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Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu

Year 2024, EARLY VIEW, 1 - 1
https://doi.org/10.2339/politeknik.1302121

Abstract

ÖZ
Kanat tasarımında kritik ve dikkat edilmesi gereken parametrelerden birisi de doğal frekanstır. Kanadın doğal frekansının küçük olması kanadın daha fazla yer değiştirmesine neden olur. Diğer taraftan kanadın doğal frekansı ile havanın doğal frekansı eşit olduğunda rezonansa neden olabilir ve bu durumda kanatta yapısal hasar oluşabilir. Kanat doğal frekansını arttırmak için yapılan çalışmalar kanadın rijitliğini arttırırken aynı zamanda, kütle artışına neden olabilir. Bu çalışmada, kanat kütlesinin arttırılmadan doğal frekansının arttırılması amacıyla çok amaçlı optimizasyon problemi kurularak kanat kiriş elemanın optimizasyonu gerçekleştirilmiştir. Kesit geometrisi şekil parametreleri tasarım değişkenleri olarak alınmış, kanat ağırlığının minimizasyonu ve kanadın birinci doğal frekansının maksimizasyonu amaç fonksiyonu olarak tanımlanmıştır. Kanadın hem doğal frekansının arttırılması hem de kütlesinin azaltılması amacıyla çok amaçlı bir optimizasyon çalışması gerçekleştirilmiştir. Çalışma kapsamında kanat iç yapı elemanlarından kiriş elemanının kesit geometrisinin doğal frekans ve ağırlık açısından optimum özelliklere sahip kanat kiriş kesiti tasarlanması amaçlanmıştır. Optimizasyon işlemini gerçekleştirmek için Ansys Workbench ortamında parametrik geometri modeli oluşturulmuş, kanat üzerinde oluşan basınç hesaplanmış, statik analiz ile gerilme ve yer değiştirme, modal analiz ile doğal frekans hesaplanmıştır. Cevap yüzey yöntemi kullanılarak gerçekleştirilen optimizasyon çalışmasında çok amaçlı genetik algoritma kullanılmıştır. Çalışma sonucunda kanat birinci doğal frekansında % 14 artış sağlanırken aynı zamanda kanat ağırlığında yaklaşık %5 hafifleme sağlanmıştır.

Supporting Institution

Tübitak

Project Number

118C100

Thanks

TÜBİTAK 2244 Sanayi Doktora Programı kapsamında verilen bursiyer desteğine teşekkür ederiz (Proje No:118C100)

