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DESIGN AND OPTIMISATION OF A CHIRAL EUXETIC LATTICE STRUCTURE WITH RECTANGULAR CROSS-SECTION HAVING VARIOUS ASPECT RATIO

Year 2024, Volume: 11 Issue: 23, 265 - 282, 31.08.2024
https://doi.org/10.54365/adyumbd.1440934

Abstract

In this study, a chiral lattice is designed in a cubic form. The cross-section is rectangular. Polyethylene, Ti6Al4V, AlSi10Mg, 316 stainless steel, polyamide-6, polypropylene, and resin polyamide/Nylon-66 were used as materials. One end of the structure is fixed with an anchored support while the free end is subjected to axial displacement. Finite element based simulations were used for structural analysis. As a result of the simulation, stress, deformation and Poisson's ratio values were obtained. These parameters were subjected to genetic algorithm based optimisation. The aim of the optimisation is to obtain maximum strength in the structure with minimum size. Because lightweight structures are preferred in terms of both construction and material costs. As a result, the best-fit-for-purpose dimensions were determined. In addition, a response function showing the relationship between the parameters was obtained. The optimum cross section is 0.5x0.2 mm and in this case the structure could withstand a displacement of -0.9 mm A stress of 23.636 MPa occurred on the structure. This value is far below the yield strength of the material. In this case, the mass of the structure is 0.298 grams.

