the structural design, which cannot be defined by distinguishing periodic and aperiodic unit cells arrangement. As for the classification of lattice structures, according to the arrangement of unit cells in lattice structures, lattice structures are generally divided into random lattice structures and periodic lattice structures [2; 4; 7; 10]. With the design and optimization of topology structures, [PERSON] and [PERSON] proposed the conformal lattice structures originally [75]. Compared with periodic lattice structures, conformal lattice structures can strengthen or consolidate complex surfaces. [PERSON] et al. [23] described the classification of lattice structures in detail. They divided lattice structures into three categories, the first category is random lattice structures or disordered lattice structures (as shown in Figure 2a). The unit cells of random lattice structures are randomly distributed in the design space, and have different topological structures and sizes. The second category is periodic lattice structures. This kind of lattice structures can be regarded as the structure formed by periodic repeated arrangement of lattice cells with certain shape, topology, and size in three-dimensional Euclidean space (as shown in Figure 2b). The third kind is pseudo periodic lattice structures (also called conformal lattice structures). In pseudo lattice structures (i.e., conformal lattice structures proposed by [PERSON] and [PERSON]), each unit cell only has the same topology, but its size is different (as shown in Figure 2c). Although lattice structures are divided into random, periodic, and pseudo, they can represent the unit cells arrangement in space, it is difficult to represent the unit cells arrangement form for gradient lattice structure.