References

  • [1] Naing Lin Aung, Oleg Tatarnikov., Phyo Wai Aung, “Approach to optimization of composite aircraft wing structure”, IOP Conf. Ser. Mater. Sci. Eng., 9712, 022058, (2020).
  • [2] Sohaib, M.,”Parameterized Automated Generic Model for Aircraft Wing Structural Design and Mesh Generation for Finite Element Analysis” Yüksek Lisans Tezi, Linkoping’s Üniversitesi, (2011).
  • [3] Dogan C. “Design optimization of composite I-beam wing spars with the corrugated web”, Yüksek Lisans Tezi, Mechanical Engineering, Doğuş Üniversitesi, (2014).
  • [4] Wan, Z., D. Liu, C. Tang, and C. Yang, “Studies on the influence of spar position on aeroelastic optimization of a large aircraft wing”, Science China Technological Sciences, 55, 117–124, (2012).
  • [5] Grbovic, A. and B. Rasuo,” FEM based fatigue crack growth predictions for spar of light aircraft under variable amplitude loading”, Engineering Failure Analysis,26, 5064, (2012).
  • [6] Visnjic, G., D. Nozak, F. Kosel and T. Kosel,” Shear-lag influence on maximum specific bending stiffness and strength of composite I-beam wing spar”, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 225,501511, (2010).
  • [7] Falek, M., E. Szymczyk and J. Jachimowicz,” Study on Possible Replacement of the Aluminum Spar with a Composite Structure Illustrated with the Case of Agricultural Aircraft”, Fatigue of Aircraft Structures,8599, (2017).
  • [8] Maute, K. and M. Allen, “Conceptual design of aeroelastic structures by topology optimization”, Structural and Multidisciplinary Optimization”, 27, 2742, (2004).
  • [9] Lim, J., S. Choi, S. Shin and D. Lee, “Wing Design Optimization of a Solar-HALE Aircraft”, International Journal of Aeronautical and Space Sciences,15, 219231, (2014).
  • [10] Bindolino, G., Ghiringhelli, G. L., Ricci, S., and Terraneo, M., “Multilevel Structural Optimization for Preliminary Wing-Box Weight Estimation”, AIAA, 47(2), 475–489, (2010).
  • [11] Mohamed, H.A. and S.Nithiyakalyani, “Design and Structural Analysis of the Ribs and Spars of Swept Back Wing” , International Journal of Emerging Technology and Advanced Engineering, 4, 208-213, (2014).
  • [12] Park, H.,” A study on forced vibration behaviors of composite main wing structure of the 20 seat class small scale WIG craft”, Aerospace Science and Technology, 29, 445-452, (2013).
  • [13] Stanford, B. K. ve P. D. Dunning,” Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads”, Journal of Aircraft, 52, 1298-1311, (2015).
  • [14] Lickley, R. L., “Aircraft Construction: A Review of Modern Stressed Skin Systems”, Wilkinson Rubber Linatex Ltd., 1-4, Great Tower St., London, E.C.3., (1940).
  • [15] Aviation Maintenance Technician Handbook” Airframe. Chapter 1: Aircraft Structures,” Vol. 1, U. S. Department of Transportation Federal Aviation Administration, (2012).
  • [16] Lovely Son ”The Effect of Wing Spar Cross Sectional Profile Variation on the Unmanned Aerial Vehicle (UAV) Natural Frequency”, IOP Conf. Ser.: Mater. Sci. Eng. 1062 012032,(2021).
  • [17] Xie, Q., and M. Rais-Rohani, “Probabilistic design optimization of aircraft structures with reliability, manufacturability, and cost constraints”, Structures, Structural Dynamics, and Materials Conference, AIAA, 2003-1631. (2003).
  • [18] Adam D and Wiktor K,” The optimal design of UAV wing structure “AIP Conf. Proc. 1922 120009.(2018).
  • [19] Phyo Wai Aung et al ,” Structural optimization of a light aircraft composite wing”, IOP Conf. Ser.: Mater. Sci. Eng. 709 044094. (2020).
  • [20] Bhachu, K. S., R. T. Haftka, G. Waycaster and N. H. Kim, “Probabilistic Manufacturing Tolerance Optimization of Damage-Tolerant Aircraft Structures Using Measured Data” , Journal of Aircraft, 52, 1412–1421. (2015).
  • [21] Hutchison, M.G., Unger, E. R., Mason, W. H., and Grossman, B.,” Variable- Complexity Aerodynamic Optimization of an HSCT Wing Using Structural Wing-Weight Equations”, Journal of Aircraft, 31(1),110-116, (1994).
  • [22] R. Sun, G. Chen, C. Zhou,” Multidisciplinary design optimization of adaptive wing leading edge”, Sci. China, Technol. Sci. 56(7), 1790–1797, (2013).
  • [23] Kroo, I., Gallman, J., and Smith, S., “Aerodynamic and Structural Studies of Joined-Wing Aircraft”, Journal of Aircraft, 28(1),74-81, (1991).
  • [24] Kuran, B., Taşkınoğlu, E. E., ve Çiçek, B. C.” Effect of vibration loads on the service life of solid rocket propellants.” SAVIAC, 81st Schock and Vibration Symposium, Orlando, Florida, USA, Ekim 24-28, (2020).
  • [25] B. Y. Yıldırım, “Aerodynamic shape optimization of a wing using 3d flow solutions with su2 and response surface methodology,” M.Sc. Yüksek Lisans Tezi, Middle East Technical University, (2021).
  • [26] Wei, W., Peng, F., Li, Y., Chen, B., Xu, Y., Wei, Y.,” Optimization Design of Extrusion Roller of RP1814 Roller Press Based on ANSYS Workbench.” Appl. Sci.,11(20), 9584, (2021).
  • [27] K. Cheng, “Finite element analysis and structural optimization of the box on the ANSYS workbench,” Advanced Materials Research, 211,434–439, (2011).
  • [28] Sun, Y.; Huang, P.; Cao, Y.; Jiang, G.; Yuan, Z.; Dongxu, B.; Liu, X.,” Multi-objective optimization design of ladle refractory lining based on genetic algorithm.”, Front. Bioeng. Biotechnol. 10, 900655, (2022).
  • [29] Lee, S. H., and Lee, J.,” Optimization of three-dimensional wings in ground effect using multiobjective genetic algorithm.” Journal of Aircraft, 48(5), 1633-1645, (2011).
  • [30] Bruce RR.“Initial and progressive failure analysis of a composite wing spar structure” JMech Eng 2017; 14(2): 167–183, (2017).
  • [31] Ajith V S, Dr. Ravi Kumar Paramasivam, “Study of Optimal Design of Spar Beam for the Wing of an Aircraft,” Journal of Aircraft,5,179-187, (2017).
  • [32] Martinez, M. P., A. Messac and M. Rais-Rohani,” Manufacturability Based Optimization of Aircraft Structures Using Physical Programming “, AIAA, 39,517-525, (2001).
  • [33] Li, H., L. Zhu, G. Sun, M. Dong and J. Qiao, Defection monitoring of thin-walled wing spar subjected to bending load using multi-element FBG sensors, Optik,164, 691-700, (2018).
  • [34] Gorgulu Y. F., Ozgur M. A. ve Kose R., “CFD analysis of a NACA 0009 aerofoil at a low reynolds number”, Politeknik Dergisi ,24(3): 1237-1242, (2021).
  • [35] Fatahian, E., Fatahian, H., Simultaneous effect of suction and cavity for controlling f low separation on NACA 0012 airfoil–CFD approach. Gazi University Journal of Science 34 (1), 235–249, (2021).
  • [36] Steenwijk, B.; Druetta, P. Numerical Study of Turbulent Flows over a NACA0012Airfoil: Insights into Its Performance and the Addition of a Slotted Flap. Appl. Sci.13(13), 7890, (2023).
  • [37] Yılmaz, M., Köten, H., Çetinkaya, E., Coşar, Z. “A comparative CFD analysis of NACA0012 and NACA4412 airfoils” Journal of Energy Systems, 2(4), 145-159, (2018).
  • [38] Yousefi, K., Saleh, R. “The effects of trailing edge blowing on aerodynamic characteristics of the NACA 0012 airfoil and optimization of the blowing slot geometry" Journal of Theoretical and Applied Mechanics, 52, 165-179, (2014).
  • [39] Akın A.G., Tanürün H. E. ve Acır A. “Rüzgâr türbinlerinde kiriş yapısının performansa etkisinin sayısal olarak incelenmesi”, Politeknik Dergisi, 24(3), 1219 - 1226, (2021).
  • [40] Selimli S., “Yüzey geometrisinin mermi aerodinamik davranışları üzerine etkisinin nümerik incelenmesi”, Politeknik Dergisi, 24(1): 299 304, (2021).
  • [41] Kaya A.F., “Investigation of a rib structure effect on the aerodynamic performance of a plain flapped symmetrical airfoil”, Politeknik Dergisi,
  • [42] Tola, Ceyhun & Cetiner, Abdullah & Güzel, Göktan & Buluş, Halil. “Jenerik bir mühimmat kanadına ait geometrik parametrelerin disiplinler arası çok amaçlı optimizasyonu.” 9. Ulusal Havacılık ve Uzay Konferansı, (2022).
  • [43] Kostić, Č. “Review of the Spalart-Allmaras turbulence model and its modifications to three dimensional supersonic configurations” Scientific Technical Review, 65(1): 43-49. (2015).
  • [44] Sathyanarayanan, S., Adluri, S. M. R., “Incorporation of Friction Coefficient in the Design Equations for Elevated Temperature Tanks.” Journal of Pressure Vessel Technology, 135(2): 021205 (2013).
  • [45] Mechanical APDL Element Reference, ANSYS Inc, Canonsburg Pennsylvania, PA, USA, 952, (2013).
  • [46] DesignXplorer Optimization Tutorials, Ansys Inc., (2021).

