# Bioinspired Design for Lightweighting and Vibration Behavior Optimization in Large-Scale Aeronautical Tooling: A Comparative Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Selected Methodologies and Software

## 3. Use Case Presentation

#### 3.1. Material

^{3}, Poisson’s Ratio of 0.33, and yield stress of 170 MPa which can be regarded as moderate [35]. Cu- or Zn-based Al alloys could show better properties, but their viscosity is higher, putting the manufacturing process at risk.

#### 3.2. Loads, Constraints, and Objectives

- (1)
- 1000 N for each fixation in −X direction
- (2)
- 1000 N for each fixation in +X direction
- (3)
- 1000 N for each fixation, upper fixation with −X and the lower fixation with +X direction
- (4)
- 1000 N for each fixation, upper fixation with +X and the lower fixation with −X direction

^{2}and it is assumed that the average thickness of the covering of the structure is 5 mm (it can vary between 1 and 10 mm). The total volume of the material of the wing’s covering would be:

## 4. Designing Methodology for Each Software

#### 4.1. Generative Design with Level-Set Topology Optimization (Fusion 360)

#### 4.2. SIMP Topology Optimization (Altair Optistruct)

#### 4.3. Hybrid Method (Generative Engineering) (Synera)

## 5. Results

## 6. Discussion

- Mass: 100 kg to reduce the mass to 30% of the reference design. If the design is lighter than this limit; it would be accepted.
- First eigenfrequency: Minimum first natural frequency of 60 Hz. All the designs with a lower value are rejected.
- Safety factor: Limit of a minimum safety factor 40 as a sufficiently laudable value for tooling structures. Values below this limit are rejected.
- Deformation to height ratio: Two different values for two different studies, one for the load cases (operational and structural) and other for the case of resonance. The limit was set to a value a bit bigger than the average of all, so the most deviated deformations are discarded. Thus, the results above those limits are rejected.

^{6}cycles and with the Goodman criteria, as can be seen in Figure 15. As predicted, with the load case studied here, the outcome is far from the Goodman line, which means that it is far from failure because of fatigue.