References

  • Ha CS, Plesha M, Lakes R. Chiral three-dimensional isotropic lattices with negative Poisson's ratio: Chiral 3D isotropic lattices with negative Poisson's ratio. physica status solidi (b). 2016; 253. 10.1002/pssb.201600055.
  • Novak N, Mauko A, Ulbin M, Krstulović-Opara L, Ren Z, Vesenjak M. Development and characterisation of novel three-dimensional axisymmetric chiral auxetic structures. Journal of Materials Research and Technology. 2022; 17. 10.1016/j.jmrt.2022.02.025.
  • Vasiliev A, Pavlov I. Models and parameters of Cosserat hexagonal lattices with chiral microstructure. IOP Conference Series: Materials Science and Engineering. 2021; 1008. 012017. 10.1088/1757-899X/1008/1/012017.
  • Andrea B, Luigi G. Simplified modelling of chiral lattice materials with local resonators. International Journal of Solids and Structures. Volume 83, April 2016, 126-141.
  • Haifeng R, Jiahong H, Dong L. Wave propagation characterization of 2D composite chiral lattice structures with circular plate inclusions. Engineering Structures. 2022; Volume 264, 1 August 2022, 114466.
  • Alessandro S., Massimo R., Stefano G., Fabrizio S. Phononic properties of hexagonal chiral lattices. Wave Motion. Volume 46, Issue 7, November 2009, 435-450.
  • Liu XN, Huang GL, Hu GK. Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices. Journal of the Mechanics and Physics of Solids. 2011; Volume 60, Issue 11, November 2012, 1907-1921.
  • Eric SA, Goerlitzer, RM, Sergey N, Kirsten V, Marcel R, Peter B, Matthias K, Nicolas V. Chiral Surface Lattice Resonances. Advanced Materials, 21 April 2020.
  • Andrew JG. Chiral Surfaces: Accomplishments and Challenges. January 26, 2010. ACS Nano 2010, 4, 1, 5–10.
  • Gerhard HF., Kübler J, Felser C. Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups. Materials (Basel) 2022 Aug 23;15(17):5812. doi: 10.3390/ma15175812.
  • Erdoğan İ, Toktas İ. Investigation of The Effect of Geometry Inner Thickness on New Designed Auxetic Structure. Politeknik Dergisi, 2023-a; 26(2), 901-912. https://doi.org/10.2339/politeknik.1094739
  • Nergis FB, Candan C, Duru SC. A novel yarn for personel protection in knitted sportswear. Tekstil Ve Mühendis. 2023; 30(131), 249-252. https://doi.org/10.7216/teksmuh.1365889
  • Kaya O, Bademlioğlu AH, Kaboğlu C. Performance Optimization of Auxetic Structures on Energy Absorption of Cylindrical Sandwich Using Taguchi and ANOVA Methods, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2023-a; vol. 12, no. 2, pp. 445–454, doi: 10.17798/bitlisfen.1237388.
  • Erdoğan İ, Toktas İ. Investigation of the Auxetic of a novel geometric structure and improvement of Poisson’s ratio at different inner thicknesses. Gazi University Journal of Science Part C: Design and Technology. 2023-b; 11(4), 893-902. https://doi.org/10.29109/gujsc.1346281
  • Kaya N, Eldem C, Toktas I. Investigation of the auxetic behavior of an original lattice structure design. Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım ve Teknoloji. 2023-b; 11(4), 1081 - 1091. 10.29109/gujsc.1367616
  • Cetin E, Seyitoglu SS. A bibliometric overview of research on auxetic structures: Trends and patterns. International Journal of Automotive Science And Technology. 2024; 8(1), 65-77. https://doi.org/10.30939/ijastech..1374313
  • Kaboğlu C. Statik yükleme altında oksetik iç yapılı sandviç kompozitlerin incelenmesi, El-Cezeri Journal of Science and Engineering, 2022; c. 9, sy. 1, ss. 350–359, doi: 10.31202/ecjse.978310.
  • Becergen B, Çakmak M, Maral MF, Dayanç A, vd. Design Approaches on Inner Bodies of Gears with Methods Topology Optimization and Lattice Structures. Avrupa Bilim Ve Teknoloji Dergisi. 2022; (39), 85-90. https://doi.org/10.31590/ejosat.1144818
  • Akgün M, Süvari F, Eren R, Yurdakul T. Investigation of Auxetic Performance and Various Physical Properties of Fabrics Woven with Braid Yarns. Textile and Apparel. 2022; 32(3), 220-231. https://doi.org/10.32710/tekstilvekonfeksiyon.1033681
  • Özkan E, Khosravi F. Experimental and numerical investigation of the mechanical behavior of the modified metal auxetic structure. Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi, 2023; 9(1), 48-62. https://doi.org/10.34186/klujes.1222192
  • Kaya O, Hafızoğlu H, Babacan N. Effect of Unit Cell Height on the Ballistic Performance of the Body-Centered Lattice Structures. International Journal of Innovative Engineering Applications, 2022; 6(1), 30-34. https://doi.org/10.46460/ijiea.1054219
  • Üzün A., Kayacan MY. Investigation of over obstacle performance analysis of auxetic airless tyres. International Journal of 3D Printing Technologies and Digital Industry, 2023; 7(3), 415-427. https://doi.org/10.46519/ij3dptdi.1336826
  • Akbulut A, Top N, Gökçe H. Eİ için tasarlanan kafes yapıların yapısal davranışlarının incelenmesi. İmalat Teknolojileri ve Uygulamaları. 2023; 4(2), 92-100. https://doi.org/10.52795/mateca.1332895
  • Öykünç D, Yıldızdag ME. Venüs’ün Çiçek Sepeti Süngerinden Esinlenerek Tasarlanmış Bir Kafes Sistemin Yapısal Davranışının İncelenmesi. Gemi Ve Deniz Teknolojisi. 2023; (222), 64-75. https://doi.org/10.54926/gdt.1156139
  • Çelebi A, İmanç, MM. Evaluation of Mechanical Properties of PLA Auxetic Structures Produced by Additive Manufacturing. Journal of Materials and Mechatronics: A. 2023; 4(2), 384-396. https://doi.org/10.55546/jmm.1309858
  • Körner C, Liebold-Ribeiro Y. A systematic approach to identify cellular auxetic materials. Smart Mater Struct. 2014; 24:025013 https://doi.org/10.1088/0964-1726/24/2/025013.
  • Warmuth F, Körner C. Phononic band gaps in 2D quadratic and 3D cubic cellular structures. Materials (Basel). 2014; 8:8327–37. https://doi.org/10.3390/ma8125463.
  • Wormser M, Warmuth F, Körner C. Evolution of full phononic band gaps in periodic cellular structures. Appl Phys A. 2017;123.
  • Warmuth F, Osmanlic F, Adler L. Fabrication and characterisation of a fully auxetic 3D lattice structure via selective electron beam melting. Smart Mater Struct. 2017; 26:8.
  • Ansys, Theory Manual Version 9.0, Canonsburg, PA, USA., ANSYS Inc., 2004.
  • Korkmaz C, Kacar İ. Hesaplamalı Akışkanlar Dinamiği Simülasyonları İçin Optimum Eleman Ağ Yapısının Belirlenmesi, 7 January 2022, Editör: Deniz Yılmaz; Osman Gökdoğan; Önder Uysal; Mehmet Emin Gökduman; Ahmet Süslü, Tarımsal Mekanizasyon ve Enerji Üzerine Güncel Araştırmalar. 2022; ISBN: 978-625-8037-52-4
  • Büyüköztürk Ş, Çokluk-Bökeoğlu Ö, Köklü N. Statistics for Social Sciences, 27th ed. Pegem Press, Ankara, Turkey, 2011.
  • Vigliotti A, Pasini D. Mechanical properties of hierarchical lattices, Mechanics of Materials. 2013; Vol. 62, Pages 32-43.
  • Gülcan O, Simsek U, Kavas B. Eklemeli İmalatla üretilen işlevsel olarak derecelendirilmiş metal yapılar, Mühendis ve Makine. 2021; Cilt. 62, Sayı 702, Sayfa 1-12.
  • Park K-M, Min K-S, Roh Y-S. Design optimization of lattice structures under compression: study of unit cell types and cell arrangements. 2022; Materials, Vol. 15, Issue 1, Pages 97-102.
  • Fernandes RR, Tamijani AY. Design optimization of lattice structures with stress constraints, Materials and Design. 2021; Vol. 210, Issue 110026.
  • Khan N, Acanfora V. Non-Conventional wing structure design with lattice infilled through design for additive manufacturing. 2024; Vol. 17, Issue 7, Pages 1470-1478.

FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU

Year 2024, Volume: 11 Issue: 23, 265 - 282, 31.08.2024
https://doi.org/10.54365/adyumbd.1440934

Abstract

Bu çalışmada kübik formda bir kiral kafes yapısı tasarlanmıştır. Kesit dörtgenseldir. Malzeme olarak polietilen, Ti6Al4V, AlSi10Mg, 316 paslanmaz çelik, polyamid-6, polipropilen ve reçine polyamid/Naylon-66 kullanılmıştır. Yapının bir ucu ankastre mesnet ile sabitlenmişken serbest ucu ise eksenel yer değiştirmeye maruz bırakılmıştır. Yapısal analiz için sonlu eleman esaslı simülasyon kullanılmıştır. Simülasyon sonucunda gerilme, deformasyon, Poisson oranı değerleri elde edilmiştir. Bu parametreler genetik algoritma esaslı optimizasyona tabi tutulmuştur. Optimizasyonun amacı, minimum boyuta sahip yapıda, maksimum dayanım elde edebilmektir. Zira hafif yapılar hem inşa hem de malzeme maliyetleri açısından tercih edilmektedir. Amaca uyan en iyi boyutlar tespit edilmiştir. Ayrıca parametreler arasındaki ilişkiyi gösteren bir cevap fonksiyonu elde edilmiştir. Optimum kesit 0,5x0,2 mm olup bu durumda yapı -0,9 mm'lik bir yer değiştirmeye dayanabilmiştir. Yapıda en fazla 23,636 MPa çekme ve 1,3266 MPa basma gerilmesi oluşmuştur. Bu değer malzemenin akma dayanımının altındadır. Bu hâli ile yapı kütlesi 0,298 gramdır.

Thanks

Bu çalışmanın inceleme ve değerlendirme aşamasında yapmış oldukları değerli katkılardan dolayı editör, hakem ve emeği geçenlere içten teşekkür ederim.