Multi-Objective Optimization of an Aircraft Wing Spar Section

Year 2024, EARLY VIEW, 1 - 1
https://doi.org/10.2339/politeknik.1302121

Abstract

ABSTRACT
Natural frequency is a critical parameter in wing design. The fact that the natural frequency of the wing is small causes the wing to displace more, while at the same time, it can cause resonance when the natural frequency of the wing and the natural frequency of the air are equal. Studies carried out to increase the natural frequency of the wing can increase the rigidity of the wing while increasing its mass. This study identified a multiobjective optimization problem for increasing the natural frequency of wings without increasing the wing mass. For this objective, optimization of the wing spar element was carried out. The wing cross-sectional geometry parameters are taken as design variables. Minimizing the weight of the wing and maximizing the first natural frequency of the wing are defined as objective functions. A multiobjective optimization study was carried out to increase the natural frequency of the wing and reduce its mass. This research aims to design a wing spar section with optimum properties in terms of natural frequency and weight of the cross-sectional geometry of the spar element from the wing internal structure elements. To perform the optimization process, modeling the parametric geometry, calculation of the pressure distribution on the wing, stress and displacement by static analysis, and calculation of the natural frequency by the modal analysis model was constructed via the Ansys Workbench environment. A multiobjective genetic algorithm was used in the optimization study using the response surface method. As a result of the study, the wing’s first natural frequency increased by 14%, and the wing mass decreased by about 5%.

