Comparative assessment of element types for evaluating local elastic buckling behavior of rectangular hollow sections using finite element analysis

Abstract

This study systematically evaluates the performance of conventional shell elements in Abaqus for predicting the local elastic buckling behavior of rectangular hollow sections (RHSs) under various loading conditions, including axial compression, major axis bending, and minor axis bending. Theoretical local buckling coefficients were first derived based on the cross-sectional dimensions of RHSs and used to calculate the critical local buckling stress for each loading scenario. Finite element analyses (FEA) were then performed using different shell element types, including four-node and eight-node elements, to assess their accuracy and computational efficiency. The results indicate that four-node shell elements (S4, S4R) offer a favorable balance of accuracy and significantly reduced computational time, making them the most efficient option. In contrast, eight-node elements (S8R, S8R5) provide marginally higher accuracy but require substantially longer computation times and have limited applicability. This study underscores the importance of selecting appropriate elements to achieve a balance between accuracy and efficiency, providing valuable guidance for engineers in structural design. By optimizing element selection for modeling local elastic buckling in RHSs, the research improves computational efficiency and supports the development of more reliable, cost-effective designs.

Keywords

• Axial compression
• Major axis bending
• Minor axis bending
• Local elastic buckling
• Rectangular hollow sections (RHSs)
• Element types
• Finite element analysis

Sonlu elemanlar analizi kullanılarak dikdörtgen içi boş kesitlerin yerel elastik burkulma davranışının değerlendirilmesinde eleman tiplerinin karşılaştırmalı değerlendirilmesi

Abstract

Bu çalışma, eksenel basma, büyük eksen eğilmesi ve küçük eksen eğilmesi dahil olmak üzere çeşitli yükleme koşulları altında içi boş dikdörtgen kesitlerin (İBDK'lar) yerel elastik burkulma davranışını tahmin etmek için Abaqus'taki geleneksel kabuk elemanlarının performansını sistematik olarak değerlendirir. Teorik yerel burkulma katsayıları ilk önce İBDK'ların enine kesit boyutlarına dayanarak türetilmiş ve her yükleme senaryosu için kritik yerel burkulma gerilimini hesaplamak için kullanılmıştır. Daha sonra, doğruluklarını ve hesaplama verimliliklerini değerlendirmek için dört düğümlü ve sekiz düğümlü elemanlar dahil olmak üzere farklı kabuk eleman tipleri kullanılarak sonlu eleman analizleri (SEA) gerçekleştirilmiştir. Sonuçlar, dört düğümlü kabuk elemanlarının (S4, S4R) doğruluk ve önemli ölçüde azaltılmış hesaplama süresi arasında uygun bir denge sunduğunu ve bunları en verimli seçenek haline getirdiğini göstermektedir. Bunun aksine, sekiz düğümlü elemanlar (S8R, S8R5) marjinal olarak daha yüksek doğruluk sağlar, ancak önemli ölçüde daha uzun hesaplama süreleri gerektirir ve sınırlı uygulanabilirliğe sahiptir. Bu çalışma, doğruluk ve verimlilik arasında bir denge sağlamak için uygun elemanların seçilmesinin önemini vurgulayarak, yapısal tasarımda mühendislere değerli rehberlik sağlar. Araştırma, İBDK'larda yerel elastik burkulmayı modellemek için eleman seçimini optimize ederek hesaplama verimliliğini artırır ve daha güvenilir, maliyet açısından etkili tasarımların geliştirilmesini destekler.