## 7. Design Validation

**Figure 19.**The FRF of the signal from one of the acquisition nodes in two directions X and Y (

**Up**). The results comparison of the generic material properties selected for the FEA (

**left**) and the results of the modal test (

**right**) (

**Down**).

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Darwin, C. On the Origin of Species by Means of Natural Selection, or Preservation of Favoured Races in the Struggle for Life; Murray: London, UK, 1859. [Google Scholar]
- Dawkins, R. The Blind Watchmaker; Penguin: London, UK, 1986. [Google Scholar]
- Ball, P. The Self-Made Tapestry: Pattern Formation in Nature; Oxford University Press: Oxford, UK, 1999. [Google Scholar]
- Romanesco broccoli (Brassica oleracea)-Romanesco broccoli-Wikipedia. Available online: https://en.wikipedia.org/wiki/Romanesco_broccoli#/media/File:Romanesco_broccoli_(Brassica_oleracea).jpg (accessed on 16 November 2023).
- Dragonfly Wings|Zoomed/Cropped Previous Image|Joi Ito|Flickr. Available online: https://www.flickr.com/photos/35034362831@N01/698898343/ (accessed on 16 November 2023).
- Blue Spotted Tail|Juan Castillo|Flickr. Available online: https://www.flickr.com/photos/chichondepiso/6731055529/in/photolist-bfNqix-ofqCew-MTsGYF-c5hU5E-a74H7y-21eheAY-9bXSSH-dFb8S9-aAHNwq-rYDDr-rUmro5-pjjZCp-cYWGyu-fw3EwR-GAhdHi-x3zzW9-bE1n6c-adNozF-8Dtr4J-5QwnuT-4txraD-9DRAzc-aDYxdc-6sKj9Z-qPjxE-HkLM1E-sr4Ui6-8zd6Cg-7QNe5o-npbycC-2Wb6RR-rPjuZ3-4icMq1-8HCLSG-GF7EBR-8MwLDC-6NVKEL-97P7Fc-97Sckm-6ePDLb-9BaDav-uzJYG-5Xckee-nqfPQ5-FUqYcy-BE9e1v-WXWsZd-UqKJAk-oUi6iG-7VETQV (accessed on 16 November 2023).
- Nautilus|Rainy City|Flickr. Available online: https://www.flickr.com/photos/furphotos/49872038707/in/photolist-2iZ2eAk-bAgCtn-bnmKFj-bAgCuM-2jZ7M9t-2o8zTsg-218C3j7-ybG5G-2oTojx5-8cK6F-9DD41-poF65L-66bdaX-76Z85Z-5zabUM-2o8AmUP-4gLaTS-EQttEk-CX4awT-2k1We5g-2oTpUCr-2oTpsLi-GFVW2A-43SQwS-7MHNXa-SD35RF-2hqyB9z-29gVZDZ-4F5vC1-2iWahCf-4iQY7z-2oTpTDN-Ff7m8u-oypGFH-4749L4-7Kc7Mh-dUM7DS-2oFQyvB-4dXFJp-53YtUb-2aUA3CU-2fp34-e4vvaC-2oTjtw3-23dSG8N-9aZ5XG-2mRES1y-a6xPCF-a7oFDC-61RyuY (accessed on 27 November 2023).
- Schmitt, O. Some interesting and useful biomimetic transforms. In Proceedings of the Third International Biophysics Congress, Boston, MA, USA, 29 August–3 September 1969. [Google Scholar]
- Benyus, J.M. Biomimicry: Innovation Inspired by Nature; Morrow: New York, NY, USA, 1997. [Google Scholar]
- Steele, J.E. Living prototypes. In Bionics Symposium; Directorate of Advanced Systems Technology, Wright Air Development Division, Air Research and Development Command, U.S. Air Force: Fairfax County, VA, USA, 1960. [Google Scholar]
- Hashemi Farzaneh, H.; Lindemann, U. A Practical Guide to Bio-Inspired Design; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar] [CrossRef]
- Nachtigall, W.; Wisser, A. Bionics by Examples: 250 Scenarios from Classical to Modern Times; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- du Plessis, A.; Broeckhoven, C.; Yadroitsava, I.; Yadroitsev, I.; Hands, C.H.; Kunju, R.; Bhate, D. Beautiful and Functional: A Review of Biomimetic Design in Additive Manufacturing. Addit. Manuf.
