Araştırma Makalesi
BibTex RIS Kaynak Göster

Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety

Yıl 2026, Cilt: 38 Sayı: 1 , 201 - 212 , 29.03.2026
https://doi.org/10.35234/fumbd.1790146
https://izlik.org/JA42XR62ME

Öz

In this study, the impact strength of automotive side door beams reinforced with multi-cell thin-walled structures was investigated under three-point bending loads. Six different configurations (cylindrical and square outer geometries with 3, 4, and 5 inner cells) made of AA6063-T1 aluminum alloy were analyzed using the finite element method. The models developed in HyperMesh were validated with the experimental data of Zhang and Fu, and an error of less than 1.1% was achieved. The results revealed that increasing the number of inner cells significantly increased the energy absorption, average crushing force, and specific energy absorption. The square-profile K5 design achieved the best performance with 0.1617 kJ EA and 0.885 kJ/kg SEA, outperforming its cylindrical counterpart (S5) by 43% and 13%, respectively. The square geometries also exhibited a 69% higher peak crushing force due to their superior vertical load-carrying behavior. The findings indicate that multicellular thin-walled structures offer significant advantages over traditional single-cell designs, providing up to 27-42% improvement in crash performance and are an effective design strategy for lightweight automotive safety components.

Kaynakça

  • Tarlochan F. Sandwich structures for energy absorption applications: A review. Materials 2021;14(16):Article 16. doi:10.3390/ma14164731
  • Yang J, et al. Laser additive manufacturing of bio-inspired metallic structures. Chin J Mech Eng Addit Manuf Front 2022;1(1):100013. doi:10.1016/j.cjmeam.2022.100013
  • Zhang W, Xu J, Yu TX. Dynamic behaviors of bio-inspired structures: Design, mechanisms, and models. Eng Struct 2022;265:114490. doi:10.1016/j.engstruct.2022.114490
  • Zou Y, Fu J, Chen Z, Ren L. The effect of microstructure on mechanical properties of corn cob. Micron 2021;146:103070. doi:10.1016/j.micron.2021.103070
  • Yao SN. Equalization in ambisonics. Appl Acoust 2018;139:129–139. doi:10.1016/j.apacoust.2018.04.027
  • Yao S, Li Z, Ma W, Xu P. Crashworthiness analysis of a straight-tapered shrink tube. Int J Mech Sci 2019;157–158:512–527. doi:10.1016/j.ijmecsci.2019.04.058
  • Andrews KRF, England GL, Ghani E. Classification of the axial collapse of cylindrical tubes under quasi-static loading. Int J Mech Sci 1983;25(9):687–696. doi:10.1016/0020-7403(83)90076-0
  • Kopar M, Yıldız AR. Experimental and numerical investigation of crash performances of additively manufactured novel multi-cell crash box made with CF15PET, PLA, and ABS. Mater Test 2024;66(9):1510–1518. doi:10.1515/mt-2024-0100
  • Xie S, Jing K, Zhou H, Liu X. Mechanical properties of Nomex honeycomb sandwich panels under dynamic impact. Compos Struct 2020;235:111814. doi:10.1016/j.compstruct.2019.111814
  • Xu X, Zhang Y, Chen X, Liu Z, Xu Y, Gao Y. Crash behaviors of hierarchical sandwich-walled columns. Int J Mech Sci 2019;161–162:105021. doi:10.1016/j.ijmecsci.2019.105021
  • Li QQ, Li E, Chen T, Wu L, Wang GQ, He ZC. Improve the frontal crashworthiness of vehicle through the design of front rail. Thin-Walled Struct 2021;162:107588. doi:10.1016/j.tws.2021.107588
  • Huang Z, Zhang X. Crashworthiness and optimization design of quadruple-cell aluminum/CFRP hybrid tubes under transverse bending. Compos Struct 2020;235:111753. doi:10.1016/j.compstruct.2019.111753
  • Wang H, Tan D, Liu Z, Yin H, Wen G. On crashworthiness of novel porous structure based on composite TPMS structures. Eng Struct 2022;252:113640. doi:10.1016/j.engstruct.2021.113640
  • Zhang XW, Zhang QM, Ren XJ. Theoretical study on the dynamic compression and energy absorption of porous materials filled with magneto-rheological fluid. Int J Impact Eng 2022;161:104105. doi:10.1016/j.ijimpeng.2021.104105
  • Huang L, et al. Bionic composite metamaterials for harvesting of microwave and integration of multifunctionality. Compos Sci Technol 2021;204:108640. doi:10.1016/j.compscitech.2020.108640
  • Ha NS, Pham TM, Chen W, Hao H, Lu G. Crashworthiness analysis of bio-inspired fractal tree-like multi-cell circular tubes under axial crash. Thin-Walled Struct 2021;169:108315. doi:10.1016/j.tws.2021.108315
  • Hu J, Luo Y, Liu S. Two-scale concurrent topology optimization method of hierarchical structures with self-connected multiple lattice-material domains. Compos Struct 2021;272:114224. doi:10.1016/j.compstruct.2021.114224
