L-Shaped Stringer Tailoring to Enhance Axial Buckling of FGM Elliptical Cylindrical Shells

Document Type : Research Paper

Authors
1 Department of Civil Engineering, Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz, Ahvaz, Iran
2 Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Abstract
A review of the literature indicates that buckling of longitudinal stiffeners is one of the primary challenges faced by stiffened cylindrical shells under axial compressive loads. In this study, conventional longitudinal stiffeners with rectangular cross-sections were replaced by innovative L-shaped stiffeners, aiming to enhance the structural stability of stiffened composite cylindrical shells. To demonstrate this concept, a functionally graded material (FGM) shell, an advanced form of composite with continuously varying properties, was modeled using the semi-analytical finite strip method in the FORTRAN environment. The results from the developed model were compared with those obtained from the finite element method to assess the model’s accuracy. Through a comprehensive parametric study, the effects of shell geometry, L-shaped stiffener configuration, and the FGM power index on the axial buckling performance of the stiffened shell were investigated. The findings revealed that, for certain combinations of the investigated parameters, the axial buckling load of shells with L-shaped stiffeners can be approximately 40-70% higher than that of shells with conventional rectangular stiffeners, despite using the same material and stiffener cross-sectional area. This demonstrates that adopting alternative stiffener geometries provides a practical and effective strategy for enhancing the buckling resistance of composite structural shells in construction engineering applications.
Keywords
Subjects

