Topology optimization methods for morphing aircraft design: a review
Abstract
Current aeronautical research efforts are increasingly focused on weight reduction and the integration of advanced materials analysing dynamic properties. These efforts encompass cellular structures, flexible skins, and modifiable primary and secondary structural elements (e.g., wings). The development of technologies for morphing aircraft design enhances aerodynamic performance and structural efficiency, thereby optimizing the mechanical design of these systems. The authors provide a comprehensive review of the current state of topology optimization methods in morphing aircraft design, highlighting the number of publications in this field and identifying the key journals contributing to this research. It also offers an in-depth analysis of the Solid Isotropic Material with Penalization (SIMP) method, the Evolutionary Structural Optimization (ESO), Bidirectional Evolutionary Structural Optimization (BESO), the recent Proportional Topology Optimization (PTO) and evaluates their effectiveness in achieving efficient designs. Additionally, the review discusses of future challenges and potential advancements in topology optimization for morphing aircraft, offering a thorough overview of the field.
Keyword : topology optimization, morphing aircraft, solid isotropic material with penalization, SIMP, evolutionary structural optimization, ESO, bidirec- tional evolutionary structural optimization, BESO, proportional topology optimization, PTO
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Ajaj, R. M., Parancheerivilakkathil, M. S., Amoozgar, M., Friswell, M. I., & Cantwell, W. J. (2021). Recent developments in the aeroelasticity of morphing aircraft. Progress in Aerospace Sciences, 120, Article 100682. https://doi.org/10.1016/j.paerosci.2020.100682
Alacoque, L., Watkins, R. T., & Tamijani, A. Y. (2021). Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures. Computer Methods in Applied Mechanics and Engineering, 379, Article 113749. https://doi.org/10.1016/j.cma.2021.113749
Allaire, G., Jouve, F., & Toader, A.-M. (2004). Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics, 194(1), 363–393. https://doi.org/10.1016/j.jcp.2003.09.032
Alphonse, M., Bupesh Raja, V. K., Gopala Krishna, V., Kiran, R. S. U., Subbaiah, B. V., & Chandra, L. V. R. (2021). Mechanical behavior of sandwich structures with varying core material – A review. Materials Today: Proceedings, 44, 3751–3759. https://doi.org/10.1016/j.matpr.2020.11.722
Arredondo-Soto, M., Cuan-Urquizo, E., & Gómez-Espinosa, A. (2021). A review on tailoring stiffness in compliant systems, via removing material: Cellular materials and topology optimization. Applied Sciences, 11(8), Article 3538. https://doi.org/10.3390/app11083538
Bai, J. B., Chen, D., Xiong, J. J., & Shenoi, R. A. (2017). A corrugated flexible composite skin for morphing applications. Composites Part B: Engineering, 131, 134–143. https://doi.org/10.1016/j.compositesb.2017.07.056
Barbarino, S., Bilgen, O., Ajaj, R. M., Friswell, M. I., & Inman, D. J. (2011). A review of morphing aircraft. Journal of Intelligent Material Systems and Structures, 22(9), 823–877. https://doi.org/10.1177/1045389X11414084
Bendsøe, M. P., & Kikuchi, N. (1988). Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71(2), 197–224. https://doi.org/10.1016/0045-7825(88)90086-2
Bendsoe, M. P., & Sigmund, O. (2013). Topology optimization: Theory, methods, and applications. Springer Science & Business Media.
Biyikli, E., & To, A. C. (2015). Proportional topology optimization: A new non-sensitivity method for solving stress constrained and minimum compliance problems and its implementation in MATLAB. PLOS ONE, 10(12), e0145041. https://doi.org/10.1371/journal.pone.0145041
Capasso, G., Morlier, J., Charlotte, M., & Coniglio, S. (2020). Stress-based topology optimization of compliant mechanisms using nonlinear mechanics. Mechanics & Industry, 21(3), Article 304. https://doi.org/10.1051/meca/2020011
Casas, W. J. P., Cesconeto, E. M., Lisboa, E. de S., Moreira, J. B. D., Medeiros, J. E., & Ribeiro, T. S. (2016). Topology optimization of an aircraft component as a fluid- structure system with unstructured mesh. Semantic Scholar.
