×

zbMATH — the first resource for mathematics

Buckling of cylindrical shells with general axisymmetric thickness imperfections under external pressure. (English) Zbl 1347.74036
Summary: This study focuses on the buckling of cylindrical shells under external pressure with general axisymmetric thickness imperfections. Firstly, the result of uniform thickness imperfection and recent study result of axisymmetric modal thickness imperfection are reviewed briefly. Secondly, asymptotic formulas of the buckling load, which are in terms of the thickness imperfection parameter up to arbitrary order, are determined through asymptotic analyses. The analyses are based on a system of linearized governing partial differential equations of perfect shells with variable thickness. Thirdly, the effects led by three patterns of thickness imperfections on the buckling of the laterally pressured cylindrical shells, which are uniform, axisymmetric modal and parabolic, are respectively investigated. Buckling loads of uniform and axisymmetric modal thickness imperfections coincide with the known results. In addition to the analytic investigation, numerical analyses and comparisons are also carried out. The analytical study results presented in the paper can be utilized to evaluate the stabilities of cylindrical shells under external pressure with general axisymmetric imperfections in thickness, once the thickness imperfection is known.

MSC:
74G60 Bifurcation and buckling
74K25 Shells
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Amazigo, J. C.; Fraser, W. B., Buckling under external pressure of cylindrical shells with dimple shaped initial imperfections, International Journal of Solids and Structures, 7, 883-900, (1971) · Zbl 0229.73050
[2] Aghajari, S.; Abedi, K.; Showkati, H., Buckling and post-buckling behavior of thin-walled cylindrical steel shells with varying thickness subjected to uniform external pressure, Thin-walled Structures, 44, 904-909, (2006)
[3] Arbocz, J.; Hol, J. M.A. M., Collapse of axially compressed cylindrical shell with random imperfections, AIAA Journal, 29, 2247-2256, (1991) · Zbl 0800.73211
[4] Ali, L.; Jalal, E. B.; Abdellatif, K.; Larbi, E. B., Effect of multiple localized geometric imperfections on stability of thin axisymmetric cylindrical shells under axial compression, International Journal of Solids and Structures, 48, 1034-1043, (2011) · Zbl 1236.74086
[5] Chen, L.; Rotter, J. M.; Doerich, C., Buckling of cylindrical shells with stepwise variable wall thickness under uniform external pressure, Engineering Structures, 33, 3570-3578, (2011)
[6] Combescure, A.; Gusic, G., Nonlinear buckling of cylinders under lateral pressure with nonaxisymmetric thickness imperfections using the COMI axisymmetric shell element, International Journal of Solids and Structures, 38, 6207-6226, (2001) · Zbl 1075.74530
[7] Donnell, L. H.; Wan, C. C., Effect of imperfections on buckling of thin cylinders and columns under axial compression, Journal of Applied Mechanics, 17, 73-83, (1950) · Zbl 0039.20203
[8] Elishakoff, I.; Li, Y. W.; Starners, J. H., Non-classical problem in theory of elastic stability, (2001), Cambridge University Press Cambridge, pp. 44-46
[9] Gusic, G.; Combescure, A.; Jullien, J. F., The influence of circumferential thickness variations on the buckling of cylindrical shells under lateral pressure, Computers and Structures, 74, 461-477, (2000)
[10] Koiter, W. T.; Elishakoff, I.; Li, Y. W.; Starnes, J. H., Buckling of an axially compressed cylindrical perfect shell of variable thickness, International Journal of Solids and Structures, 31, 797-807, (1994) · Zbl 0802.73028
[11] Khamlichi, A.; Bezzazi, M.; Limam, A., Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections, Thin-walled Structures, 42, 1035-1047, (2004)
[12] Li, Y. W.; Elishakoff, I.; Starnes, J. H., Axial buckling of composite cylindrical shells with periodic thickness variation, Computers and Structures, 56, 65-74, (1995) · Zbl 0900.73224
[13] Nguyen, T. H.L.; Elishakoff, I.; Nguyen, T. V., Buckling under the external pressure of cylindrical shells with variable thickness, International Journal of Solids and Structures, 46, 4163-4168, (2009) · Zbl 1176.74070
[14] Rotter, J. M.; Teng, J. G., Elastic stability of cylindrical shells with weld depressions, Journal of Structural Engineering, 115, 1244-1263, (1989)
[15] Rotter, J.M., 19 April 1996. Elastic plastic buckling and collapse in internally pressurized axially compressed silo cylinders with measured axisymmetric imperfections: interactions between imperfections, residual stresses and collapse. In: Proceedings of the International Workshop on Imperfections in Metal Silos: Measurement, Characterization and Strength Analysis. CA-Silo, Lyon, France, pp. 119-140.
[16] Selein, S. S.; Kennedy, J. B., Imperfection sensitivity of stiffened cylinders subjected to external pressure, Computers and Structures, 34, 63-69, (1990) · Zbl 0703.73038
[17] Timoshenko, S. P.; Gere, J. M., Theory of elastic stability, (1961), McGraw-Hill New York
[18] Volmir, A. S., Stability of deformable systems, (1967), Nauka Moscow
[19] Yamaki, N., Elastic stability of circular cylindrical shells, (1984), Amsterdam, North-Holland · Zbl 0544.73062
[20] Yu, C. L.; Chen, Z. P.; Wang, J.; Yan, S. J.; Yang, L. C., Effect of weld reinforcement on axial plastic buckling of welded steel cylindrical shells, Journal of Zhejiang University-SCIENCE A, 13, 79-90, (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.