  • Lucarini S, Cobian L, Voitus A, Segurado J. Adaptation and validation of FFT methods for homogenization of lattice based materials. Comput Methods Appl Mech Eng 2022;388:114223. doi:10.1016/j.cma.2021.114223
  • Ma W, Li Z, Xie S. Crashworthiness analysis of thin-walled bio-inspired multi-cell corrugated tubes under quasi-static axial loading. Eng Struct 2020;204:110069. doi:10.1016/j.engstruct.2019.110069
  • Tran T, Hou S, Han X, Chau M. Crash analysis and numerical optimization of angle element structures under axial impact loading. Compos Struct 2015;119:422–435. doi:10.1016/j.compstruct.2014.09.019
  • Fan Z, Lu G, Liu K. Quasi-static axial compression of thin-walled tubes with different cross-sectional shapes. Eng Struct 2013;55:80–89. doi:10.1016/j.engstruct.2011.09.020
  • Xiang J, Du J, Li D, Scarpa F. Numerical analysis of the impact resistance in aluminum alloy bi-tubular thin-walled structures designs inspired by beetle elytra. J Mater Sci 2017;52(22):13247–13260. doi:10.1007/s10853-017-1420-z
  • Kim TH, Reid SR. Bending collapse of thin-walled rectangular section columns. Comput Struct 2001;79(20):1897–1911. doi:10.1016/S0045-7949(01)00089-X
  • Huang Z, Zhang X. Three-point bending collapse of thin-walled rectangular beams. Int J Mech Sci 2018;144:461–479. doi:10.1016/j.ijmecsci.2018.06.001
  • Jiang P, Wang Q, Yin A, Hu J, Gu X. Optimization design for foam-filled double cylindrical tubes under multiple lateral impacts. Adv Mech Eng 2018;10(12):1687814018811239. doi:10.1177/1687814018811239
  • Hwang YH, Han JH. Crashworthiness of energy absorbing structures under combined shear-compression loading: Effects of materials and geometries. Int J Aeronaut Space Sci 2025;26(2):615–628. doi:10.1007/s42405-024-00779-5
  • H. Taghipoor, A. Eyvazian, F. Musharavati, T. A. Sebaey, ve A. Ghiaskar, “Experimental investigation of the three-point bending properties of sandwich beams with polyurethane foam-filled lattice cores”, Structures, c. 28, ss. 424-432, Ara. 2020, doi: 10.1016/j.istruc.2020.08.082.
  • Gong C, Bai Z, Lv J, Zhang L. Crashworthiness analysis of bionic thin-walled tubes inspired by the evolution laws of plant stems. Thin-Walled Struct 2020;157:107081. doi:10.1016/j.tws.2020.107081
  • Halis S, Altın M. Numerical investigation of energy absorption performance in thin-walled structure under three-point bending test. Int J Automot Sci Technol 2024;8(1):Article 1. doi:10.30939/ijastech..1434645
  • Albak Eİ. Optimization for multi-cell thin-walled tubes under quasi-static three-point bending. J Braz Soc Mech Sci Eng 2022;44(5):207. doi:10.1007/s40430-022-03525-8
  • Zheng D, Zhang J, Lu B, Zhang T. Energy absorption of fully clamped multi-cell square tubes under transverse loading. Thin-Walled Struct 2021;169:108334. doi:10.1016/j.tws.2021.108334
  • Gliszczyński A, Czechowski L. Collapse of channel section composite profile subjected to bending. Part I: Numerical investigations. Compos Struct 2017;178:383–394. doi:10.1016/j.compstruct.2017.07.033
  • Zhang X, Fu X. New theoretical models for the bending moment of thin-walled beams under three-point bending. Appl Math Model 2023;121:21–42. doi:10.1016/j.apm.2023.04.015
  • Huang Z, Zhang X. Three-point bending collapse of thin-walled rectangular beams. Int J Mech Sci 2018;144:461–479. doi:10.1016/j.ijmecsci.2018.06.001
  • Huang Z, Li Y, Zhang X, Chen W, Fang D. A comparative study on the energy absorption mechanism of aluminum/CFRP hybrid beams under quasi-static and dynamic bending. Thin-Walled Struct 2021;163:107772. doi:10.1016/j.tws.2021.107772
  • Kim HC, Shin DK, Lee JJ. Characteristics of aluminum/CFRP short square hollow section beam under transverse quasi-static loading. Compos Part B Eng 2013;51:345–358. doi:10.1016/j.compositesb.2013.03.020
  • Tang Z, Liu S, Zhang Z. Analysis of energy absorption characteristics of cylindrical multi-cell columns. Thin-Walled Struct 2013;62:75–84. doi:10.1016/j.tws.2012.05.019
  • Chen T, Zhang Y, Lin J, Lu Y. Theoretical analysis and crashworthiness optimization of hybrid multi-cell structures. Thin-Walled Struct 2019;142:116–131. doi:10.1016/j.tws.2019.05.002
  • Papaiya V, Schuster J, Shaik YP. Development of a side door composite impact beam for the automotive industry. Open J Compos Mater 2024;14(1):Article 1. doi:10.4236/ojcm.2024.141001
  • Zhang X, Fu X. New theoretical models for the bending moment of thin-walled beams under three-point bending. Appl Math Model 2023;121:21–42. doi:10.1016/j.apm.2023.04.015
  • O. Gülcan, “Crashworthiness of laser powder bed fusion processed In718 auxetic metamaterials”, J. Braz. Soc. Mech. Sci. Eng., c. 46, sy 7, s. 414, Haz. 2024, doi: 10.1007/s40430-024-04927-6.

