# Design of a Distributedly Active Morphing Wing Based on Digital Metamaterials

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Reversibly Assembled Active Morphing Lattice Structures

#### 2.1. Building-Block Concept

#### 2.2. Fundamental Cells

^{®}is selected here. This material can be additively manufactured through a stereo-lithography process, which has a good fatigue property and a high machining accuracy. Considering the curing process, its specific mechanical properties are shown in Table 1.

#### 2.2.1. Rigid Cell

#### 2.2.2. Compliant Cell

#### 2.2.3. Auxetic Cell

#### 2.3. Derived Cells

#### 2.4. Reversible Assembly Manner

## 3. Optimization Methodology

#### 3.1. Encoding and Decoding

#### 3.2. Selection

#### 3.3. Crossover

^{(1)}and x

^{(2)}, and the two offspring individuals after the crossover are y

^{(1)}and y

^{(2)}, the crossover process can be illustrated with the following equations:

#### 3.4. Mutation

#### 3.5. Changing Number of Design Variables

#### 3.6. Optimization Model and Results

^{3}kg/m

^{3}and the weight of a micro-actuator is approximately 0.03 kg, the final overall weight is 0.5602 kg; as the overall space volume is 0.0139 m

^{3}, the final macro density is calculated as 40.4964 kg/m

^{3}, which is very close the critical value of the ultralight materials (below 10 kg/m

^{3}) [46]. Therefore, it can be said that the concept has an obvious weight advantage compared with other traditional metal materials (or non-ultralight structures).

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of variable thickness wing based on digital metamaterial with varied cell geometries.

**Figure 2.**Two-dimensional schematic diagram of the design of the distributed variable thickness structure based on digital metamaterials.

**Figure 3.**Three types of fundamental cells: (

**a**) Rigid cell; (

**b**) Compliant cell; and (

**c**) Auxetic cell.

**Figure 4.**The finite element models of the three types of fundamental cells for macro-mechanical performance analysis, for instance, with 3 × 3 × 3 unit cells: (

**a**) Rigid lattice; (

**b**) Compliant lattice; and (

**c**) Auxetic lattice.

**Figure 5.**The deformation mechanism diagram and geometric parameter of the rigid unit cell: (

**a**) Deformation mechanism of the rigid cell under an external load; (

**b**) The beam section size of the rigid cell (L = 70 mm).

**Figure 6.**Mechanical properties of the rigid lattice. (

**a**) The relationship between the elastic modulus and the cube side length of the rigid lattice (t = 2.5–4.5 mm); (

**b**) The relationship between the Poisson’s ratio the cube side length of the rigid lattice (t = 2.5–4.5 mm).

**Figure 7.**The deformation mechanism diagram and one of the geometric parameters of the compliant unit cell: (

**a**) Deformation mechanism of the compliant cell under an external load; (

**b**) Different S-shaped bulge heights of the compliant cell (L = 70 mm).

**Figure 8.**Mechanical properties of the compliant lattice with different S-shaped heights: (

**a**) The relationship between the elastic modulus and the cube side length (with H = 0.1–0.2 L); (

**b**) The relationship between the Poisson’s ratio and the cube side length (with H = 0.1–0.2 L).

**Figure 9.**Schematic diagram of different geometric parameters of the S-shaped bulge of the facet element of the compliant cell: (

**a**) different widths of the S-shaped bulge; (

**b**) schematic of the beam section size of the compliant cell.

**Figure 10.**Mechanical properties of compliant lattice with different S-shaped bulge widths and beam section sizes: (

**a**) The relationship between the elastic modulus and the cube side length (W = 0.05–0.09 L); (

**b**) The relationship between the Poisson’s ratio and the cube side length (W = 0.05–0.09 L); (

**c**) The relationship between the elastic modulus and the cube side length (t = 0.5–4.5 mm); and (

**d**) The relationship between the Poisson’s ratio and the cube side length (t = 0.5–4.5 mm).

**Figure 11.**The deformation mechanism diagram and different geometric parameters of the auxetic unit cell: (

**a**) Deformation mechanism of the auxetic cell under an external load; (

**b**) Different concave depths of the auxetic cell (L = 70 mm); (

**c**) Shematic diagram of the beam section size of the auxetic cell.

**Figure 12.**Mechanical properties of the auxetic lattice: (

**a**) The relationship between the elastic modulus and the cube side length (d = 0.2 L~0.4 L); (

**b**) The relationship between the Poisson’s ratio and the cube side length (d = 0.2L~0.4 L); (

**c**) The relationship between the elastic modulus and the cube side length (t = 0.5 mm~4.5 mm); and (

**d**) The relationship between the Poisson’s ratio and the cube side length (t = 0.5 mm~4.5 mm).

**Figure 17.**Component-level facet elements: (

**a**) Facet element of the rigid cell; (

**b**) Facet element of the compliant cell; (

**c**) Facet element of the auxetic cell.

**Figure 20.**Diagram of the corresponding relationship between a specific sequence and its cell combination configuration.

**Figure 24.**The comparison between the target curve and the final curve of the optimal cell arrangement.

Tensile Modulus | Poisson’s Ratio | Ultimate Tensile Strength | Elongation | Method | |
---|---|---|---|---|---|

Non-cured | 0.45 Gpa | 0.3 | 18.6 MPa | 0.67 | ASTM D 638-10 |

Post-cured | 1.26 Gpa | 0.3 | 31.8 Mpa | 0.49 | ASTM D 638-10 |

Rigid Cell | Compliant Cell | Auxetic Cell | Tensile Cell | Bending Cell | Actuator Cell | |
---|---|---|---|---|---|---|

Number of the unit cells | 10 | 6 | 3 | 6 | 3 | 5 |

Material volume of a unit cell (m^{3}) | 1.1090 × 10^{−5} | 1.4110 × 10^{−5} | 0.9059 × 10^{−5} | 1.3103 × 10^{−5} | 1.2096 × 10^{−5} | 1.4110 × 10^{−5} |

Weight of a unit cell (kg) | 1.1145 × 10^{−2} | 1.4180 × 10^{−2} | 0.9104 × 10^{−2} | 1.3168 × 10^{−2} | 1.2156 × 10^{−2} | 6.4180 × 10^{−2} |

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**MDPI and ACS Style**

Wang, Z.; Wu, Q.; Lu, Y.; Bao, P.; Yang, Y.; Li, D.; Sun, X.; Xiang, J.
Design of a Distributedly Active Morphing Wing Based on Digital Metamaterials. *Aerospace* **2022**, *9*, 762.
https://doi.org/10.3390/aerospace9120762

**AMA Style**

Wang Z, Wu Q, Lu Y, Bao P, Yang Y, Li D, Sun X, Xiang J.
Design of a Distributedly Active Morphing Wing Based on Digital Metamaterials. *Aerospace*. 2022; 9(12):762.
https://doi.org/10.3390/aerospace9120762

**Chicago/Turabian Style**

Wang, Zhigang, Qi Wu, Yifei Lu, Panpan Bao, Yu Yang, Daochun Li, Xiasheng Sun, and Jinwu Xiang.
2022. "Design of a Distributedly Active Morphing Wing Based on Digital Metamaterials" *Aerospace* 9, no. 12: 762.
https://doi.org/10.3390/aerospace9120762