Cavalieri, V., De Gaspari, A., & Ricci, S. (2020). Optimization of compliant adaptive structures in the design of a morphing droop nose. Smart Materials and Structures, 29(7), Article 075020. https://doi.org/10.1088/1361-665X/ab8902
Chang, L., & Shen, X. (2018). Design of cellular based structures in sandwiched morphing skin via topology optimization. Structural and Multidisciplinary Optimization, 58, 2085–2098. https://doi.org/10.1007/s00158-018-2020-5
Chang, L., Shen, X., Dai, Y., Wang, T., & Zhang, L. (2020). Investigation on the mechanical properties of topologically optimized cellular structures for sandwiched morphing skins. Composite Structures, 250, Article 112555. https://doi.org/10.1016/j.compstruct.2020.112555
Chapkin, W. A., Walgren, P., Frank, G. J., Seifert, D. R., Hartl, D. J., & Baur, J. W. (2020). Design and optimization of high-strain, cylindrical composite skins for morphing fuselages. Materials & Design, 187, Article 108395. https://doi.org/10.1016/j.matdes.2019.108395
Cheng, K.-T., & Olhoff, N. (1981). An investigation concerning optimal design of solid elastic plates. International Journal of Solids and Structures, 17(3), 305–323. https://doi.org/10.1016/0020-7683(81)90065-2
Cheng, W., Wang, H., Zhang, M., & Du, R. (2021). Improved proportional topology optimization algorithm for minimum volume problem with stress constraints. Engineering Computations, 38(1), 392–412. https://doi.org/10.1108/EC-12-2019-0560
Clausen, A., Wang, F., Jensen, J. S., Sigmund, O., & Lewis, J. A. (2015). Topology optimized architectures with programmable Poisson’s ratio over large deformations. Advanced Materials, 27(37), 5523–5527. https://doi.org/10.1002/adma.201502485
Cramer, N. B., Cellucci, D. W., Formoso, O. B., Gregg, C. E., Jenett, B. E., Kim, J. H., Lendraitis, M., Swei, S. S., Trinh, G. T., Trinh, K. V., & Cheung, K. C. (2019). Elastic shape morphing of ultralight structures by programmable assembly. Smart Materials and Structures, 28(5), Article 055006. https://doi.org/10.1088/1361-665X/ab0ea2
Criollo, L., Mena-Arciniega, C., & Xing, S. (2024). Classification, military applications, and opportunities of unmanned aerial vehicles. Aviation, 28(2), 115–127. https://doi.org/10.3846/aviation.2024.21672
Criollo, L., Sánchez Sánchez, X., Abatta-Jácome, L., & Haro, E. E. (2022). Finite element simulation of aircraft wing with fluid-structure interaction. In M. Botto-Tobar, H. Cruz, & A. Diaz Cadena (Eds.), Recent advances in electrical engineering, electronics and energy (Vol. 932, pp. 31–43). Springer International Publishing. https://doi.org/10.1007/978-3-031-08288-7_3
Dalaq, A. S., & Barthelat, F. (2020). Manipulating the geometry of architectured beams for maximum toughness and strength. Materials & Design, 194, Article 108889. https://doi.org/10.1016/j.matdes.2020.108889
Das, G. K., Ranjan, P., & James, K. A. (2022, June 27). 3D topology optimization of aircraft wings with conventional and non-conventional layouts: A comparative study. In AIAA AVIATION 2022 Forum. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2022-3725
Das, R., & Jones, R. (2011). Topology optimisation of a bulkhead component used in aircrafts using an evolutionary algorithm. Procedia Engineering, 10, 2867–2872. https://doi.org/10.1016/j.proeng.2011.04.476
Dexl, F., Hauffe, A., & Wolf, K. (2020). Multidisciplinary multi-objective design optimization of an active morphing wing section. Structural and Multidisciplinary Optimization, 62(5), 2423–2440. https://doi.org/10.1007/s00158-020-02613-4
Dunning, P. D., Brampton, C. J., & Kim, H. A. (2013). Multidisciplinary level set topology optimization of the internal structure of an aircraft wing. In 10th World Congress on Structural and Multidisciplinary Optimization (pp. 19–24). Orlando, Florida, USA.
