# Wrapping Deployment Simulation Analysis of Leaf-Inspired Membrane Structures

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## Abstract

**:**

## 1. Introduction

## 2. The Deployment Patterns

#### 2.1. The One-Leaf Unit

_{i}, β

_{i}(i = 0,1 … n). The assumption about the geometrical angles defining the creases is given by:

_{i}= β

_{i},

_{i}are expressed as:

_{i}can be expressed as:

#### 2.2. Candidate Deployment Patterns

## 3. Deployment Simulation of Wrapping Membrane Structures

#### 3.1. Form-Finding

#### 3.2. Deployment Simulation

#### 3.3. Deployment Responses

_{i}is the distance from node i to the ideal plane. For the structural settings illustrated in Figure 9f, Figure 10f and Figure 11f, the coordinates for the 3 corner nodes are summarized in Table 1. A, B, C are the three loading points of the thin membrane driving position. The equations of the plane defined by these three nodes are also given. The smoothness indexes of the folded patterns are 1.348618 mm, 0.95647 mm, and 1.0080 mm, respectively.

## 4. Crease Optimization Strategy

#### 4.1. Creases Distribution

#### 4.2. Deployment Performance

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Three typical deployable patterns of the one-leaf unit around the hub. (

**a**) Type 1; (

**b**) Type 2; (

**c**) Type 3.

**Figure 4.**Three typical deployable patterns of plane wrapping origami membrane structures. (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3.

**Figure 5.**Folding sequences of the origami model of Pattern 1. (

**a**) Completely deployed; (

**b**) Folding process 1; (

**c**) Folding process 2; (

**d**) Completely folded.

**Figure 6.**Folding sequences of the origami model of Pattern 2. (

**a**) Completely deployed; (

**b**) Folding process 1; (

**c**) Folding process 2; (

**d**) Completely folded.

**Figure 7.**Folding sequences of the origami model of Pattern 3. (

**a**) Completely deployed; (

**b**) Folding process 1; (

**c**) Folding process 2; (

**d**) Completely folded.

**Figure 8.**Form-finding of Patterns 1–3. (

**a**) Pattern 1: (

**i**) Before form-finding, (

**ii**) After form-finding; (

**b**) Pattern 2: (

**i**) Before form-finding, (

**ii**) After form-finding; (

**c**) Pattern 3: (

**i**) Before form-finding, (

**ii**) After form-finding.

**Figure 9.**Locations of constraints and loadings on the FE model. (

**a**) Fully folded state (

**b**) Fully deployed state.

**Figure 10.**Stress contour plot of Pattern 1 during deployment (MPa). (

**a**) Fully folded state; (

**b**) 10% deployment; (

**c**) 30% deployment; (

**d**) 50% deployment; (

**e**) 70% deployment; (

**f**) 100% deployment.

**Figure 11.**Stress contour plot of Pattern 2 during deployment (MPa). (

**a**) Fully folded state; (

**b**) 10% deployment; (

**c**) 30% deployment; (

**d**) 50% deployment; (

**e**) 70% deployment; (

**f**) 100% deployment.

**Figure 12.**Stress contour plot of Pattern 3 during deployment (MPa). (

**a**) Fully folded state; (

**b**) 10% deployment; (

**c**) 30% deployment; (

**d**) 50% deployment; (

**e**) 70% deployment; (

**f**) 100% deployment.

**Figure 16.**Schematic diagram of two different variants of Pattern 2. (

**a**) Pattern 2a: Adding two creases; (

**b**) Pattern 2b: Adding four creases.

**Figure 17.**Stress contour diagram of the deploying process of Patterns 2a (MPa). (

**a**) Fully folded state; (

**b**) 10% deployment; (

**c**) 30% deployment; (

**d**) 50% deployment; (

**e**) 70% deployment; (

**f**) 100% deployment.

**Figure 18.**Stress contour diagram of the deploying process of Patterns 2b (MPa). (

**a**) Fully folded state; (

**b**) 10% deployment; (

**c**) 30% deployment; (

**d**) 50% deployment; (

**e**) 70% deployment; (

**f**) 100% deployment.

Pattern | Coordinate | A | B | C | Equation of Idea Planes |
---|---|---|---|---|---|

Pattern 1 | X | −59.751 | −45.048 | −41.672 | 120.86 z-2752.02 = 0 |

Y | 146.414 | 162.394 | 157.843 | ||

Z | 22.770 | 22.770 | 22.770 | ||

Pattern 2 | X | −70.9675 | −40.9819 | −28.8771 | 480.35 z-21,884.55 = 0 |

Y | 154.728 | 150.593 | 164.943 | ||

Z | 45.5599 | 45.5599 | 45.5599 | ||

Pattern 3 | X | 137.304 | 137.235 | 138.985 | 5.85 z-195.40 = 0 |

Y | −210.955 | −213.832 | −225.654 | ||

Z | 33.3995 | 33.3995 | 33.3712 |

Pattern | Maximum Stress (MPa) | Maximum Driving Force (N) | Maximum Strain Energy (mJ) | Smoothness Index (mm) | Folding Height (cm) |
---|---|---|---|---|---|

Pattern 1 | 75 | 5.22 | 19.81 | 1.49 | 46.19 |

Pattern 2 | 55 | 0.28 | 4.18 | 0.96 | 138.56 |

Pattern 3 | 60 | 1.51 | 3.35 | 1.01 | 69.28 |

Pattern | Coordinate | A | B | C |
---|---|---|---|---|

Pattern 2a | X | 94.3535 | 92.3292 | 90.1491 |

Y | 40.4019 | 42.3878 | 46.1852 | |

Z | 50.4973 | 50.4973 | 50.4973 | |

Pattern 2b | X | 50.6343 | 42.6613 | 30.7569 |

Y | 66.5513 | 80.6865 | 73.4856 | |

Z | 31.2555 | 31.2555 | 31.2555 |

Pattern | Maximum Stress (MPa) | Maximum Driving Force (N) | Maximum Strain Energy (mJ) | Smoothness Index (mm) | Folding Height (cm) |
---|---|---|---|---|---|

Pattern 2 | 55 | 0.28 | 4.18 | 0.96 | 138.56 |

Pattern 2a | 66 | 0.30 | 5.86 | 1.20 | 69.39 |

Pattern 2b | 78 | 0.33 | 6.38 | 1.49 | 46.19 |

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**MDPI and ACS Style**

Lin, Q.; Jia, W.; Wu, H.; Kueh, A.B.H.; Wang, Y.; Wang, K.; Cai, J.
Wrapping Deployment Simulation Analysis of Leaf-Inspired Membrane Structures. *Aerospace* **2021**, *8*, 218.
https://doi.org/10.3390/aerospace8080218

**AMA Style**

Lin Q, Jia W, Wu H, Kueh ABH, Wang Y, Wang K, Cai J.
Wrapping Deployment Simulation Analysis of Leaf-Inspired Membrane Structures. *Aerospace*. 2021; 8(8):218.
https://doi.org/10.3390/aerospace8080218

**Chicago/Turabian Style**

Lin, Qiuhong, Wenwen Jia, Huiying Wu, Ahmad B. H. Kueh, Yutao Wang, Kexin Wang, and Jianguo Cai.
2021. "Wrapping Deployment Simulation Analysis of Leaf-Inspired Membrane Structures" *Aerospace* 8, no. 8: 218.
https://doi.org/10.3390/aerospace8080218