Keywords

• Eksenel basma
• Ana eksen eğilme
• Küçük eksen eğilme
• Yerel elastik burkulma
• İçi boş dikdörtgen kesitler (İBDK
• Eleman tipleri
• Sonlu elemanlar analizi

References

1. Gardner L, Fieber A, Macorini L (2019) Formulae for Calculating Elastic Local Buckling Stresses of Full Structural Cross-sections. Structures 17:2–20. https://doi.org/10.1016/j.istruc.2019.01.012
2. Nuraliyev M, Dundar MA, Sahin DE (2022) Determination of optimal dimensions of polymer-based rectangular hollow sections based on both adequate-strength and local buckling criteria: Analytical and numerical studies. Mech Based Des Struct Mach 1–31. https://doi.org/10.1080/15397734.2022.2139720
3. Singh TG, Chan T-M (2021) Effect of access openings on the buckling performance of square hollow section module stub columns. J Constr Steel Res 177:106438. https://doi.org/10.1016/j.jcsr.2020.106438
4. Hämäläinen O-P, Halme T, Björk T (2018) Local Buckling of Welded Box Beams Made of Ultrahigh-Strength Steels. J Struct Eng 144(7), 6018003.
5. Dundar MA, Nuraliyev M (2024) Parametric study on the assessment of the local buckling behavior of perforated square hollow sections with non-uniform wall thickness under axial compression TT - Düzgün olmayan duvar kalınlığına sahip delikli kare içi boş profillerin eksenel basınç alt. J Innov Eng Nat Sci 4(2):326–353. https://doi.org/10.61112/jiens.1397391
6. Shahbazian A, Wang YC (2011) Calculating the global buckling resistance of thin-walled steel members with uniform and non-uniform elevated temperatures under axial compression. Thin-Walled Struct 49(11):1415–1428. https://doi.org/https://doi.org/10.1016/j.tws.2011.07.001
7. Shahbazian A, Wang YC (2011) Application of the Direct Strength Method to local buckling resistance of thin-walled steel members with non-uniform elevated temperatures under axial compression. Thin-Walled Struct 49(12):1573–1583.
8. Yang D, Hancock GJ (2006) Numerical simulation of high-strength steel box-shaped columns failing in local and overall buckling modes. J Struct Eng 132(4):541–549.