References

  • Ha CS, Plesha M, Lakes R. Chiral three-dimensional isotropic lattices with negative Poisson's ratio: Chiral 3D isotropic lattices with negative Poisson's ratio. physica status solidi (b). 2016; 253. 10.1002/pssb.201600055.
  • Novak N, Mauko A, Ulbin M, Krstulović-Opara L, Ren Z, Vesenjak M. Development and characterisation of novel three-dimensional axisymmetric chiral auxetic structures. Journal of Materials Research and Technology. 2022; 17. 10.1016/j.jmrt.2022.02.025.
  • Vasiliev A, Pavlov I. Models and parameters of Cosserat hexagonal lattices with chiral microstructure. IOP Conference Series: Materials Science and Engineering. 2021; 1008. 012017. 10.1088/1757-899X/1008/1/012017.
  • Andrea B, Luigi G. Simplified modelling of chiral lattice materials with local resonators. International Journal of Solids and Structures. Volume 83, April 2016, 126-141.
  • Haifeng R, Jiahong H, Dong L. Wave propagation characterization of 2D composite chiral lattice structures with circular plate inclusions. Engineering Structures. 2022; Volume 264, 1 August 2022, 114466.
  • Alessandro S., Massimo R., Stefano G., Fabrizio S. Phononic properties of hexagonal chiral lattices. Wave Motion. Volume 46, Issue 7, November 2009, 435-450.
  • Liu XN, Huang GL, Hu GK. Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices. Journal of the Mechanics and Physics of Solids. 2011; Volume 60, Issue 11, November 2012, 1907-1921.
  • Eric SA, Goerlitzer, RM, Sergey N, Kirsten V, Marcel R, Peter B, Matthias K, Nicolas V. Chiral Surface Lattice Resonances. Advanced Materials, 21 April 2020.
  • Andrew JG. Chiral Surfaces: Accomplishments and Challenges. January 26, 2010. ACS Nano 2010, 4, 1, 5–10.
  • Gerhard HF., Kübler J, Felser C. Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups. Materials (Basel) 2022 Aug 23;15(17):5812. doi: 10.3390/ma15175812.
  • Erdoğan İ, Toktas İ. Investigation of The Effect of Geometry Inner Thickness on New Designed Auxetic Structure. Politeknik Dergisi, 2023-a; 26(2), 901-912. https://doi.org/10.2339/politeknik.1094739
  • Nergis FB, Candan C, Duru SC. A novel yarn for personel protection in knitted sportswear. Tekstil Ve Mühendis. 2023; 30(131), 249-252. https://doi.org/10.7216/teksmuh.1365889
  • Kaya O, Bademlioğlu AH, Kaboğlu C. Performance Optimization of Auxetic Structures on Energy Absorption of Cylindrical Sandwich Using Taguchi and ANOVA Methods, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2023-a; vol. 12, no. 2, pp. 445–454, doi: 10.17798/bitlisfen.1237388.
  • Erdoğan İ, Toktas İ. Investigation of the Auxetic of a novel geometric structure and improvement of Poisson’s ratio at different inner thicknesses. Gazi University Journal of Science Part C: Design and Technology. 2023-b; 11(4), 893-902. https://doi.org/10.29109/gujsc.1346281
  • Kaya N, Eldem C, Toktas I. Investigation of the auxetic behavior of an original lattice structure design. Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım ve Teknoloji. 2023-b; 11(4), 1081 - 1091. 10.29109/gujsc.1367616
  • Cetin E, Seyitoglu SS. A bibliometric overview of research on auxetic structures: Trends and patterns. International Journal of Automotive Science And Technology. 2024; 8(1), 65-77. https://doi.org/10.30939/ijastech..1374313
  • Kaboğlu C. Statik yükleme altında oksetik iç yapılı sandviç kompozitlerin incelenmesi, El-Cezeri Journal of Science and Engineering, 2022; c. 9, sy. 1, ss. 350–359, doi: 10.31202/ecjse.978310.
  • Becergen B, Çakmak M, Maral MF, Dayanç A, vd. Design Approaches on Inner Bodies of Gears with Methods Topology Optimization and Lattice Structures. Avrupa Bilim Ve Teknoloji Dergisi. 2022; (39), 85-90. https://doi.org/10.31590/ejosat.1144818
  • Akgün M, Süvari F, Eren R, Yurdakul T. Investigation of Auxetic Performance and Various Physical Properties of Fabrics Woven with Braid Yarns. Textile and Apparel. 2022; 32(3), 220-231. https://doi.org/10.32710/tekstilvekonfeksiyon.1033681
  • Özkan E, Khosravi F. Experimental and numerical investigation of the mechanical behavior of the modified metal auxetic structure. Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi, 2023; 9(1), 48-62. https://doi.org/10.34186/klujes.1222192
  • Kaya O, Hafızoğlu H, Babacan N. Effect of Unit Cell Height on the Ballistic Performance of the Body-Centered Lattice Structures. International Journal of Innovative Engineering Applications, 2022; 6(1), 30-34. https://doi.org/10.46460/ijiea.1054219
  • Üzün A., Kayacan MY. Investigation of over obstacle performance analysis of auxetic airless tyres. International Journal of 3D Printing Technologies and Digital Industry, 2023; 7(3), 415-427. https://doi.org/10.46519/ij3dptdi.1336826
  • Akbulut A, Top N, Gökçe H. Eİ için tasarlanan kafes yapıların yapısal davranışlarının incelenmesi. İmalat Teknolojileri ve Uygulamaları. 2023; 4(2), 92-100. https://doi.org/10.52795/mateca.1332895
  • Öykünç D, Yıldızdag ME. Venüs’ün Çiçek Sepeti Süngerinden Esinlenerek Tasarlanmış Bir Kafes Sistemin Yapısal Davranışının İncelenmesi. Gemi Ve Deniz Teknolojisi. 2023; (222), 64-75. https://doi.org/10.54926/gdt.1156139
  • Çelebi A, İmanç, MM. Evaluation of Mechanical Properties of PLA Auxetic Structures Produced by Additive Manufacturing. Journal of Materials and Mechatronics: A. 2023; 4(2), 384-396. https://doi.org/10.55546/jmm.1309858
  • Körner C, Liebold-Ribeiro Y. A systematic approach to identify cellular auxetic materials. Smart Mater Struct. 2014; 24:025013 https://doi.org/10.1088/0964-1726/24/2/025013.
  • Warmuth F, Körner C. Phononic band gaps in 2D quadratic and 3D cubic cellular structures. Materials (Basel). 2014; 8:8327–37. https://doi.org/10.3390/ma8125463.
  • Wormser M, Warmuth F, Körner C. Evolution of full phononic band gaps in periodic cellular structures. Appl Phys A. 2017;123.
  • Warmuth F, Osmanlic F, Adler L. Fabrication and characterisation of a fully auxetic 3D lattice structure via selective electron beam melting. Smart Mater Struct. 2017; 26:8.
  • Ansys, Theory Manual Version 9.0, Canonsburg, PA, USA., ANSYS Inc., 2004.
  • Korkmaz C, Kacar İ. Hesaplamalı Akışkanlar Dinamiği Simülasyonları İçin Optimum Eleman Ağ Yapısının Belirlenmesi, 7 January 2022, Editör: Deniz Yılmaz; Osman Gökdoğan; Önder Uysal; Mehmet Emin Gökduman; Ahmet Süslü, Tarımsal Mekanizasyon ve Enerji Üzerine Güncel Araştırmalar. 2022; ISBN: 978-625-8037-52-4
  • Büyüköztürk Ş, Çokluk-Bökeoğlu Ö, Köklü N. Statistics for Social Sciences, 27th ed. Pegem Press, Ankara, Turkey, 2011.
  • Vigliotti A, Pasini D. Mechanical properties of hierarchical lattices, Mechanics of Materials. 2013; Vol. 62, Pages 32-43.
  • Gülcan O, Simsek U, Kavas B. Eklemeli İmalatla üretilen işlevsel olarak derecelendirilmiş metal yapılar, Mühendis ve Makine. 2021; Cilt. 62, Sayı 702, Sayfa 1-12.
  • Park K-M, Min K-S, Roh Y-S. Design optimization of lattice structures under compression: study of unit cell types and cell arrangements. 2022; Materials, Vol. 15, Issue 1, Pages 97-102.
  • Fernandes RR, Tamijani AY. Design optimization of lattice structures with stress constraints, Materials and Design. 2021; Vol. 210, Issue 110026.
  • Khan N, Acanfora V. Non-Conventional wing structure design with lattice infilled through design for additive manufacturing. 2024; Vol. 17, Issue 7, Pages 1470-1478.
There are 37 citations in total.