Project Number

118C100

References

  • [1] Naing Lin Aung, Oleg Tatarnikov., Phyo Wai Aung, “Approach to optimization of composite aircraft wing structure”, IOP Conf. Ser. Mater. Sci. Eng., 9712, 022058, (2020).
  • [2] Sohaib, M.,”Parameterized Automated Generic Model for Aircraft Wing Structural Design and Mesh Generation for Finite Element Analysis” Yüksek Lisans Tezi, Linkoping’s Üniversitesi, (2011).
  • [3] Dogan C. “Design optimization of composite I-beam wing spars with the corrugated web”, Yüksek Lisans Tezi, Mechanical Engineering, Doğuş Üniversitesi, (2014).
  • [4] Wan, Z., D. Liu, C. Tang, and C. Yang, “Studies on the influence of spar position on aeroelastic optimization of a large aircraft wing”, Science China Technological Sciences, 55, 117–124, (2012).
  • [5] Grbovic, A. and B. Rasuo,” FEM based fatigue crack growth predictions for spar of light aircraft under variable amplitude loading”, Engineering Failure Analysis,26, 5064, (2012).
  • [6] Visnjic, G., D. Nozak, F. Kosel and T. Kosel,” Shear-lag influence on maximum specific bending stiffness and strength of composite I-beam wing spar”, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 225,501511, (2010).
  • [7] Falek, M., E. Szymczyk and J. Jachimowicz,” Study on Possible Replacement of the Aluminum Spar with a Composite Structure Illustrated with the Case of Agricultural Aircraft”, Fatigue of Aircraft Structures,8599, (2017).
  • [8] Maute, K. and M. Allen, “Conceptual design of aeroelastic structures by topology optimization”, Structural and Multidisciplinary Optimization”, 27, 2742, (2004).
  • [9] Lim, J., S. Choi, S. Shin and D. Lee, “Wing Design Optimization of a Solar-HALE Aircraft”, International Journal of Aeronautical and Space Sciences,15, 219231, (2014).
  • [10] Bindolino, G., Ghiringhelli, G. L., Ricci, S., and Terraneo, M., “Multilevel Structural Optimization for Preliminary Wing-Box Weight Estimation”, AIAA, 47(2), 475–489, (2010).
  • [11] Mohamed, H.A. and S.Nithiyakalyani, “Design and Structural Analysis of the Ribs and Spars of Swept Back Wing” , International Journal of Emerging Technology and Advanced Engineering, 4, 208-213, (2014).
  • [12] Park, H.,” A study on forced vibration behaviors of composite main wing structure of the 20 seat class small scale WIG craft”, Aerospace Science and Technology, 29, 445-452, (2013).
  • [13] Stanford, B. K. ve P. D. Dunning,” Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads”, Journal of Aircraft, 52, 1298-1311, (2015).
  • [14] Lickley, R. L., “Aircraft Construction: A Review of Modern Stressed Skin Systems”, Wilkinson Rubber Linatex Ltd., 1-4, Great Tower St., London, E.C.3., (1940).
  • [15] Aviation Maintenance Technician Handbook” Airframe. Chapter 1: Aircraft Structures,” Vol. 1, U. S. Department of Transportation Federal Aviation Administration, (2012).
  • [16] Lovely Son ”The Effect of Wing Spar Cross Sectional Profile Variation on the Unmanned Aerial Vehicle (UAV) Natural Frequency”, IOP Conf. Ser.: Mater. Sci. Eng. 1062 012032,(2021).
  • [17] Xie, Q., and M. Rais-Rohani, “Probabilistic design optimization of aircraft structures with reliability, manufacturability, and cost constraints”, Structures, Structural Dynamics, and Materials Conference, AIAA, 2003-1631. (2003).
  • [18] Adam D and Wiktor K,” The optimal design of UAV wing structure “AIP Conf. Proc. 1922 120009.(2018).
  • [19] Phyo Wai Aung et al ,” Structural optimization of a light aircraft composite wing”, IOP Conf. Ser.: Mater. Sci. Eng. 709 044094. (2020).
  • [20] Bhachu, K. S., R. T. Haftka, G. Waycaster and N. H. Kim, “Probabilistic Manufacturing Tolerance Optimization of Damage-Tolerant Aircraft Structures Using Measured Data” , Journal of Aircraft, 52, 1412–1421. (2015).
  • [21] Hutchison, M.G., Unger, E. R., Mason, W. H., and Grossman, B.,” Variable- Complexity Aerodynamic Optimization of an HSCT Wing Using Structural Wing-Weight Equations”, Journal of Aircraft, 31(1),110-116, (1994).
  • [22] R. Sun, G. Chen, C. Zhou,” Multidisciplinary design optimization of adaptive wing leading edge”, Sci. China, Technol. Sci. 56(7), 1790–1797, (2013).
  • [23] Kroo, I., Gallman, J., and Smith, S., “Aerodynamic and Structural Studies of Joined-Wing Aircraft”, Journal of Aircraft, 28(1),74-81, (1991).