9. Shen J, Wadee MA, Sadowski AJ (2017) Interactive buckling in long thin-walled rectangular hollow section struts. Int J Non Linear Mech 89:43–58. https://doi.org/10.1016/j.ijnonlinmec.2016.11.007
10. McCann F, Fang C, Gardner L, Silvestre N (2016) Local buckling and ultimate strength of slender elliptical hollow sections in compression. Eng Struct 111:104–118.
11. Thai H-T, Uy B, Khan M (2015) A modified stress-strain model accounting for the local buckling of thin-walled stub columns under axial compression. J Constr Steel Res 111:57–69.
12. Yu C, Schafer BW (2007) Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method. J Constr Steel Res 63(5):581–590.
13. Dai Y, Roy K, Fang Z, Chen B, Raftery GM, Lim JBP (2024) Buckling resistance of axially loaded cold-formed steel built-up stiffened box sections through experimental testing and finite element analysis. Eng Struct 302:117379. https://doi.org/10.1016/j.engstruct.2023.117379
14. DUNDAR MA, Nuraliyev M, Sahin DE (2022) Determination of Optimal Dimensions of Polymer-Based Rectangular Hollow Sections Based on Both Adequate-Strength and Local Buckling Criteria: Analytical and Numerical Study. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2022.2139720
15. Liu M, Zhang L, Wang P, Chang Y (2015) Buckling behaviors of section aluminum alloy columns under axial compression. Eng Struct 95:127–137.
16. Paul B, Roy K, Lim JBP, Fang Z, McCollum K, Bell D (2023) Moment-capacity of bolted side-plates for apex joint of nested tapered box beam portal frames. J Build Eng 76:107011. https://doi.org/10.1016/j.jobe.2023.107011
17. Ozenc O, Dundar MA, Sahin DE (2023) Examination of compressive and flexural behaviors of acrylonitrile-butadiene-styrene filled with hemp fiber particles. J Thermoplast Compos Mater 37(2):743–771. https://doi.org/10.1177/08927057231186326
18. Gunalan S, Heva YB, Mahendran M (2015) Local buckling studies of cold-formed steel compression members at elevated temperatures. J Constr Steel Res 108:31–45.
19. Systèmes D (2014) ABAQUS Documentation (Dassault Systèmes, Providence, RI)
20. Hughes OF, Ghosh B, Chen Y (2004) Improved prediction of simultaneous local and overall buckling of stiffened panels. Thin-Walled Struct 42(6):827–856. https://doi.org/10.1016/j.tws.2004.01.003
21. Sadowski AJ, Rotter MJ (2013) On the relationship between mesh and stress field orientations in linear stability analyses of thin plates and shells. Finite Elem Anal Des 73:42–54. https://doi.org/10.1016/j.finel.2013.05.004
22. Anapayan T, Mahendran M (2012) Improved design rules for hollow flange sections subject to lateral distortional buckling. Thin-Walled Struct 50(1):128–140. https://doi.org/10.1016/j.tws.2011.09.004
23. Elglaad S, Elghandour M, Sharaf T, Elsabbagh A (2021) Assessment of the Finite Element Analysis of Portal Steel Frames with Cold Formed Rectangular Hollow Sections Including Imperfections and Residual Stresses. Port-Said Eng Res J 25(2):60–79.
24. Ozyurt E, Wang YC (2018) Resistance of Axially Loaded T- and X-Joints of Elliptical Hollow Sections at Elevated Temperatures – A Finite Element Study. Structures 14:15–31. https://doi.org/10.1016/j.istruc.2018.01.004
25. Grilo LF, Fakury RH, Rodrigues FC, Daldegan VP (2018) Behavior and design of built-up compressed steel members composed of concentric hot rolled circular hollow sections. Lat Am J Solids Struct 15:e51.
26. Mahmoud A, Torabian S, Jay A, Myers A, Smith E, Schafer BW (2015) Modeling protocols for elastic buckling and collapse analysis of spirally welded circular hollow thin-walled sections. Struct Stab Res Counc, AISC (American Institute of Steel Construction), Nashville, TN, USA, March 24-27, 1-16. https://doi.org/10.13140/2.1.4893.7763
27. Shariati M, Saemi J, Sedighi, M, Eipakchi HR (2011) Experimental and numerical studies on buckling and post-buckling behavior of cylindrical panels subjected to compressive axial load. Strength Mater 43:190–200. https://doi.org/10.1007/s11223-011-9285-x
28. Rokilan M, Mahendran M (2021) Design of cold-formed steel columns subject to local buckling at elevated temperatures. J Constr Steel Res 179:106539.
29. Wadee MA, Bai L (2014) Cellular buckling in I-section struts. Thin-Walled Struct 81:89–100.
30. Wadee MA, Farsi M (2014) Local–global mode interaction in stringer-stiffened plates. Thin-Walled Struct 85:419–430. https://doi.org/10.1016/j.tws.2014.09.012
31. Yuan HX, Wang YQ, Gardner L, Shi YJ (2014) Local–overall interactive buckling of welded stainless steel box section compression members. Eng Struct 67:62–76. https://doi.org/10.1016/j.engstruct.2014.02.012