Ermakova, A., & Dayyani, I. (2017). Shape optimisation of composite corrugated morphing skins. Composites Part B: Engineering, 115, 87–101. https://doi.org/10.1016/j.compositesb.2016.10.029
Esfarjani, S. M., Dadashi, A., & Azadi, M. (2022). Topology optimization of additive-manufactured metamaterial structures: A review focused on multi-material types. Forces in Mechanics, 7, Article 100100. https://doi.org/10.1016/j.finmec.2022.100100
Ferrari, F., & Sigmund, O. (2020). A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Structural and Multidisciplinary Optimization, 62(4), 2211–2228. https://doi.org/10.1007/s00158-020-02629-w
Francfort, G. A., & Murat, F. (1986). Homogenization and optimal bounds in linear elasticity. Archive for Rational mechanics and Analysis, 94, 307–334. https://doi.org/10.1007/BF00280908
Gao, J., Li, H., Gao, L., & Xiao, M. (2018). Topological shape optimization of 3D micro-structured materials using energy-based homogenization method. Advances in Engineering Software, 116, 89–102. https://doi.org/10.1016/j.advengsoft.2017.12.002
Gaspari, A. D., & Ricci, S. (2010). Combining shape and structural optimization for the design of morphing airfoils. In 2nd International Conference on Engineering Optimization (pp. 1–12). ResearchGate.
Gong, X., Ren, C., Sun, J., Zhang, P., Du, L., & Xie, F. (2022). 3D Zero Poisson’s ratio honeycomb structure for morphing wing applications. Biomimetics, 7(4), Article 198. https://doi.org/10.3390/biomimetics7040198
Guest, J. K., & Moen, C. D. (2010). Reinforced concrete design with topology optimization. Structures Congress, 2010, 445–454. https://doi.org/10.1061/41131(370)39
Guo, X., Zhang, W., & Zhong, W. (2014). Doing topology optimization explicitly and geometrically – a new moving morphable components based framework. Journal of Applied Mechanics, 81(8), Article 081009. https://doi.org/10.1115/1.4027609
Gupta, S., Tyagi, R. K., Pratiksha, P., & Gairola, A. (2022). A review on evolution of airfoils and their characteristics in last three centuries. Part-1: Evolution of flights and shapes of wing sections before 1930 and NACA series. AIP Conference Proceedings, 2597(1). https://doi.org/10.1063/5.0117406
Haro, E. E., Odeshi, A. G., Castellanos, S., Sanchez, X., Abatta, L., Criollo, L., Alban, A., & Szpunar, J. A. (2023). Ballistic impact performance of hybrid composite armors made of aluminum foam containing the dispersion of shear thickening fluid made of various synthetic nano-fillers. Composites Part C: Open Access, 12, Article 100420. https://doi.org/10.1016/j.jcomc.2023.100420
Hodson, J. D., Christopherson, A. P., Deaton, J. D., Pankonien, A. M., Reich, G. W., & Beran, P. S. (2019, January 7). Aeroelastic topology optimization of a morphing airfoil in supersonic flow using evolutionary design. In AIAA Scitech 2019 Forum. San Diego, California. https://doi.org/10.2514/6.2019-1466
Huang, J., Zhang, Q., & Leng, J. (2017). Topology optimization of zero Poisson’s ratio honeycomb structures for lighter weight. In International Conference on Composite Materials. ICCM.