  • [24] Kuran, B., Taşkınoğlu, E. E., ve Çiçek, B. C.” Effect of vibration loads on the service life of solid rocket propellants.” SAVIAC, 81st Schock and Vibration Symposium, Orlando, Florida, USA, Ekim 24-28, (2020).
  • [25] B. Y. Yıldırım, “Aerodynamic shape optimization of a wing using 3d flow solutions with su2 and response surface methodology,” M.Sc. Yüksek Lisans Tezi, Middle East Technical University, (2021).
  • [26] Wei, W., Peng, F., Li, Y., Chen, B., Xu, Y., Wei, Y.,” Optimization Design of Extrusion Roller of RP1814 Roller Press Based on ANSYS Workbench.” Appl. Sci.,11(20), 9584, (2021).
  • [27] K. Cheng, “Finite element analysis and structural optimization of the box on the ANSYS workbench,” Advanced Materials Research, 211,434–439, (2011).
  • [28] Sun, Y.; Huang, P.; Cao, Y.; Jiang, G.; Yuan, Z.; Dongxu, B.; Liu, X.,” Multi-objective optimization design of ladle refractory lining based on genetic algorithm.”, Front. Bioeng. Biotechnol. 10, 900655, (2022).
  • [29] Lee, S. H., and Lee, J.,” Optimization of three-dimensional wings in ground effect using multiobjective genetic algorithm.” Journal of Aircraft, 48(5), 1633-1645, (2011).
  • [30] Bruce RR.“Initial and progressive failure analysis of a composite wing spar structure” JMech Eng 2017; 14(2): 167–183, (2017).
  • [31] Ajith V S, Dr. Ravi Kumar Paramasivam, “Study of Optimal Design of Spar Beam for the Wing of an Aircraft,” Journal of Aircraft,5,179-187, (2017).
  • [32] Martinez, M. P., A. Messac and M. Rais-Rohani,” Manufacturability Based Optimization of Aircraft Structures Using Physical Programming “, AIAA, 39,517-525, (2001).
  • [33] Li, H., L. Zhu, G. Sun, M. Dong and J. Qiao, Defection monitoring of thin-walled wing spar subjected to bending load using multi-element FBG sensors, Optik,164, 691-700, (2018).
  • [34] Gorgulu Y. F., Ozgur M. A. ve Kose R., “CFD analysis of a NACA 0009 aerofoil at a low reynolds number”, Politeknik Dergisi ,24(3): 1237-1242, (2021).
  • [35] Fatahian, E., Fatahian, H., Simultaneous effect of suction and cavity for controlling f low separation on NACA 0012 airfoil–CFD approach. Gazi University Journal of Science 34 (1), 235–249, (2021).
  • [36] Steenwijk, B.; Druetta, P. Numerical Study of Turbulent Flows over a NACA0012Airfoil: Insights into Its Performance and the Addition of a Slotted Flap. Appl. Sci.13(13), 7890, (2023).
  • [37] Yılmaz, M., Köten, H., Çetinkaya, E., Coşar, Z. “A comparative CFD analysis of NACA0012 and NACA4412 airfoils” Journal of Energy Systems, 2(4), 145-159, (2018).
  • [38] Yousefi, K., Saleh, R. “The effects of trailing edge blowing on aerodynamic characteristics of the NACA 0012 airfoil and optimization of the blowing slot geometry" Journal of Theoretical and Applied Mechanics, 52, 165-179, (2014).
  • [39] Akın A.G., Tanürün H. E. ve Acır A. “Rüzgâr türbinlerinde kiriş yapısının performansa etkisinin sayısal olarak incelenmesi”, Politeknik Dergisi, 24(3), 1219 - 1226, (2021).
  • [40] Selimli S., “Yüzey geometrisinin mermi aerodinamik davranışları üzerine etkisinin nümerik incelenmesi”, Politeknik Dergisi, 24(1): 299 304, (2021).
  • [41] Kaya A.F., “Investigation of a rib structure effect on the aerodynamic performance of a plain flapped symmetrical airfoil”, Politeknik Dergisi,
  • [42] Tola, Ceyhun & Cetiner, Abdullah & Güzel, Göktan & Buluş, Halil. “Jenerik bir mühimmat kanadına ait geometrik parametrelerin disiplinler arası çok amaçlı optimizasyonu.” 9. Ulusal Havacılık ve Uzay Konferansı, (2022).
  • [43] Kostić, Č. “Review of the Spalart-Allmaras turbulence model and its modifications to three dimensional supersonic configurations” Scientific Technical Review, 65(1): 43-49. (2015).
  • [44] Sathyanarayanan, S., Adluri, S. M. R., “Incorporation of Friction Coefficient in the Design Equations for Elevated Temperature Tanks.” Journal of Pressure Vessel Technology, 135(2): 021205 (2013).
  • [45] Mechanical APDL Element Reference, ANSYS Inc, Canonsburg Pennsylvania, PA, USA, 952, (2013).
  • [46] DesignXplorer Optimization Tutorials, Ansys Inc., (2021).
There are 46 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Article
Authors