**2019**, 27, 408–442. [Google Scholar] [CrossRef] - Vaneker, T.; Bernard, A.; Moroni, G.; Gibson, I.; Zhang, Y. Design for additive manufacturing: Framework and methodology. CIRP Annals.
**2020**, 69, 578–599. [Google Scholar] [CrossRef] - Li, J.; Huang, Z.; Liu, G.; An, Q.; Chen, M. Topology optimization design and research of lightweight biomimetic three-dimensional lattice structures based on laser powder bed fusion. J. Manuf. Process.
**2022**, 74, 220–232. [Google Scholar] [CrossRef] - Zhao, Y.F.; Sun, S.; Velivela, P.T.; Letov, N. Challenges and Opportunities in Geometric Modeling of Complex Bio-Inspired Three-Dimensional Objects Designed for Additive Manufacturing. J. Mech. Des. Trans. ASME
**2021**, 143, 121705. [Google Scholar] [CrossRef] - Saadlaoui, Y.; Milan, J.L.; Rossi, J.M.; Chabrand, P. Topology optimization and additive manufacturing: Comparison of conception methods using industrial codes. J. Manuf. Syst.
**2017**, 43, 178–186. [Google Scholar] [CrossRef] - Buonamici, F.; Carfagni, M.; Furferi, R.; Volpe, Y.; Governi, L. Generative design: An explorative study. Comput. Aided Des. Appl.
**2020**, 18, 144–155. [Google Scholar] [CrossRef] - Tee, Y.L.; Maconachie, T.; Pille, P.; Leary, M.; Do, T.; Tran, P. From nature to additive manufacturing: Biomimicry of porcupine quill. Mater Des.
**2021**, 210, 110041. [Google Scholar] [CrossRef] - Al Khalil, M.; Belkebir, H.; Lebaal, N.; Demoly, F.; Roth, S. A Biomimetic Design Method for 3D-Printed Lightweight Structures Using L-Systems and Parametric Optimization. Appl. Sci.
**2022**, 12, 5530. [Google Scholar] [CrossRef] - Breish, F.; Hamm, C.; Kienzler, R. Diatom-inspired stiffness optimization for plates and cellular solids. Bioinspiration Biomim.
**2023**, 18, 036004. [Google Scholar] [CrossRef] - Shangguan, H.; Kang, J.; Deng, C.; Hu, Y.; Huang, T. 3D-printed shell-truss sand mold for aluminum castings. J. Am. Acad. Dermatol.
**2017**, 250, 247–253. [Google Scholar] [CrossRef] - Walker, J.; Harris, E.; Lynagh, C.; Beck, A.; Lonardo, R.; Vuksanovich, B.; Thiel, J.; Rogers, K.; Conner, B.; MacDonald, E. 3D Printed Smart Molds for Sand Casting. Int. J. Met.
**2018**, 12, 785–796. [Google Scholar] [CrossRef] - Walsh, J.; Meintjes, K. Understanding a Generative Design Enabled Design Process Paradigm Shift. ASSESS Initiative, USA 2019. Available online: https://www.nafems.org/publications/resource_center/c_jun_20_americas_99/ (accessed on 15 April 2023).
- Li, B.; Liu, H.; Yang, Z.; Zhang, J. Thin-Walled Structures Sti ff ness design of plate/shell structures by evolutionary topology optimization. Thin Walled Struct.
**2019**, 141, 232–250. [Google Scholar] [CrossRef] - Wolfram, S. Cellular automata as models of complexity. Nature
**1984**, 311, 419–424. [Google Scholar] [CrossRef] - Gen, M.; Lin, L. Genetic algorithms. Wiley Encycl. Comput. Sci. Eng.
**2008**, 6, 1–15. [Google Scholar] - Russell, S.J.; Norvig, P. Artifcial Intelligence: A Modern Approach; Pearson Education Inc.: Upper Saddle River, NJ, USA, 2010. [Google Scholar]
- Savage, R. Fusion 360 Introduction to Generative Design. Available online: https://www.autodesk.com/autodesk-university/article/Fusion-360-Introduction-Generative-Design-2020 (accessed on 15 April 2023).
- intrinSIM LLC: A Vision for Generative Design—A Market Report. IntrinSIM LLC, Georgia, USA, 2019, 1–34. Available online: https://intrinsim.com/PDFs/A%20VISION%20FOR%20GENERATIVE%20DESIGN%20V2_4.pdf (accessed on 15 April 2023).
- Plocher, J.; Panesar, A. Review on design and structural optimisation in additive manufacturing: Towards next-generation lightweight structures. Mater. Des.
**2019**, 183, 108164. [Google Scholar] [CrossRef] - MIDACO-SOLVER. Available online: http://www.midaco-solver.com/ (accessed on 14 November 2023).
- Dwyer-Lindgren, J. Boeing Says Wing Production Has Started for 737 MAX Jets. Available online: https://eu.usatoday.com/story/todayinthesky/2015/06/02/boeing-says-wing-production-has-started-for-737-max-jets/28372587/ (accessed on 14 November 2023).
