Abstract
This paper presents the optimization frameworks for designing cellular internal structures of an aircraft wing subjected to aerodynamic loads. Inspired by natural cellular materials, this study employs lattice and foam cells as the internal structures of the aircraft wing. The distribution of the cell materials is optimized by minimizing the mass and maximizing the stiffness while avoiding the global buckling of the wing. The optimization variables for the lattice structure are the cell size distribution field and the strut radii (or cell face thicknesses). Various weighting factor combinations are applied to the two competing objectives to obtain the optimal solution, considering different priorities of reducing mass or increasing stiffness. The results demonstrate that the wings with optimized cellular internal structures have higher structural efficiency than the reference wings with uniform cellular internal structures. The optimized wings also achieve higher structural efficiency than conventional wing designs when requiring heavy loading or a balanced tradeoff between load-bearing capacity and mass.
Issue Section:
Research Papers
References
1.
Zhu
, L.
, Li
, N.
, and Childs
, P.
, 2018
, “Light-Weighting in Aerospace Component and System Design
,” Propuls. Power Res.
, 7
(2
), pp. 103
–119
. 2.
Del Olmo
, E.
, Grande
, E.
, Samartin
, C.
, Bezdenejnykh
, M.
, Torres
, J.
, Blanco
, N.
, Frovel
, M.
, and Canas
, J.
, 2012
, “Lattice Structures for Aerospace Applications
,” Proceedings of the 12th European Conference on Spacecraft Structures, Materials and Environmental Testing
, Noordwijk, Netherlands
, Mar. 20–23
, p. 6
.3.
Gibson
, L. J.
, 1989
, “Modelling the Mechanical Behavior of Cellular Materials
,” Mater. Sci. Eng. A
, 110
, pp. 1
–36
. 4.
Ashby
, M. F.
, and Medalist
, R. M.
, 1983
, The Mechanical Properties of Cellular Solids
, Springer
, New York
.5.
Schaedler
, T. A.
, and Carter
, W. B.
, 2016
, “Architected Cellular Materials
,” Annu. Rev. Mater. Res.
, 46
(1
), pp. 187
–210
. 6.
Sullivan
, T. N.
, Wang
, B.
, Espinosa
, H. D.
, and Meyers
, M. A.
, 2017
, “Extreme Lightweight Structures: Avian Feathers and Bones
,” Mater. Today
, 20
(7
), pp. 377
–391
. 7.
Aage
, N.
, Andreassen
, E.
, Lazarov
, B. S.
, and Sigmund
, O.
, 2017
, “Giga-Voxel Computational Morphogenesis for Structural Design
,” Nature
, 550
(7674
), pp. 84
–86
. 8.
Bhate
, D.
, 2019
, “Four Questions in Cellular Material Design
,” Materials
, 12
(7
), p. 1060
. 9.
Park
, K.-M.
, Min
, K.-S.
, and Roh
, Y.-S.
, 2022
, “Design Optimization of Lattice Structures Under Compression: Study of Unit Cell Types and Cell Arrangements
,” Materials
, 15
(1
), p. 97
. 10.
Robbins
, J.
, Owen
, S.
, Clark
, B.
, and Voth
, T.
, 2016
, “An Efficient and Scalable Approach for Generating Topologically Optimized Cellular Structures for Additive Manufacturing
,” Addit. Manuf.
, 12
(Part B
), pp. 296
–304
. 11.
Telgen
, B.
, Sigmund
, O.
, and Kochmann
, D. M.
, 2022
, “Topology Optimization of Graded Truss Lattices Based on On-the-Fly Homogenization
,” ASME J. Appl. Mech.
, 89
(6
), p. 061006
. 12.
Tamijani
, A. Y.
, Velasco
, S. P.
, and Alacoque
, L.
, 2020
, “Topological and Morphological Design of Additively-Manufacturable Spatially-Varying Periodic Cellular Solids
,” Mater. Des.
, 196
, p. 109155
. 13.
Cheng
, L.
, Zhang
, P.
, Biyikli
, E.
, Bai
, J.
, Robbins
, J.
, and To
, A.
, 2017
, “Efficient Design Optimization of Variable-Density Cellular Structures for Additive Manufacturing: Theory and Experimental Validation
,” Rapid Prototyp. J.
, 23
(1
), pp. 660
–677
. 14.
Chen
, W.
, Watts
, S.
, Jackson
, J. A.
, Smith
, W. L.
, Tortorelli
, D. A.
, and Spadaccini
, C. M.