Hakan Demir 0000-0001-9819-2167

Necmettin Kaya 0000-0002-8297-0777

Project Number 118C100
Early Pub Date August 26, 2024
Publication Date
Submission Date May 25, 2023
Published in Issue Year 2024 EARLY VIEW

Cite

APA Demir, H., & Kaya, N. (2024). Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu. Politeknik Dergisi1-1. https://doi.org/10.2339/politeknik.1302121
AMA Demir H, Kaya N. Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu. Politeknik Dergisi. Published online August 1, 2024:1-1. doi:10.2339/politeknik.1302121
Chicago Demir, Hakan, and Necmettin Kaya. “Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu”. Politeknik Dergisi, August (August 2024), 1-1. https://doi.org/10.2339/politeknik.1302121.
EndNote Demir H, Kaya N (August 1, 2024) Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu. Politeknik Dergisi 1–1.
IEEE H. Demir and N. Kaya, “Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu”, Politeknik Dergisi, pp. 1–1, August 2024, doi: 10.2339/politeknik.1302121.
ISNAD Demir, Hakan - Kaya, Necmettin. “Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu”. Politeknik Dergisi. August 2024. 1-1. https://doi.org/10.2339/politeknik.1302121.
JAMA Demir H, Kaya N. Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu. Politeknik Dergisi. 2024;:1–1.
MLA Demir, Hakan and Necmettin Kaya. “Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu”. Politeknik Dergisi, 2024, pp. 1-1, doi:10.2339/politeknik.1302121.
Vancouver Demir H, Kaya N. Bir Hava Aracının Çok Amaçlı Kanat Kiriş Kesit Optimizasyonu. Politeknik Dergisi. 2024:1-.