Otomotiv Güvenliği Açısından Çok Hücreli İnce Duvarlı Kirişlerin Üç Nokta Bükülme Altında Sayısal Değerlendirilmesi

Yıl 2026, Cilt: 38 Sayı: 1 , 201 - 212 , 29.03.2026
https://doi.org/10.35234/fumbd.1790146
https://izlik.org/JA42XR62ME

Öz

Bu çalışmada, çok hücreli ince duvarlı yapılarla güçlendirilmiş otomotiv yan kapı kirişlerinin üç noktalı bükülme yükleri altında çarpma dayanıklılığı araştırılmıştır. AA6063-T1 alüminyum alaşımından yapılmış altı farklı konfigürasyon (3, 4 ve 5 iç hücreli silindirik ve kare dış geometriler) sonlu elemanlar yöntemi kullanılarak analiz edilmiştir. HyperMesh'te geliştirilen modeller, Zhang ve Fu'nun deneysel verileriyle doğrulanmış ve %1,1'den daha az hata elde edilmiştir. Sonuçlar, iç hücrelerin sayısının arttırılmasının enerji emilimini, ortalama kırma kuvvetini ve spesifik enerji emilimini önemli ölçüde arttırdığını ortaya çıkarmıştır. Kare profilli K5 tasarımı, 0,1617 kJ EA ve 0,885 kJ/kg SEA ile en iyi performansı elde ederek silindirik muadilini (S5) sırasıyla % 43 ve %13 oranında daha iyi değerlere sahip olduğu belirlenmiştir. Kare geometriler ayrıca üstün dikey yük taşıma davranışı nedeniyle % 69 daha yüksek tepe kırma kuvveti göstermiştir. Bulgular, çok hücreli güçlendirilmiş kare yapıların, geleneksel tek hücreli tasarımlara göre önemli avantajlar sunduğunu, çarpışma performansında %27-42'ye kadar iyileşme sağladığını ve hafif otomotiv güvenlik bileşenleri için etkili bir tasarım stratejisi olduğu belirlenmiştir.