, 2019
, “Stiff Isotropic Lattices Beyond the Maxwell Criterion
,” Sci. Adv.
, 5
(9
), p. eaaw1937
. 15.
Yi
, B.
, Zhou
, Y.
, Yoon
, G. H.
, and Saitou
, K.
, 2019
, “Topology Optimization of Functionally-Graded Lattice Structures With Buckling Constraints
,” Comput. Methods Appl. Mech. Eng.
, 354
, pp. 593
–619
. 16.
Jia
, Y.
, Meng
, W.
, Du
, Z.
, Liu
, C.
, Li
, S.
, Wang
, C.
, Ge
, Z.
, Su
, R.
, and Guo
, X.
, 2024
, “Explicit Design Optimization of Air Rudders for Maximizing Stiffness and Fundamental Frequency
,” Thin Walled Struct.
, 203
, p. 112152
. 17.
Zhou
, Y.
, Gao
, L.
, and Li
, H.
, 2023
, “Topology Optimization Design of Graded Infills for 3D Curved Volume by a Conformal Sweeping Method
,” Comput. Methods Appl. Mech. Eng.
, 412
, p. 116009
. 18.
Gorguluarslan
, R. M.
, Gandhi
, U. N.
, Mandapati
, R.
, and Choi
, S.-K.
, 2016
, “Design and Fabrication of Periodic Lattice-Based Cellular Structures
,” Comput.-Aided Des. Appl.
, 13
(1
), pp. 50
–62
. 19.
Zhang
, M.
, Zhao
, C.
, Li
, G.
, and Luo
, K.
, 2023
, “Mechanical Properties of the Composite Lattice Structure With Variable Density and Multi-configuration
,” Compos. Struct.
, 304
(Part 1
), p. 116405
. 20.
Bai
, L.
, Gong
, C.
, Chen
, X.
, Sun
, Y.
, Xin
, L.
, Pu
, H.
, Peng
, Y.
, and Luo
, J.
, 2020
, “Mechanical Properties and Energy Absorption Capabilities of Functionally Graded Lattice Structures: Experiments and Simulations
,” Int. J. Mech. Sci.
, 182
, p. 105735
. 21.
Alkhader
, M.
, and Vural
, M.
, 2008
, “Mechanical Response of Cellular Solids: Role of Cellular Topology and Microstructural Irregularity
,” Int. J. Eng. Sci.
, 46
(10
), pp. 1035
–1051
. 22.
Wang
, G.
, Shen
, L.
, Zhao
, J.
, Liang
, H.
, Xie
, D.
, Tian
, Z.
, and Wang
, C.
, 2018
, “Design and Compressive Behavior of Controllable Irregular Porous Scaffolds: Based on Voronoi-Tessellation and for Additive Manufacturing
,” ACS Biomater. Sci. Eng.
, 4
(2
), pp. 719
–727
. 23.
Ćurković
, P.
, 2021
, “Optimization of Generatively Encoded Multi-material Lattice Structures for Desired Deformation Behavior
,” Symmetry
, 13
(2
), p. 293
. 24.
Kader
, M. A.
, Hazell
, P. J.
, Brown
, A. D.
, Tahtali
, M.
, Ahmed
, S.
, Escobedo
, J. P.
, and Saadatfar
, M.
, 2020
, “Novel Design of Closed-Cell Foam Structures for Property Enhancement
,” Addit. Manuf.
, 31
, p. 100976
. 25.
Chen
, Y.
, Das
, R.
, and Battley
, M.
, 2015
, “Effects of Cell Size and Cell Wall Thickness Variations on the Stiffness of Closed-Cell Foams
,” Int. J. Solids Struct.
, 52
, pp. 150
–164
. 26.
Barbier
, C.
, Michaud
, P.
, Baillis
, D.
, Randrianalisoa
, J.
, and Combescure
, A.
, 2014
, “New Laws for the Tension/Compression Properties of Voronoi Closed-Cell Polymer Foams in Relation to Their Microstructure
,” Eur. J. Mech.-A/Solids
, 45
, pp. 110
–122
. 27.
Verma
, K. S.
, Muchhala
, D.
, Panthi
, S. K.
, and Mondal
, D.
, 2022
, “Influences of Cell Size, Cell Wall Thickness and Cell Circularity on the Compressive Responses of Closed-Cell Aluminum Foam and Its FEA Analysis
,” Int. J. Metalcast.
, 16
(2
), pp. 798
–813
. 28.
Zhang
, X.
, Tang
, L.
, Liu
, Z.
, Jiang
, Z.
, Liu
, Y.
, and Wu
, Y.