Huang, J., Zhang, Q., Scarpa, F., Liu, Y., & Leng, J. (2018). Multi-stiffness topology optimization of zero Poisson’s ratio cellular structures. Composites Part B: Engineering, 140, 35–43. https://doi.org/10.1016/j.compositesb.2017.12.014
Huang, X., Radman, A., & Xie, Y. M. (2011). Topological design of microstructures of cellular materials for maximum bulk or shear modulus. Computational Materials Science, 50(6), 1861–1870. https://doi.org/10.1016/j.commatsci.2011.01.030
Ikonen, T. J., & Sobester, A. (2016). Ground structure approaches for the evolutionary optimization of aircraft wing structures. In 16th AIAA Aviation Technology, Integration, and Operations Conference (pp. 1–21). American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2016-3286
James, K. (2013). Aerostructural shape and topology optimization of aircraft wings. Library and Archives Canada.
James, K., & Martins, J. R. R. A. (2008, September 10). Three-dimensional structural topology optimization of an aircraft wing using level set methods. In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2008-6081
Jensen, P. D. L., Wang, F., Dimino, I., & Sigmund, O. (2021). Topology optimization of large-scale 3D morphing wing structures. Actuators, 10(9), Article 217. https://doi.org/10.3390/act10090217
Jha, A., & Dayyani, I. (2021). Shape optimisation and buckling analysis of large strain zero Poisson’s ratio fish-cells metamaterial for morphing structures. Composite Structures, 268, Article 113995. https://doi.org/10.1016/j.compstruct.2021.113995
Keng-Tuno, C. (1981). On non-smoothness in optimal design of solid, elastic plates. International Journal of Solids and Structures, 17(8), 795–810. https://doi.org/10.1016/0020-7683(81)90089-5
Kollmann, H. T., Abueidda, D. W., Koric, S., Guleryuz, E., & Sobh, N. A. (2020). Deep learning for topology optimization of 2D metamaterials. Materials & Design, 196, Article 109098. https://doi.org/10.1016/j.matdes.2020.109098
Krog, L., Tucker, A., Kemp, M., & Boyd, R. (2004, August 30). Topology optimisation of aircraft wing box ribs. In 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2004-4481
Kumar, P., Sauer, R. A., & Saxena, A. (2021). On topology optimization of large deformation contact-aided shape morphing compliant mechanisms. Mechanism and Machine Theory, 156, Article 104135. https://doi.org/10.1016/j.mechmachtheory.2020.104135
Lampeas, G. (2020). Additive manufacturing: Design (topology optimization), materials, and processes. In S. Pantelakis & K. Tserpes (Eds.), Revolutionizing aircraft materials and processes (pp. 115–136). Springer International Publishing. https://doi.org/10.1007/978-3-030-35346-9_5
Lim, J., You, C., & Dayyani, I. (2020). Multi-objective topology optimization and structural analysis of periodic spaceframe structures. Materials & Design, 190, Article 108552. https://doi.org/10.1016/j.matdes.2020.108552
Lin, P. T., Lin, C.-Y., & Cheng, T.-Y. (2019). Automatic truss design based on topology optimization and image processing techniques. In T. Uhl (Ed.), Advances in mechanism and machine science (pp. 459–468). Springer International Publishing. https://doi.org/10.1007/978-3-030-20131-9_46
Lumpe, T. S., & Shea, K. (2021). Computational design of 3D-printed active lattice structures for reversible shape morphing. Journal of Materials Research, 36(18), 3642–3655. https://doi.org/10.1557/s43578-021-00225-2
Maute, K., & Reich, G. (2004, abril 19). An aeroelastic topology optimization approach for adaptive wing design. In 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference (pp. 1–10). American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2004-1805