- Neuser, M.; Grydin, O.; Frolov, Y.; Schaper, M. Influence of solidification rates and heat treatment on the mechanical performance and joinability of the cast aluminium alloy AlSi10Mg. Prod. Eng.
**2022**, 16, 193–202. [Google Scholar] [CrossRef] - Aluminum 360.0-F Die Casting Alloy. Available online: https://www.matweb.com/search/DataSheet.aspx?MatGUID=46cc3a20683748718693cbb6039bec68 (accessed on 27 November 2023).
- Rozvany, G.I.N.; Lewiński, T. CISM International Centre for Mechanical Sciences. 549 Courses and Lectures Topology Optimization in Structural and Continuum Mechanics; International Centre for Mechanical Sciences; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Kaiser, N.; Goossens, N.; Jimenez, A.; Laraudogoitia, I.; Psarras, S.; Tsantzalis, S. Advanced manufacturing concept of a bio-inspired reaction wheel rotor for small- and medium-sized constellation satellites. CEAS Space J.
**2023**, 1, 1–14. [Google Scholar] [CrossRef] - Caggiano, A.; Nele, L.; Teti, R. Drilling of Fiber-Reinforced Composite Materials for Aeronautical Assembly Processes. Intech
**2013**, 32, 137–144. [Google Scholar] - Alonso-Pinillos, U.; Girot-Mata, F.A.; Polvorosa-Teijeiro, R.; López-De-Lacalle-Marcaide, L.N. Taladrado de materiales compuestos: Problemas, prácticas recomendadas y técnicas avanzadas. DYNA-Ing. Ind.
**2017**, 92, 188–194. [Google Scholar] [CrossRef] - Boeing: Boeing Next-Generation 737. Available online: https://www.boeing.com/commercial/737ng/ (accessed on 25 May 2023).
- Hamm, C. Evolution of Lightweight Structures; Springer: Dordrecht, The Netherlands, 2015. [Google Scholar] [CrossRef]
- Hamm, C.E.; Merkel, R.; Springer, O.; Jurkojc, P.; Maiert, C.; Prechtelt, K.; Smetacek, V. Architecture and material properties of diatom shells provide effective mechanical protection. Nature
**2003**, 421, 841–843. [Google Scholar] [CrossRef] - Jongerius, S.R.; Lentink, D. Structural Analysis of a Dragonfly Wing. Exp. Mech.
**2010**, 50, 1323–1334. [Google Scholar] [CrossRef] - Aid, A.; Bendouba, M.; Aminallah, L.; Amrouche, A.; Benseddiq, N.; Benguediab, M. An equivalent stress process for fatigue life estimation under multiaxial loadings based on a new non linear damage model. Mater. Sci. Eng. A
**2012**, 538, 20–27. [Google Scholar] [CrossRef] - Domfang Ngnekou, J.N.; Nadot, Y.; Henaff, G.; Nicolai, J.; Kan, W.H.; Cairney, J.M.; Ridosz, L. Fatigue properties of AlSi10Mg produced by Additive Layer Manufacturing. Int. J. Fatigue
**2019**, 119, 160–172. [Google Scholar] [CrossRef] - Dou, W.; Zhang, L.; Chang, H.; Zhang, H.; Liu, C. Fatigue Characterization on a Cast Aluminum Beam of a High-Speed Train Through Numerical Simulation and Experiments. Chin. J. Mech. Eng. (Engl. Ed.)
**2021**, 34, 108. [Google Scholar] [CrossRef] - Avilés González, R. Análisis de Fatiga en Máquinas; Thomson-Paraninfo: Madrid, Spain, 2005. [Google Scholar]
- Budynas, R.G.; Keith Nisbett., J. Shigley’s Mechanical Engineering Design; McGraw-Hill: New York, NY, USA, 2011. [Google Scholar]
- Pilkey, W.D.; Peterson, R.E. Peterson’s Stress Concentration Factors; Wiley: Hoboken, NJ, USA, 1997. [Google Scholar]
- Yan, Q.; Song, B.; Shi, Y. Comparative study of performance comparison of AlSi10Mg alloy prepared by selective laser melting and casting. J. Mater. Sci. Technol.
**2020**, 41, 199–208. [Google Scholar] [CrossRef] - Sanchez, J.M. Propiedades Tribológicas y de Fatiga de Nuevas Aleaciones de Aluminio Basadas en el Concepto de Alta Entropía. 2021. Available online: https://addi.ehu.es/handle/10810/52941 (accessed on 30 May 2023).