32. Saliba N, Gardner L (2013) Experimental study of the shear response of lean duplex stainless steel plate girders. Eng Struct 46:375–391.
33. Zhou F, Young B (2013) Web crippling behaviour of cold-formed duplex stainless steel tubular sections at elevated temperatures. Eng Struct 57:51–62.
34. Hassanein MF (2010) Imperfection analysis of austenitic stainless steel plate girders failing by shear. Eng Struct 32(3):704–713.
35. Siahaan R, Keerthan P, Mahendran M (2016) Finite element modeling of rivet fastened rectangular hollow flange channel beams subject to local buckling. Eng Struct 126:311–327.
36. Becque J, Rasmussen KJR (2008) Numerical investigation and design methods for stainless steel columns failing by interaction of local and overall buckling, Research Report R888, School of Civil Engineering, University of Sydney.
37. Killpack M, Abed-Meraim F (2011) Limit-point buckling analyses using solid, shell and solid-shell elements. J Mech Sci Technol 25:1105–1117.
38. Nuraliyev M, Dundar MA, Akyildiz HK (2024) A novel analytical method for local buckling check of box sections with unequal wall thicknesses subjected to bending. Mech Adv Mater Struct 1–24. https://doi.org/10.1080/15376494.2024.2369262
39. Vieira L (2018) On the local buckling of RHS members under axial force and biaxial bending. Thin-Walled Struct 129:10–19. https://doi.org/10.1016/j.tws.2018.03.022
40. Seif M, Schafer BW (2010) Local buckling of structural steel shapes. J Constr Steel Res 66(10):1232–1247. https://doi.org/10.1016/j.jcsr.2010.03.015
41. Kroll WD, Fisher GP, Heimerl GJ (1943) Charts for calculation of the critical stress for local instability of columns with I-, Z-, channel, and rectangular-tube section. National Advisory Committee for Aeronautics. Report Number: NACA-WR-L-429
42. Radwan M, Kövesdi B (2021) Local plate buckling type imperfections for NSS and HSS welded box-section columns. Structures 34:2628–2643. https://doi.org/10.1016/j.istruc.2021.09.011
43. Möcker T, Linde P, Kraschin S, Goetz F, Marsolek J, Wohlers W (2008) Abaqus FEM Analysis of The Post Buckling Behaviour of Composite Shell Structures. Available at: https://www.researchgate.net/publication/267218447
44. Dassault Systèmes (2012) Abaqus Analysis User’s Manual 6.12. http://orpheus.nchc.org.tw:2080/v6.12/. Accessed 02 Jan. 2025.
45. Ranawaka T, Mahendran M (2006) Finite element analyses of cold-formed steel columns subject to distortional buckling under simulated fire conditions. In: Proceedings of the International Colloquium on Stability and Ductility of Steel Structures. Instituto Superior Técnico, Lisbon, Portugal. pp 747–755.
46. Chandra KSS, Rao KV, Rajanna T (2020) Effect of Varying Ιn-Plane Loads and Cutout Size on Buckling Behavior of Laminated Panels. In: Advances in Mechanical Engineering: Select Proceedings of ICAME 2020. Springer, pp 671–678.
47. El Bahaoui J, El Bakkali L, Khamlichi A (2012) Buckling strength of axially compressed thin axisymmetric shells as affected by localized initial geometric imperfections. Int Rev Appl Sci Eng 3(1):1–14.
48. Bin Kamarudin MN, Mohamed Ali JS, Aabid A, Ibrahim YE (2022) Buckling analysis of a thin-walled structure using finite element method and design of experiments. Aerospace 9(10):541:1-31. https://doi.org/10.3390/aerospace9100541
49. Lu W, Liu H, Waqas A, Long L (2023) Study on buckling behavior of multilayer pyramid lattice structures. Mech Adv Mater Struct 31(28):10059–10069. https://doi.org/10.1080/15376494.2023.2284271
50. Duarte APC, Pereira GB, Silvestre N (2021) Numerical study of the influence of the stringers cross-section geometry on the mechanical behavior of compressed curved stiffened composite panels. Mech Adv Mater Struct 28(5):516–529. https://doi.org/10.1080/15376494.2019.1578009
51. Ragheb WF (2010) Hybridization Effectiveness in Improving Local Buckling Capacity of Pultruded I-Beams. Mech Adv Mater Struct 17(6):448–457. https://doi.org/10.1080/15376494.2010.483328
52. Zhu J, Li L-Y (2019) Effect of shear stress on distortional buckling of CFS beams subjected to uniformly distributed transverse loading. Mech Adv Mater Struct 26(17):1423–1429. https://doi.org/10.1080/15376494.2018.1432798
53. Masood SN, Gaddikeri KM, Viswamurthy SR (2021) Experimental and finite element numerical studies on the post-buckling behavior of composite stiffened panels. Mech Adv Mater Struct 28(16):1677–1690. https://doi.org/10.1080/15376494.2019.1701151
54. Zhao W, Xie Z, Wang X, Li X, Hao J (2019) Buckling behavior of stiffened composite panels with variable thickness skin under compression. Mech Adv Mater Struct 26(3):215–223. https://doi.org/10.1080/15376494.2018.1495795