, 2017
, “Yield Properties of Closed-Cell Aluminum Foam Under Triaxial Loadings by a 3D Voronoi Model
,” Mech. Mater.
, 104
, pp. 73
–84
. 29.
Niknam
, H.
, and Akbarzadeh
, A.
, 2018
, “In-Plane and Out-of-Plane Buckling of Architected Cellular Plates: Numerical and Experimental Study
,” Compos. Struct.
, 206
, pp. 739
–749
. 30.
Bhate
, D.
, Penick
, C. A.
, Ferry
, L. A.
, and Lee
, C.
, 2019
, “Classification and Selection of Cellular Materials in Mechanical Design: Engineering and Biomimetic Approaches
,” Designs
, 3
(1
), p. 19
. 31.
Megson
, T. H. G.
, 2016
, Aircraft Structures for Engineering Students
, Butterworth-Heinemann
, Oxford, UK
.32.
Cramer
, N. B.
, Cellucci
, D. W.
, Formoso
, O. B.
, Gregg
, C. E.
, Jenett
, B. E.
, Kim
, J. H.
, Lendraitis
, M.
, et al, 2019
, “Elastic Shape Morphing of Ultralight Structures by Programmable Assembly
,” Smart Mater. Struct.
, 28
(5
), p. 055006
. 33.
Jenett
, B.
, Calisch
, S.
, Cellucci
, D.
, Cramer
, N.
, Gershenfeld
, N.
, Swei
, S.
, and Cheung
, K. C.
, 2017
, “Digital Morphing Wing: Active Wing Shaping Concept Using Composite Lattice-Based Cellular Structures
,” Soft Rob.
, 4
(1
), pp. 33
–48
. 34.
Rodríguez-Panes
, A.
, Claver
, J.
, and Camacho
, A. M.
, 2018
, “The Influence of Manufacturing Parameters on the Mechanical Behaviour of PLA and ABS Pieces Manufactured by FDM: A Comparative Analysis
,” Materials
, 11
(8
), p. 1333
. 35.
Drela
, M.
, 2024
, “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils
,” Proceedings of the Low Reynolds Number Aerodynamics: Proceedings of the Conference
, Notre Dame, IN
, June 5–7
, Springer
, pp. 1
–12
.36.
Schrenk
, O.
, 1941
, “A Simple Approximation Method for Obtaining the Spanwise Lift Distribution
,” Aeronaut. J.
, 45
(370
), pp. 331
–336
. 37.
Moerman
, K. M.
, 2018
, “GIBBON: The Geometry and Image-Based Bioengineering Add-On
,” J. Open Source Softw.
, 3
(22
), pp. 506
. 38.
Hansen
, N.
, Müller
, S. D.
, and Koumoutsakos
, P.
, 2003
, “Reducing the Time Complexity of the Derandomized Evolution Strategy With Covariance Matrix Adaptation (CMA-ES)
,” Evol. Comput.
, 11
(1
), pp. 1
–18
. 39.
Hansen
, N.
, 2016
, “The CMA Evolution Strategy: A Tutorial
,” arXiv preprint arXiv:1604.00772. 40.
Hansen
, N.
, and Kern
, S.
, 2004
, “Evaluating the CMA Evolution Strategy on Multimodal Test Functions
,” Proceedings of the International Conference on Parallel Problem Solving From Nature
, Birmingham, UK
, Sept. 18–22
, Springer, pp. 282
–291
.41.
Anis
, M.
, Pendurkar
, S.
, Yi
, Y. K.
, and Sharon
, G.
, 2023
, “Comparison Between Popular Genetic Algorithm (GA)-Based Tool and Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES) for Optimizing Indoor Daylight
,” Proceedings of Building Simulation 2023: 18th Conference of IBPSA
, Shanghai, China
, Sept. 4–6
.42.
Ning
, X.
, and Pellegrino
, S.
, 2015
, “Imperfection-Insensitive Axially Loaded Thin Cylindrical Shells
,” Int. J. Solids Struct.
, 62
, pp. 39
–51
. 43.
Gunantara
, N.
, 2018
, “A Review of Multi-objective Optimization: Methods and Its Applications
,” Cogent Eng.
, 5
(1
), pp. 1502242
. 44.
Ngatchou
, P.
, Zarei
, A.
, and El-Sharkawi
, A.
, 2005
, “Pareto Multi Objective Optimization
,” Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems
, Arlington, VA
, Nov. 6–10
, IEEE, pp. 84
–91
.Copyright © 2025 by ASME
You do not currently have access to this content.