Details

Primary Language Turkish
Subjects Optimization Techniques in Mechanical Engineering, Machine Design and Machine Equipment, Material Design and Behaviors
Journal Section Makaleler
Authors

Cem Yılmaz This is me 0009-0004-7439-9904

İlyas Kacar 0000-0002-5887-8807

Publication Date August 31, 2024
Submission Date February 22, 2024
Acceptance Date August 9, 2024
Published in Issue Year 2024 Volume: 11 Issue: 23

Cite

APA Yılmaz, C., & Kacar, İ. (2024). FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, 11(23), 265-282. https://doi.org/10.54365/adyumbd.1440934
AMA Yılmaz C, Kacar İ. FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. August 2024;11(23):265-282. doi:10.54365/adyumbd.1440934
Chicago Yılmaz, Cem, and İlyas Kacar. “FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 11, no. 23 (August 2024): 265-82. https://doi.org/10.54365/adyumbd.1440934.
EndNote Yılmaz C, Kacar İ (August 1, 2024) FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 11 23 265–282.
IEEE C. Yılmaz and İ. Kacar, “FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU”, Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, vol. 11, no. 23, pp. 265–282, 2024, doi: 10.54365/adyumbd.1440934.
ISNAD Yılmaz, Cem - Kacar, İlyas. “FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 11/23 (August 2024), 265-282. https://doi.org/10.54365/adyumbd.1440934.
JAMA Yılmaz C, Kacar İ. FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2024;11:265–282.
MLA Yılmaz, Cem and İlyas Kacar. “FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, vol. 11, no. 23, 2024, pp. 265-82, doi:10.54365/adyumbd.1440934.
Vancouver Yılmaz C, Kacar İ. FARKLI EN/BOY ORANINA SAHİP DÖRTGENSEL KESİTLİ BİR KİRAL ÖKZETİK HÜCRESEL YAPININ TASARIM VE OPTİMİZASYONU. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2024;11(23):265-82.