Mcknight, G., Doty, R., Keefe, A., Herrera, G., & Henry, C. (2010). Segmented reinforcement variable stiffness materials for reconfigurable surfaces. Journal of Intelligent Material Systems and Structures, 21(17), 1783–1793. https://doi.org/10.1177/1045389X10386399
Michell, A. G. M. (1904). LVIII. The limits of economy of material in frame-structures. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 8(47), 589–597. https://doi.org/10.1080/14786440409463229
Mlejnek, H. P. (1992). Some aspects of the genesis of structures. Structural Optimization, 5(1–2), 64–69. https://doi.org/10.1007/BF01744697
Munk, D. J., Boyd, D. W., & Vio, G. A. (2016). SIMP for complex structures. Applied Mechanics and Materials, 846, 535–540. https://doi.org/10.4028/www.scientific.net/AMM.846.535
Munk, D. J., & Miller, J. D. (2021). Topology optimization of aircraft components for increased sustainability. AIAA Journal, 60(1), 1–16. https://doi.org/10.2514/1.J060259
Munk, D. J., Vio, G. A., & Steven, G. P. (2015). Aerothermoelastic structural topology optimisation for a hypersonic transport aircraft wing. In 11th World Congress on Structural and Multidisciplinary Optimization. Sydney, Australia. https://web.aeromech.usyd.edu.au/WCSMO2015/papers/1013_paper.pdf
Narváez‐Muñoz, C., Zamora‐Ledezma, C., Ryzhakov, P., Pons‐Prats, J., Elango, J., Mena, C., Navarrete, F., Morales‐Flórez, V., Cano‐Crespo, R., & Segura, L. J. (2023). Improving glass-fiber epoxy composites via interlayer toughening with polyacrylonitrile/multiwalled carbon nanotubes electrospun fibers. Journal of Applied Polymer Science, 140(5), Article e53400. https://doi.org/10.1002/app.53400
Negahban, M. H., Bashir, M., Traisnel, V., & Botez, R. M. (2024). Seamless morphing trailing edge flaps for UAS-S45 using high-fidelity aerodynamic optimization. Chinese Journal of Aeronautics, 37(2), 12–29. https://doi.org/10.1016/j.cja.2023.10.024
Nguyen, M. N., Tran, M. T., Nguyen, H. Q., & Bui, T. Q. (2023). A multi-material proportional topology optimization approach for compliant mechanism problems. European Journal of Mechanics – A/Solids, 100, Article 104957. https://doi.org/10.1016/j.euromechsol.2023.104957
Niordson, F. (1983). Optimal design of elastic plates with a constraint on the slope of the thickness function. International Journal of Solids and Structures, 19(2), 141–151. https://doi.org/10.1016/0020-7683(83)90005-7
Olivett, A., Corrao, P., & Karami, M. A. (2021). Flow control and separation delay in morphing wing aircraft using traveling wave actuation. Smart Materials and Structures, 30(2). https://doi.org/10.1088/1361-665X/abd347
Olympio, K. R., & Gandhi, F. (2010). Flexible skins for morphing aircraft using cellular honeycomb cores. Journal of Intelligent Material Systems and Structures, 21(17), 1719–1735. https://doi.org/10.1177/1045389X09350331
Olympio, K. R., & Gandhi, F. (2012). Optimal cellular core topologies for one-dimensional morphing aircraft structures. Journal of Mechanical Design, 134(8). https://doi.org/10.1115/1.4007087
Ouyang, Y., Gu, Y., Kou, X., & Yang, Z. (2021). Active flutter suppression of wing with morphing flap. Aerospace Science and Technology, 110, Article 106457. https://doi.org/10.1016/j.ast.2020.106457
Özgen, S., Yaman, Y., Şahin, M., Seber, G., Ünlüsoy, L., Sakarya, E., İnsuyu, T., Bayram, G., Uludağ, Y., & Yılmaz, A. (2010). Morphing air vehicle concepts. In Proceedings of the International Workshop on Unmanned Vehicles (UVW2010). http://ae.metu.edu.tr/~melin/PDFs/Conferences/UVW2010/UVW-2010-5.pdf
Papanicolau, G., Bensoussan, A., & Lions, J.-L. (1978). Asymptotic analysis for periodic structures. Elsevier.