Kaynakça

  • Tarlochan F. Sandwich structures for energy absorption applications: A review. Materials 2021;14(16):Article 16. doi:10.3390/ma14164731
  • Yang J, et al. Laser additive manufacturing of bio-inspired metallic structures. Chin J Mech Eng Addit Manuf Front 2022;1(1):100013. doi:10.1016/j.cjmeam.2022.100013
  • Zhang W, Xu J, Yu TX. Dynamic behaviors of bio-inspired structures: Design, mechanisms, and models. Eng Struct 2022;265:114490. doi:10.1016/j.engstruct.2022.114490
  • Zou Y, Fu J, Chen Z, Ren L. The effect of microstructure on mechanical properties of corn cob. Micron 2021;146:103070. doi:10.1016/j.micron.2021.103070
  • Yao SN. Equalization in ambisonics. Appl Acoust 2018;139:129–139. doi:10.1016/j.apacoust.2018.04.027
  • Yao S, Li Z, Ma W, Xu P. Crashworthiness analysis of a straight-tapered shrink tube. Int J Mech Sci 2019;157–158:512–527. doi:10.1016/j.ijmecsci.2019.04.058
  • Andrews KRF, England GL, Ghani E. Classification of the axial collapse of cylindrical tubes under quasi-static loading. Int J Mech Sci 1983;25(9):687–696. doi:10.1016/0020-7403(83)90076-0
  • Kopar M, Yıldız AR. Experimental and numerical investigation of crash performances of additively manufactured novel multi-cell crash box made with CF15PET, PLA, and ABS. Mater Test 2024;66(9):1510–1518. doi:10.1515/mt-2024-0100
  • Xie S, Jing K, Zhou H, Liu X. Mechanical properties of Nomex honeycomb sandwich panels under dynamic impact. Compos Struct 2020;235:111814. doi:10.1016/j.compstruct.2019.111814
  • Xu X, Zhang Y, Chen X, Liu Z, Xu Y, Gao Y. Crash behaviors of hierarchical sandwich-walled columns. Int J Mech Sci 2019;161–162:105021. doi:10.1016/j.ijmecsci.2019.105021
  • Li QQ, Li E, Chen T, Wu L, Wang GQ, He ZC. Improve the frontal crashworthiness of vehicle through the design of front rail. Thin-Walled Struct 2021;162:107588. doi:10.1016/j.tws.2021.107588
  • Huang Z, Zhang X. Crashworthiness and optimization design of quadruple-cell aluminum/CFRP hybrid tubes under transverse bending. Compos Struct 2020;235:111753. doi:10.1016/j.compstruct.2019.111753
  • Wang H, Tan D, Liu Z, Yin H, Wen G. On crashworthiness of novel porous structure based on composite TPMS structures. Eng Struct 2022;252:113640. doi:10.1016/j.engstruct.2021.113640
  • Zhang XW, Zhang QM, Ren XJ. Theoretical study on the dynamic compression and energy absorption of porous materials filled with magneto-rheological fluid. Int J Impact Eng 2022;161:104105. doi:10.1016/j.ijimpeng.2021.104105
  • Huang L, et al. Bionic composite metamaterials for harvesting of microwave and integration of multifunctionality. Compos Sci Technol 2021;204:108640. doi:10.1016/j.compscitech.2020.108640
  • Ha NS, Pham TM, Chen W, Hao H, Lu G. Crashworthiness analysis of bio-inspired fractal tree-like multi-cell circular tubes under axial crash. Thin-Walled Struct 2021;169:108315. doi:10.1016/j.tws.2021.108315
  • Hu J, Luo Y, Liu S. Two-scale concurrent topology optimization method of hierarchical structures with self-connected multiple lattice-material domains. Compos Struct 2021;272:114224. doi:10.1016/j.compstruct.2021.114224
  • Lucarini S, Cobian L, Voitus A, Segurado J. Adaptation and validation of FFT methods for homogenization of lattice based materials. Comput Methods Appl Mech Eng 2022;388:114223. doi:10.1016/j.cma.2021.114223
  • Ma W, Li Z, Xie S. Crashworthiness analysis of thin-walled bio-inspired multi-cell corrugated tubes under quasi-static axial loading. Eng Struct 2020;204:110069. doi:10.1016/j.engstruct.2019.110069
  • Tran T, Hou S, Han X, Chau M. Crash analysis and numerical optimization of angle element structures under axial impact loading. Compos Struct 2015;119:422–435. doi:10.1016/j.compstruct.2014.09.019
  • Fan Z, Lu G, Liu K. Quasi-static axial compression of thin-walled tubes with different cross-sectional shapes. Eng Struct 2013;55:80–89. doi:10.1016/j.engstruct.2011.09.020
