# Design and Optimization of Lattice Structures: A Review
## 1 Introduction
For example, in the field of aerospace, structural design not only requires excellent mechanical properties, but also meets the requirements of lightweight materials. In this way, scientific materials with low cost and high performance can be realized and achieved. With the application of cellular structure, it reduces the weight of structure, and realizes the design application of lightweight and high strength. Taking truss structure as an example, the hollow truss structure designed by filling the truss with cellular material has higher second-order moment of inertia. Compared with the solid truss structure, the cellular structure can improve the bearing capacity of the truss [28]. However, in terms of application, foams, honeycombs and lattices are not exactly the same (as listed in Table 1). Although these three structures have common applications such as aerospace, automotive, marine, and biomedical engineering, and so on, lattice structures are more widely used because of satisfying specific functional requirements. In view of the excellent properties, various unit cells and wide applications of lattice structures among cellular structures (including foams, honeycombs and lattices), lattice structures are becoming the research hot topic in academia and worthy to be reported. Compared with the review literature [33; 48; 66; 67; 68] of cellular structures, this manuscript has the following innovative perspectives about lattice structures. \begin{table}
\begin{tabular}{c c} \hline
**Type of Cellular Structures** & **Applications** \\ \hline \multirow{2}{*}{Foams} & Energy absorbers [1; 2; 8; 9], Filters [9; 29], Silencers [9], Flame arresters [9], \\  & Heaters and heat exchangers [9; 29], Electro-chemical devices [9; 29]. \\ \hline \multirow{2}{*}{Honeycombs} & Energy absorbers [1; 2; 15; 30; 31; 32; 33], Biomedical implants [30; 31; 32], Filters [34; 35], \\  & Sensors [34; 35], Actuators [34; 35], Vibration absorber or damper [36; 37; 38; 39]. \\ \hline \multirow{4}{*}{Lattices} & Energy absorbers [1; 2; 40; 41; 42], Heaters and heat exchangers [23; 27; 43; 44; 45; 46], \\  & Engine hood [47], Biomedical implants [48; 49; 50; 51; 52; 53; 54; 55], Wings [56], Gas turbine \\ \cline{1-1}  & engine fan blades [57], Vibration absorber [58; 59; 60; 61], Robotic system [62], \\ \cline{1-1}  & Spacecraft and aircraft structures (i.e., fuselage, rib) [63; 64; 65]. \\ \hline \end{tabular}
\end{table} 
Table 1: Applications of cellular structures. Figure 1: Different types of cellular structures: (a) foam [2]; (b) honeycomb; (c) lattice structure [20]. 1. The manuscript especially distinguishes the differences between lattices and foams and honeycombs from aspects of structure and properties. Additionally, the manuscript divides lattice structures into cellular structures. 2. The manuscript reviews the definition and classification, properties and applications, and manufacturing methods of lattice structures. Especially, there are some shortcomings in the definition of lattice structures in some literature. Therefore, based on the understanding of lattice structures, the definition is given new content, which makes the definition more perfect. 3. The most excellent work is to reclassify the lattice structures, which is divided into uniform lattice structure and non-uniform lattice structure. The design and optimization methods of lattice structure are reviewed comprehensively over existing literature. 4. The manuscript also emphasizes the lattice structure of non-uniform Poisson's ratio, which is rarely involved in other literature. The lattice structures with different Poisson's ratios are discussed in detail. Consequently, in the second part of the manuscript, the definition and classification, properties and applications, and manufacturing methods of lattice structures are introduced. In the third part, different methods of designing and optimizing uniform lattice structures are reviewed. Similarly, different methods of designing and optimizing non-uniform lattice structures are reviewed in the fourth part of this paper.