Parancheerivilakkathil, M. S., Pilakkadan, J. S., Ajaj, R. M., Amoozgar, M., Asadi, D., Zweiri, Y., & Friswell, M. I. (2024). A review of control strategies used for morphing aircraft applications. Chinese Journal of Aeronautics, 37(4), 436–463. https://doi.org/10.1016/j.cja.2023.12.035
Peel, L. D., Mejia, J., Narvaez, B., Thompson, K., & Lingala, M. (2009). Development of a simple morphing wing using elastomeric composites as skins and actuators. Journal of Mechanical Design, 131(9), Article 091003. https://doi.org/10.1115/1.3159043
Qin, H., Yang, D., & Ren, C. (2018). Modelling theory of functional element design for metamaterials with arbitrary negative Poisson’s ratio. Computational Materials Science, 150, 121–133. https://doi.org/10.1016/j.commatsci.2018.03.056
Qu, F., Jiang, S., Wang, R., Zhu, B., & Zhang, X. (2022). A mechanical metamaterial structure with chiral concave quadrilateral negative Poisson’s ratio. In 2022 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS) (pp. 1–5). IEEE. https://doi.org/10.1109/MARSS55884.2022.9870507
Rao, X., Du, R., Cheng, W., & Yang, Y. (2024). Modified proportional topology optimization algorithm for multiple optimization problems. Mechanics, 30(1), 36–45. https://doi.org/10.5755/j02.mech.34367
Rozvany, G. I. N., & Zhou, M. (1991). Applications of the COC algorithm in layout optimization. In H. A. Eschenauer, C. Mattheck, & N. Olhoff (Eds.), Engineering optimization in design processes (Vol. 63, pp. 59–70). Springer. https://doi.org/10.1007/978-3-642-84397-6_6
Rudnick-Cohen, E. S., Reich, G. W., Pankonien, A. M., & Beran, P. S. (2023). Robust optimal design and trajectory planning of an aircraft with morphing airfoil sections. Structural and Multidisciplinary Optimization, 66(10), Article 214. https://doi.org/10.1007/s00158-023-03664-z
Saeed, N., Long, K., & Rehman, A. (2020). A review of structural optimization techniques for wind turbines. In 2020 3rd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET) (pp. 1–8). IEEE. https://doi.org/10.1109/iCoMET48670.2020.9074067
Selim, O., Gowree, E. R., Lagemann, C., Talboys, E., Jagadeesh, C., & Bruecker, C. (2020). The Peregrine Falcon’s Dive: On the pull-out maneuver and flight control through wing-morphing (arXiv:2008.03948). Cornell University. http://arxiv.org/abs/2008.03948
Sigmund, O. (2000). A new class of extremal composites. Journal of the Mechanics and Physics of Solids, 48(2), 397–428. https://doi.org/10.1016/S0022-5096(99)00034-4
Sigmund, O. (2001). A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization, 21, 120–127. https://doi.org/10.1007/s001580050176
Sofla, A. Y. N., Meguid, S. A., Tan, K. T., & Yeo, W. K. (2010). Shape morphing of aircraft wing: Status and challenges. Materials & Design, 31(3), 1284–1292. https://doi.org/10.1016/j.matdes.2009.09.011
Sokolowski, J., & Zochowski, A. (1999). Topological derivatives for elliptic problems. Inverse Problems, 15(1), Article 123. https://doi.org/10.1088/0266-5611/15/1/016
Splichal, J., Pistek, A., & Hlinka, J. (2015). Dynamic tests of composite panels of an aircraft wing. Progress in Aerospace Sciences, 78, 50–61. https://doi.org/10.1016/j.paerosci.2015.05.005
Steven, G. P., Li, Q., & Xie, Y. M. (2000). Evolutionary topology and shape design for general physical field problems. Computational Mechanics, 26(2), 129–139. https://doi.org/10.1007/s004660000160
Sun, L., Du, J., & Su, C. (2012). Methods and application on research of structural topology optimization. In Proceedings of International Conference on Modelling, Identification and Control. IEEE.