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[1] Semenov, A., Dynamic Buckling of Stiffened Shell Structures with Transverse Shears under Linearly Increasing Load, Journal of Applied and Computational Mechanics, 8(4), 2022, 1343-1357. 
[2] Shahani, A.R., Kiarasi, F., Numerical and Experimental Investigation on Post-buckling Behavior of Stiffened Cylindrical Shells with Cutout subject to Uniform Axial Compression, Journal of Applied and Computational Mechanics, 9(1), 2023, 25-44. 
[3] Poorveis, D., Khajehdezfuly, A., Oulapour, M., Aalipour, K., Curvature-guided thickness tailoring for enhanced axial buckling capacity of functionally graded elliptical cylindrical shells, Mechanics of Advanced Materials and Structures, 33(1), 2026, 2704685.
[4] Poorveis, D., Khajehdezfuly, A., Oulapour, M., Tamimi, H., Buckling of elliptical cylindrical shell with variable circumferential thickness under fluid lateral pressure, Journal of Hydraulic Structures, 12(3), 2026, 1-18.
[5] Poorveis, D., Khajehdezfuly, A., Sardari, M.R., Moradi, S., Interaction of stress distribution and stringer slenderness on buckling of stiffened composite elliptical cylindrical shell under axial compression, Mechanics Based Design of Structures and Machines, 54(1), 2026, 2585351.
[6] Moradi, A., Poorveis, D., Khajehdezfuly, A., Buckling of FGM elliptical cylindrical shell under follower lateral pressure, Steel and Composite Structures, 45(2), 2022, 175-191. 
[7] Khajehdezfuly, A., Poorveis, D., Nazarinia, S., Comparison between linear and nonlinear buckling loads of FGM cylindrical panel with cutout, International Journal of Non-Linear Mechanics, 150, 2023, 104361. 
[8] Poorveis, D., Khajehdezfuly, A., Moradi, S., Shirshekan, E., A simple spline finite strip for buckling analysis of composite cylindrical panel with cutout, Latin American Journal of Solids and Structures, 16(8), 2019, e227. 
[9] Mishurenko, N., Semenov, A., Influence of Discretely Introduced Cutouts on the Buckling of Shallow Shells with Double Curvature, Journal of Applied and Computational Mechanics, 10(1), 2024, 55-63.
[10] Krause, M., Lyssakow, P., Friedrich, L., Schröder, K.U., Panel buckling of stiffened shell structures with torsional stiff stringer, Aerospace Science and Technology, 107, 2020, 106257.
[11] Yaffe, R., Abramovich, H., Dynamic buckling of cylindrical stringer stiffened shells, Computers & Structures, 81(8-11), 2003, 1031-1039.
[12] Pasternak, H., Li, Z., Juozapaitis, A., Daniunas, A., Ring stiffened cylindrical shell structures: State-of-the-art review, Applied Sciences, 12(22), 2022, 11665.
[13] Ismail, M.S., Purbolaksono, J., Analysis using finite element method of the buckling characteristics of stiffened cylindrical shells, Australian Journal of Structural Engineering, 26(4), 2025, 321-331. 
[14] Tian, J., Wang, C.M., Swaddiwudhipong, S., Elastic buckling analysis of ring-stiffened cylindrical shells under general pressure loading via the Ritz method, Thin-Walled Structures, 35(1), 1999, 1-24.
[15] Barani, S., Poorveis, D., Moradi, S., Buckling analysis of ring-stiffened laminated composite cylindrical shells by Fourier-expansion based differential quadrature method, Applied Mechanics and Materials, 225, 2012, 207-212.
[16] Fang, M., Zhu, X., Li, T., Zhang, G., Free vibration characteristics of a finite ring-stiffened elliptic cylindrical shell, Journal of Vibration and Acoustics, 139(6), 2017, 061012. 
[17] Bai, X., Xu, W., Ren, H., Li, J., Analysis of the influence of stiffness reduction on the load carrying capacity of ring-stiffened cylindrical shell, Ocean Engineering, 135, 2017, 52-62. 
[18] Li, Z., Pasternak, H., Jäger-Cañás, A., Buckling of ring-stiffened cylindrical shell under axial compression: Experiment and numerical simulation, Thin-Walled Structures, 164, 2021, 107888. 
[19] Yang, Z., Zhang, X., Pan, G., Xu, Y., Buckling and strength failure for unstiffened and ring-stiffened composite shells, Ocean Engineering, 278, 2023, 114513.
[20] Rathinam, N., Prabu, B., Anbazhaghan, N., Buckling analysis of ring stiffened thin cylindrical shell under external pressure, Journal of Ocean Engineering and Science, 6(4), 2021, 360-366.
[21] Li, M., Zhang, L., Huang, B., Zhu, H., Fan, H., Multi-failure theory of non-uniformly ring-stiffened composite shells under hydrostatic pressure, Ocean Engineering, 299, 2024, 117161.
[22] Zhang, B., Zhao, Y., Zhang, J., Zhang, A., Wan, Z., Experimental and numerical studies on the collapse of Titanium alloy ring-stiffened cylinder, Engineering Failure Analysis, 167, 2025, 108928.
[23] Chen, Y., Hu, Z., Zhu, B., Tong, G., Guo, Y., Wang, J., Stability design of axially loaded stringer-stiffened moderately-thick cylindrical shells in steel tubular transmission towers, Thin-Walled Structures, 172, 2022, 108874.
[24] Do, Q.T., Muttaqie, T., Park, S.H., Shin, H.K., Cho, S.R., Ultimate strength of intact and dented steel stringer-stiffened cylinders under hydrostatic pressure, Thin-Walled Structures, 132, 2018, 442-460. 
[25] Kabir, M.Z., Poorveis, D., Buckling of discretely stringer-stiffened composite cylindrical shells under combined axial compression and external pressure, Scientia Iranica, 13(2), 2006, 113-123. 
[26] Krasovsky, V.L., Kostyrko, V.V., Experimental studying of buckling of stringer cylindrical shells under axial compression, Thin-Walled Structures, 45(10-11), 2007, 877-882. 
[27] Naghsh, A., Saadatpour, M.M., Azhari, M., Free vibration analysis of stringer stiffened general shells of revolution using a meridional finite strip method, Thin-Walled Structures, 94, 2015, 651-662.
[28] Sadeghifar, M., Bagheri, M., Jafari, A.A., Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity, Archive of Applied Mechanics, 81, 2011, 875-886.
[29] Poorveis, D., Khajehdezfuly, A., Sardari, M.R., Moradi, S., An accurate approach for buckling analysis of stringer stiffened laminated composite cylindrical shells under axial compression, Steel and Composite Structures, 51(5), 2024, 543-562.
[30] Ghorbanpour Arani, A., Loghman, A., Mosallaie Barzoki, A.A., Kolahchi, R., Elastic buckling analysis of ring and stringer-stiffened cylindrical shells under general pressure and axial compression via the Ritz method, Journal of Solid Mechanics, 2(4), 2010, 332-347. 
[31] Yu, H., Qiao, P., An efficient compound strip method for buckling analysis of stiffened cylinders, Thin-Walled Structures, 198, 2024, 111646. 
[32] Shahgholian-Ghahfarokhi, D., Rahimi, G., Buckling load prediction of grid-stiffened composite cylindrical shells using the vibration correlation technique, Composites Science and Technology, 167, 2018, 470-481.
[33] Ghahfarokhi, D.S., Rahimi, G., An analytical approach for global buckling of composite sandwich cylindrical shells with lattice cores, International Journal of Solids and Structures, 146, 2018, 69-79.
[34] Shahgholian, D., Safarpour, M., Rahimi, A.R., Alibeigloo, A., Buckling analyses of functionally graded graphene-reinforced porous cylindrical shell using the Rayleigh-Ritz method, Acta Mechanica, 231(5), 2020, 1887-1902.
[35] Shahgholian-Ghahfarokhi, D., Rahimi, G., Khodadadi, A., Salehipour, H., Afrand, M., Buckling analyses of FG porous nanocomposite cylindrical shells with graphene platelet reinforcement subjected to uniform external lateral pressure, Mechanics Based Design of Structures and Machines, 49(7), 2021, 1059-1079.
[36] Rodrigues, F., Vellasco, P.D.S., de Lima, L.R.O., da Silva, A.T., Structural assessment of stainless steel stiffened panels, Structures, 57, 2023, 105162. 
[37] Elumalai, E.S., Krishnaveni, G., Kumar, R.S., Xavier, D.D., Kavitha, G., Seralathan, S., Hariram, V., Premkumar, T.M., Buckling analysis of stiffened composite curved panels, Materials Today: Proceedings, 33(7), 2020, 3604-3611. 
[38] Khayat, M., Poorveis, D., Moradi, S., Buckling analysis of laminated composite cylindrical shell subjected to lateral displacement-dependent pressure using semi-analytical finite strip method, Steel and Composite Structures, 22(2), 2016, 301-321. 
[39] Khayat, M., Poorveis, D., Moradi, S., Hemmati, M., Buckling of thick deep laminated composite shell of revolution under follower forces, Structural Engineering and Mechanics, 58(1), 2016, 59-91. 
[40] Khayat, M., Poorveis, D., Moradi, S., Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure, Steel and Composite Structures, 23(1), 2017, 1-16. 
[41] Brush, D.O., Almroth, B.O., Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, USA, 1975.
[42] Abramovich, H., Weller, T., Singer, J., Effect of sequence of combined loading on buckling of stiffened shells, Experimental Mechanics, 28(1), 1988, 1-13.

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Available Online from 05 September 2026