  • Xiang J, Du J, Li D, Scarpa F. Numerical analysis of the impact resistance in aluminum alloy bi-tubular thin-walled structures designs inspired by beetle elytra. J Mater Sci 2017;52(22):13247–13260. doi:10.1007/s10853-017-1420-z
  • Kim TH, Reid SR. Bending collapse of thin-walled rectangular section columns. Comput Struct 2001;79(20):1897–1911. doi:10.1016/S0045-7949(01)00089-X
  • Huang Z, Zhang X. Three-point bending collapse of thin-walled rectangular beams. Int J Mech Sci 2018;144:461–479. doi:10.1016/j.ijmecsci.2018.06.001
  • Jiang P, Wang Q, Yin A, Hu J, Gu X. Optimization design for foam-filled double cylindrical tubes under multiple lateral impacts. Adv Mech Eng 2018;10(12):1687814018811239. doi:10.1177/1687814018811239
  • Hwang YH, Han JH. Crashworthiness of energy absorbing structures under combined shear-compression loading: Effects of materials and geometries. Int J Aeronaut Space Sci 2025;26(2):615–628. doi:10.1007/s42405-024-00779-5
  • H. Taghipoor, A. Eyvazian, F. Musharavati, T. A. Sebaey, ve A. Ghiaskar, “Experimental investigation of the three-point bending properties of sandwich beams with polyurethane foam-filled lattice cores”, Structures, c. 28, ss. 424-432, Ara. 2020, doi: 10.1016/j.istruc.2020.08.082.
  • Gong C, Bai Z, Lv J, Zhang L. Crashworthiness analysis of bionic thin-walled tubes inspired by the evolution laws of plant stems. Thin-Walled Struct 2020;157:107081. doi:10.1016/j.tws.2020.107081
  • Halis S, Altın M. Numerical investigation of energy absorption performance in thin-walled structure under three-point bending test. Int J Automot Sci Technol 2024;8(1):Article 1. doi:10.30939/ijastech..1434645
  • Albak Eİ. Optimization for multi-cell thin-walled tubes under quasi-static three-point bending. J Braz Soc Mech Sci Eng 2022;44(5):207. doi:10.1007/s40430-022-03525-8
  • Zheng D, Zhang J, Lu B, Zhang T. Energy absorption of fully clamped multi-cell square tubes under transverse loading. Thin-Walled Struct 2021;169:108334. doi:10.1016/j.tws.2021.108334
  • Gliszczyński A, Czechowski L. Collapse of channel section composite profile subjected to bending. Part I: Numerical investigations. Compos Struct 2017;178:383–394. doi:10.1016/j.compstruct.2017.07.033
  • Zhang X, Fu X. New theoretical models for the bending moment of thin-walled beams under three-point bending. Appl Math Model 2023;121:21–42. doi:10.1016/j.apm.2023.04.015
  • Huang Z, Zhang X. Three-point bending collapse of thin-walled rectangular beams. Int J Mech Sci 2018;144:461–479. doi:10.1016/j.ijmecsci.2018.06.001
  • Huang Z, Li Y, Zhang X, Chen W, Fang D. A comparative study on the energy absorption mechanism of aluminum/CFRP hybrid beams under quasi-static and dynamic bending. Thin-Walled Struct 2021;163:107772. doi:10.1016/j.tws.2021.107772
  • Kim HC, Shin DK, Lee JJ. Characteristics of aluminum/CFRP short square hollow section beam under transverse quasi-static loading. Compos Part B Eng 2013;51:345–358. doi:10.1016/j.compositesb.2013.03.020
  • Tang Z, Liu S, Zhang Z. Analysis of energy absorption characteristics of cylindrical multi-cell columns. Thin-Walled Struct 2013;62:75–84. doi:10.1016/j.tws.2012.05.019
  • Chen T, Zhang Y, Lin J, Lu Y. Theoretical analysis and crashworthiness optimization of hybrid multi-cell structures. Thin-Walled Struct 2019;142:116–131. doi:10.1016/j.tws.2019.05.002
  • Papaiya V, Schuster J, Shaik YP. Development of a side door composite impact beam for the automotive industry. Open J Compos Mater 2024;14(1):Article 1. doi:10.4236/ojcm.2024.141001
  • Zhang X, Fu X. New theoretical models for the bending moment of thin-walled beams under three-point bending. Appl Math Model 2023;121:21–42. doi:10.1016/j.apm.2023.04.015
  • O. Gülcan, “Crashworthiness of laser powder bed fusion processed In718 auxetic metamaterials”, J. Braz. Soc. Mech. Sci. Eng., c. 46, sy 7, s. 414, Haz. 2024, doi: 10.1007/s40430-024-04927-6.
Toplam 41 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Dinamikler, Titreşim ve Titreşim Kontrolü
Bölüm Araştırma Makalesi
Yazarlar