Super Star. (2024). Topology optimization aircraft. Super Star. https://ss.zhizhen.com
Tang, Y., Kurtz, A., & Zhao, Y. F. (2015). Bidirectional evolutionary structural optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing. Computer-Aided Design, 69, 91–101. https://doi.org/10.1016/j.cad.2015.06.001
Tanskanen, P. (2002). The evolutionary structural optimization method: Theoretical aspects. Computer Methods in Applied Mechanics and Engineering, 191(47–48), 5485–5498. https://doi.org/10.1016/S0045-7825(02)00464-4
Tapia, C., Urbina, D., Mena, C., Sánchez Sánchez, X., & Haro, E. (2023). Recovery of level III ballistic plates by reinforcing and renewing their structural components. In M. Botto-Tobar, M. Zambrano Vizuete, S. Montes León, P. Torres-Carrión, & B. Durakovic (Eds.), Applied technologies (pp. 426–437). Springer. https://doi.org/10.1007/978-3-031-24985-3_31
Thill, C., Etches, J. A., Bond, I. P., Potter, K. D., & Weaver, P. M. (2010). Composite corrugated structures for morphing wing skin applications. Smart Materials and Structures, 19(12), Article 124009. https://doi.org/10.1088/0964-1726/19/12/124009
Thill, C., Etches, J., Bond, I., Potter, K., & Weaver, P. (2008). Morphing skins. The Aeronautical Journal, 112(1129), 117–139. https://doi.org/10.1017/S0001924000002062
Thomsen, C. R., Wang, F., & Sigmund, O. (2018). Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis. Computer Methods in Applied Mechanics and Engineering, 339, 115–136. https://doi.org/10.1016/j.cma.2018.04.031
Townsend, S., & Kim, H. A. (2019). A level set topology optimization method for the buckling of shell structures. Structural and Multidisciplinary Optimization, 60(5), 1783–1800. https://doi.org/10.1007/s00158-019-02374-9
Träff, E., Sigmund, O., & Groen, J. P. (2019). Simple single-scale microstructures based on optimal rank-3 laminates. Structural and Multidisciplinary Optimization, 59(4), 1021–1031. https://doi.org/10.1007/s00158-018-2180-3
Tran, M. T., Nguyen, M. N., Bui, T. Q., & Nguyen, H. Q. (2023). An enhanced proportional topology optimization with virtual elements: Formulation and numerical implementation. Finite Elements in Analysis and Design, 222, Article 103958. https://doi.org/10.1016/j.finel.2023.103958
Ullah, Z., Ullah, B., Khan, W., & Siraj-ul-Islam. (2022). Proportional topology optimisation with maximum entropy-based meshless method for minimum compliance and stress constrained problems. Engineering with Computers, 38(6), 5541–5561. https://doi.org/10.1007/s00366-022-01683-w
Valdevit, L., & Bauer, J. (2020). Chapter 13.1 – Fabrication of 3D micro-/nanoarchitected materials. In T. Baldacchini (Ed.), Three-dimensional microfabrication using two-photon polymerization (2nd ed., pp. 541–576). William Andrew Publishing. https://doi.org/10.1016/B978-0-12-817827-0.00013-8
Vangelatos, Z., Gu, G. X., & Grigoropoulos, C. P. (2019). Architected metamaterials with tailored 3D buckling mechanisms at the microscale. Extreme Mechanics Letters, 33, Article 100580. https://doi.org/10.1016/j.eml.2019.100580
Vogiatzis, P., Chen, S., Wang, X., Li, T., & Wang, L. (2017). Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method. Computer-Aided Design, 83, 15–32. https://doi.org/10.1016/j.cad.2016.09.009
Wang, H., Cheng, W., Du, R., Wang, S., & Wang, Y. (2020). Improved proportional topology optimization algorithm for solving minimum compliance problem. Structural and Multidisciplinary Optimization, 62(2), 475–493. https://doi.org/10.1007/s00158-020-02504-8
