Dragonfly‐Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams

Advanced Science, vol. 10, pp. e2207635

Abstract

This research is taking the first steps toward applying a 2D dragonfly wing skeleton in the design of an airplane wing using artificial intelligence. The work relates the 2D morphology of the structural network of dragonfly veins to a secondary graph that is topologically dual and geometrically perpendicular to the initial network. This secondary network is referred as the reciprocal diagram proposed by Maxwell that can represent the static equilibrium of forces in the initial graph. Surprisingly, the secondary graph shows a direct relationship between the thickness of the structural members of a dragonfly wing and their in-plane static equilibrium of forces that gives the location of the primary and secondary veins in the network. The initial and the reciprocal graph of the wing are used to train an integrated and comprehensive machine-learning model that can generate similar graphs with both primary and secondary veins for a given boundary geometry. The result shows that the proposed algorithm can generate similar vein networks for an arbitrary boundary geometry with no prior topological information or the primary veins' location. The structural performance of the dragonfly wing in nature also motivated the authors to test this research's real-world application for designing the cellular structures for the core of airplane wings as cantilever porous beams. The boundary geometry of various airplane wings is used as an input for the design proccedure. The internal structure is generated using the training model of the dragonfly veins and their reciprocal graphs. One application of this method is experimentally and numerically examined for designing the cellular core, 3D printed by fused deposition modeling, of the airfoil wing; the results suggest up to 25% improvements in the out-of-plane stiffness. The findings demonstrate that the proposed machine-learning-assisted approach can facilitate the generation of multiscale architectural patterns inspired by nature to form lightweight load-bearable elements with superior structural properties.

Authors 5

1. Hao Ran Zheng

   City University of Hong Kong · University of Pennsylvania

   Affiliation as printed

   General Office, Department of Architecture and Civil Engineering City University of Hong Kong 83 Tat Chee Avenue, Kowloon Tong Kowloon HKSAR China

   Polyhedral Structures Laboratory, Department of Architecture, Weitzman School of Design University of Pennsylvania Philadelphia PA 19146 USA

   General Office, Department of Architecture and Civil Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, HKSAR, China

   Polyhedral Structures Laboratory, Department of Architecture, Weitzman School of Design, University of Pennsylvania, Philadelphia, PA, 19146 USA

2. Hossein Mofatteh

   McGill University

   Affiliation as printed

   Advanced Multifunctional and Multiphysics Metamaterials Lab (AM3L), Department of Bioresource Engineering McGill University Montreal QC H9X 3V9 Canada

   Advanced Multifunctional and Multiphysics Metamaterials Lab (AM3L), Department of Bioresource Engineering, McGill University, Montreal, QC, H9X 3V9 Canada

3. Márton Hablicsek Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute Leiden University Leiden 2333CA The Netherlands

   Mathematical Institute, Leiden University, Leiden, 2333CA The Netherlands

4. Abdolhamid Akbarzadeh corresponding

   McGill University

   Affiliation as printed

   Advanced Multifunctional and Multiphysics Metamaterials Lab (AM3L), Department of Bioresource Engineering McGill University Montreal QC H9X 3V9 Canada

   Department of Mechanical Engineering McGill University Montreal QC H3A 0C3 Canada

   Advanced Multifunctional and Multiphysics Metamaterials Lab (AM3L), Department of Bioresource Engineering, McGill University, Montreal, QC, H9X 3V9 Canada

   Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 0C3 Canada

5. Masoud Akbarzadeh corresponding

   University of Pennsylvania

   Affiliation as printed

   General Robotic, Automation, Sensing and Perception (GRASP) Lab, School of Engineering and Applied Science University of Pennsylvania 3330 Walnut St Philadelphia PA 19104 USA

   Polyhedral Structures Laboratory, Department of Architecture, Weitzman School of Design University of Pennsylvania Philadelphia PA 19146 USA

   General Robotic, Automation, Sensing and Perception (GRASP) Lab, School of Engineering and Applied Science, University of Pennsylvania, 3330 Walnut St, Philadelphia, PA, 19104 USA

   Polyhedral Structures Laboratory, Department of Architecture, Weitzman School of Design, University of Pennsylvania, Philadelphia, PA, 19146 USA