Mehmet Kopar 0000-0001-7347-4192

Medeni Sömer 0000-0003-4411-3309

Ali Arı 0000-0003-2702-2982

Gönderilme Tarihi 24 Eylül 2025
Kabul Tarihi 30 Aralık 2025
Yayımlanma Tarihi 29 Mart 2026
DOI https://doi.org/10.35234/fumbd.1790146
IZ https://izlik.org/JA42XR62ME
Yayımlandığı Sayı Yıl 2026 Cilt: 38 Sayı: 1

Kaynak Göster

APA Kopar, M., Sömer, M., & Arı, A. (2026). Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, 38(1), 201-212. https://doi.org/10.35234/fumbd.1790146
AMA 1.Kopar M, Sömer M, Arı A. Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. 2026;38(1):201-212. doi:10.35234/fumbd.1790146
Chicago Kopar, Mehmet, Medeni Sömer, ve Ali Arı. 2026. “Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety”. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 38 (1): 201-12. https://doi.org/10.35234/fumbd.1790146.
EndNote Kopar M, Sömer M, Arı A (01 Mart 2026) Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 38 1 201–212.
IEEE [1]M. Kopar, M. Sömer, ve A. Arı, “Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety”, Fırat Üniversitesi Mühendislik Bilimleri Dergisi, c. 38, sy 1, ss. 201–212, Mar. 2026, doi: 10.35234/fumbd.1790146.
ISNAD Kopar, Mehmet - Sömer, Medeni - Arı, Ali. “Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety”. Fırat Üniversitesi Mühendislik Bilimleri Dergisi 38/1 (01 Mart 2026): 201-212. https://doi.org/10.35234/fumbd.1790146.
JAMA 1.Kopar M, Sömer M, Arı A. Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. 2026;38:201–212.
MLA Kopar, Mehmet, vd. “Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety”. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, c. 38, sy 1, Mart 2026, ss. 201-12, doi:10.35234/fumbd.1790146.
Vancouver 1.Mehmet Kopar, Medeni Sömer, Ali Arı. Numerical Assessment of Multi-Cell Thin-Walled Beams under Three-Point Bending for Automotive Safety. Fırat Üniversitesi Mühendislik Bilimleri Dergisi. 01 Mart 2026;38(1):201-12. doi:10.35234/fumbd.1790146