**Figure 2.**The wing skin panels for Boeing’s first 737 MAX airplane are loaded on fixtures into an automated assembly machine in the company’s plant in Renton, Wash., on 2 June 2015 (source: [33]) [

**left**]. The simplified reference design of the assembly column based on the fixtures used in assembly lines [

**right**].

**Figure 3.**Operational load case graphic expression. (1) 1000 N for each fixation in −X direction. (2) 1000 N for each fixation in +X direction. (3) 1000 N for each fixation, upper fixation with −X and the lower fixation with +X direction. (4) 1000 N for each fixation, upper fixation with +X and the lower fixation with −X direction.

**Figure 4.**Outside boundary of the obstacle geometry (

**left**) and preserve geometry and tool clearance obstacle geometry (

**right**) of the Fusion 360 simulation.

**Figure 6.**Design space (

**left**) and non-design geometry (

**right**) for Altair Optistruct Topology Optimization.

**Figure 7.**(

**A**) Optistruct topology optimization result in element density plot. (

**B**) Outcome of the simulation translated into a solid.

**Figure 9.**The Voronoi distribution according to the load lines from Topology Optimization (

**left**). Skeleton lines extracted from the Topology Optimization (

**right**).

**Figure 10.**Evolution of designs in Elise/Synera. Reference design, Skeleton design, and Voronoi design.

**Figure 11.**Representation of the results in a percentage scale so it is possible to compare each of the designs with the others. Furthermore, a limit has been set to accept the outcomes. This limit is represented as a black dashed line and the yellow shaded areas are the ones that serve as graphic representations of acceptable values for each of the factors. Artwork made with MS Excel.

**Figure 12.**(

**Top**) Von Mises equivalent stress diagram in MPa for the 5 solutions with the initial load cases. (

**Middle**) Deformation in mm of the 5 solutions for the initial load cases (

**Bottom**).

**Figure 13.**Maximum equivalent Von Mises stress for the worst load case scenario in the Voronoi outcome.

**Figure 14.**Bending of an infinite and of a finite width plate with a single elliptical hole stress concentration factor case as defined by [49] (

**top**). The case analyzed in this study with the real dimensions (

**bottom**).

**Figure 15.**S-N curve for AlSi10Mg alloy and the modified curve to meet the axial tension samples (

**left**). Goodman line and the situation of the outcome for the studied load case (

**right**).

**Figure 16.**Changes in the structure according to the manufacturing constraints. Wall thickness correction bigger than 7 mm (

**left**) and rounding of sharp edges (

**right**).

**Figure 17.**Part manufactured after the demolding. Filling and feeding systems are also shown in this image at Tecnalia’s facilities (

**left**). Inner Skeleton features (

**right**).

**Figure 18.**Modal test configuration for free vibration conditions with the data-acquisition device, the accelerometer in the top right area of the part, and the hammer at UPV/EHU’s facilities.

Handling Appropriate Objectives and Constraints | Handling Transitions from Solid to Lattice | Handling Multiple Manufacturing Processes | Handling Cost as an Objective Constraint | Enabling Informed, Comprehensive and Efficient Exploration of the Viable Design Alternatives | Enabling Efficient & Effective Transformation to Detailed Design Analysis | Enabling Broad Accessibility to Generative Design | Mean Rating | |
---|---|---|---|---|---|---|---|---|

Ansys Discovery 2022 R2 (Canonsburg, PA, USA) | 3 | 2 | 1 | 1 | 3 | 1 | 3 | 2.0 |