Wang, L., Xia, H., Yang, Y., Cai, Y., & Qiu, Z. (2019). A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties. Rapid Prototyping Journal, 25(9), 1455–1474. https://doi.org/10.1108/RPJ-08-2017-0163
Wang, Q., Lu, Z., & Zhou, C. (2011). New topology optimization method for wing leading-edge ribs. Journal of Aircraft, 48(5), 1741–1748. https://doi.org/10.2514/1.C031362
Wang, X., Zhou, W., Xun, G., & Wu, Z. (2018). Dynamic shape control of piezocomposite-actuated morphing wings with vibration suppression. Journal of Intelligent Material Systems and Structures, 29(3), 358–370. https://doi.org/10.1177/1045389X17708039
Wegst, U. G., Bai, H., Saiz, E., Tomsia, A. P., & Ritchie, R. O. (2015). Bioinspired structural materials. Nature Materials, 14(1), 23–36. https://doi.org/10.1038/nmat4089
Wereley, N. M., & Gandhi, F. (2010). Flexible skins for morphing aircraft. Journal of Intelligent Material Systems and Structures, 21(17). https://doi.org/10.1177/1045389X10393157
Wu, J., Sigmund, O., & Groen, J. P. (2021). Topology optimization of multi-scale structures: A review. Structural and Multidisciplinary Optimization, 63(3), 1455–1480. https://doi.org/10.1007/s00158-021-02881-8
Xia, L., Xia, Q., Huang, X., & Xie, Y. M. (2018). Bi-directional evolutionary structural optimization on advanced structures and materials: A comprehensive review. Archives of Computational Methods in Engineering, 25(2), 437–478. https://doi.org/10.1007/s11831-016-9203-2
Xie, Y. M., & Steven, G. P. (1993). A simple evolutionary procedure for structural optimization. Computers & Structures, 49(5), 885–896. https://doi.org/10.1016/0045-7949(93)90035-C
Xie, Y., & Steven, G. (1997). Evolutionary structural optimization. Springer. https://doi.org/10.1007/978-1-4471-0985-3
Yousaf, R., Shahzad, A., Qadri, M. M., & Javed, A. (2021). Recent advancements in flapping mechanism and wing design of micro aerial vehicles. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235(19), 4425–4446. https://doi.org/10.1177/0954406220960783
Zhang, H., Zhang, Z., Song, C., & Yang, C. (2021). A morphing wing with cellular structure of non-uniform density. Smart Materials and Structures, 30(10), Article 105005. https://doi.org/10.1088/1361-665X/ac1bef
Zheng, H., Zhang, Y., Liu, L., Wan, W., Guo, P., Nyström, A. M., & Zou, X. (2016). One-pot synthesis of metal–organic frameworks with encapsulated target molecules and their applications for controlled drug delivery. Journal of the American Chemical Society, 138(3), 962–968. https://doi.org/10.1021/jacs.5b11720
Zheng, X., Lee, H., Weisgraber, T. H., Shusteff, M., DeOtte, J., Duoss, E. B., Kuntz, J. D., Biener, M. M., Ge, Q., Jackson, J. A., Kucheyev, S. O., Fang, N. X., & Spadaccini, C. M. (2014). Ultralight, ultrastiff mechanical metamaterials. Science, 344(6190), 1373–1377. https://doi.org/10.1126/science.1252291
Zhong, X., Huang, W., Yan, L., Wu, H., & Du, Z. (2022). Investigation on the adaptive control of shock wave/turbulent boundary layer interaction based on the secondary circulation jets. Acta Astronautica, 198, 233–250. https://doi.org/10.1016/j.actaastro.2022.06.016
Zhou, M., & Rozvany, G. I. N. (1991). The COC algorithm, Part II: Topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 89(1–3), 309–336. https://doi.org/10.1016/0045-7825(91)90046-9
Zhu, J., Yang, J., Zhang, W., Gu, X., & Zhou, H. (2023). Design and applications of morphing aircraft and their structures. Frontiers of Mechanical Engineering, 18(3), Article 34. https://doi.org/10.1007/s11465-023-0750-6