Autodesk Fusion 360 v2.16490 (San Francisco, CA, USA) | 4 | 3 | 4 | 3 | 3 | 3 | 5 | 3.6 |

nTopology 3.45 (New York, NY, USA) | 3 | 5 | 2 | 2 | 4 | 3 | 4 | 3.3 |

Dassault Systèmes CATIA Generative Design V5-6R2017 (Paris, France) | 3 | 2 | 4 | 1 | 3 | 3 | 3 | 2.7 |

Altair inspire (Troy, MI, USA) | 3 | 3 | 1 | 1 | 1 | 1 | 3 | 1.9 |

NX by Siemens v41.0 (Plano, TX, USA) | 3 | 2 | 1 | 1 | 1 | 1 | 3 | 1.7 |

Paramatters CogniCAD 4.0 (Ontario, Canada) | 3 | 5 | 2 | 2 | 2 | 1 | 5 | 2.9 |

Apex MsC 2021.3 (Stocholm, Sweden) | 3 | 4 | 1 | 1 | 3 | 1 | 3 | 2.3 |

**Table 2.**Summary of the results of all designs where mass, first eigenfrequency, maximum Von Mises stress, maximum displacements and safety factor are shown. Note that SI stands for Skeleton Improved design.

Name | Mass (kg) | Max D. Eigenfreq (mm) | Eigenfreq. (Hz) | MaxVM Stress (MPa) | MaxD. Loads (mm) | SF | D/H1 Loads (×1000) | D/H2 Loads (×1000) |
---|---|---|---|---|---|---|---|---|

Reference | 344.76 | 4.14 | 42.08 | 0.90 | 0.009 | 277.78 | 0.004 | 1.939 |

F360 | 89.08 | 17.68 | 63.65 | 1.12 | 0.031 | 151.79 | 0.014 | 8.281 |

TO | 153.05 | 14.63 | 61.8 | 3.88 | 0.026 | 43.81 | 0.012 | 6.852 |

Skeleton | 85.23 | 22.06 | 64.63 | 2.65 | 0.064 | 64.15 | 0.030 | 10.331 |

Voronoi | 90.61 | 8.98 | 60.80 | 1.87 | 0.021 | 90.91 | 0.010 | 4.206 |

**Table 3.**Experimental and corrected Young’s modulus FEA first three modes in free vibration configuration.

Hz | Experimental | FEM (Corrected E) | Error |
---|---|---|---|

Mode 1 | 119.36 | 119.1 | 0.22% |

Mode 2 | 164.907 | 165.01 | 0.06% |

Mode 3 | 212.863 | 213.2 | 0.16% |

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## Share and Cite

**MDPI and ACS Style**

Laraudogoitia Blanc, I.; Hamm, C.; García de Cortázar, M.; Kaiser, N.; Savysko, O.; Girot Mata, F.A.
Bioinspired Design for Lightweighting and Vibration Behavior Optimization in Large-Scale Aeronautical Tooling: A Comparative Study. *Machines* **2023**, *11*, 1067.
https://doi.org/10.3390/machines11121067

**AMA Style**

Laraudogoitia Blanc I, Hamm C, García de Cortázar M, Kaiser N, Savysko O, Girot Mata FA.
Bioinspired Design for Lightweighting and Vibration Behavior Optimization in Large-Scale Aeronautical Tooling: A Comparative Study. *Machines*. 2023; 11(12):1067.
https://doi.org/10.3390/machines11121067

**Chicago/Turabian Style**

Laraudogoitia Blanc, Ignacio, Christian Hamm, Maider García de Cortázar, Nils Kaiser, Oleksander Savysko, and Franck Andrés Girot Mata.
2023. "Bioinspired Design for Lightweighting and Vibration Behavior Optimization in Large-Scale Aeronautical Tooling: A Comparative Study" *Machines* 11, no. 12: 1067.
https://doi.org/10.3390/machines11121067