Numerical analysis of buckling of orthogrid-stiffened cylindrical shells under axial compression within the framework of a linear bifurcation approach in comparison with experiment
Аuthors
*, **, ***Samara National Research University named after Academician S.P. Korolev, Moskovskoe shosse, 34, Samara, Russia
*e-mail: ser85@bk.ru
**e-mail: sopromat@ssau.ru
***e-mail: sazanow@mail.ru
Abstract
The article presents solutions to buckling problems under axial compression of three orthogrid-stiffened cylindrical shells within the framework of a linear bifurcation approach using a computational model based on a numerical integration scheme and the "smearing" hypothesis, as well as models based on the finite element method. Two of these shells have three longitudinal welds, which ensure the connection of the three segments that make up each shell. Such a shell manufacturing technology can lead to the presence of initial imperfections in the resulting shell (in the form of noticeable deviations of its real shape from the ideal cylindrical shape), which can have a significant impact on the magnitude of the critical load. The third shell is made using seamless technology and has less pronounced initial imperfections. The results of the calculation for the buckling of each of these shells within the framework of the "smearing" scheme are compared with the results of calculations based on the finite element method and the empirical-statistical method, as well as with available experimental data. A computational model based on the "smearing" hypothesis and constructed using the orthogonal run procedure in combination with the Kutta-Merson scheme of numerical integration gives a result close (within 3%) to the finite element model. A comparison of the numerical simulation results with the experiment shows a good agreement on the magnitude of the critical load (within 11%). The empirical-statistical method gives a fairly conservative estimate of the magnitude of the critical load, underestimating the result by up to 38% compared with the experiment.
Keywords:
buckling under axial compression, orthogrid-stiffened cylindrical shell, numerical integration method, finite element methodReferences
1. Lizin V.T., Pyatkin V.A. Proektirovanie tonkostennykh konstruktsii. (Design of thin-walled structures). Moscow: Mashinostroenie Publ., 1976. 408 p.2. Egorov I.A. Consideration of plastic deformations in the design of wafer-type compartments. Trudy MAI. 2022. No. 122. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=164103. DOI: 10.34759/trd-2022-122-04
3. Malinin G.V. Methods of calculation of ribbed plates for strength and stability. Trudy MAI. 2021. No. 121. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=162655. DOI: 10.34759/trd-2021-121-08
4. Firsanov V.V., Vo A.Kh., Chan N.D. Studying stiffened shells stress state by the refined theory with account for ribs elasticity and clamped edge. Trudy MAI. 2018. No. 104. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=102130
5. Anisimov S.A. Numerical analysis of buckling under axial compression of orthogrid-stiffened cylindrical shells made of aluminum alloys. Trudy MAI. 2024. No. 134. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=178880
6. Anisimov S.A., Sukhomlinov L.G., Tokarev A.E. Calculated prediction of critical loads for axially compressed waffle cylindrical shells made of aluminum alloys in comparison with experiment. Kosmonavtika i raketostroenie. 2024. No.1 (134). P. 58-67. (In Russ.)
7. Wang B., Tian K., Hao P., Zheng Y., Ma Y., Wang J. Numerical-based smeared stiffener method for global buckling analysis of grid-stiffened composite cylindrical shells. Composite Structures. 2016. No. 152. P. 807-815. DOI: 10.1016/j.compstruct.2016.05.096
8. Nezvanov D.N. Ustoichivost' tsilindricheskikh obolochek vafel'nogo tipa pri osevom szhatii // V sb.: Voprosy prochnosti elementov aviatsionnykh konstruktsii (Buckling of cylindrical shells of wafer type at axial compression // In.: Questions of durability of elements of aviation designs). Kuibyshev: KuAI Publ., 1971. P. 119-132.
9. Wang B., Du K., Hao P., Zhou C., Tian K. et al. Numerically and experimentally predicted knockdown factors for stiffened shells under axial compression. Thin-Walled Structures. 2016. No. 109. P. 13-24. DOI: 10.1016/j.tws.2016.09.008
10. Wagner H.N.R., Huhne C., Niemann S., Tian K., Wang B., Hao P. Robust knockdown factors for the design of cylindrical shells under axial compression: Analysis and modeling of stiffened and unstiffened cylinders. Thin-Walled Structures. 2018. No. 127. P. 629-645. DOI: 10.1016/j.tws.2018.01.041
11. Tian K., Wang B., Hao P., Waas A.M. A high-fidelity approximate model for determining lower-bound buckling loads for stiffened shells. International Journal of Solids and Structures. 2018. No. 148-149. P. 14–23. DOI: 10.1016/j.ijsolstr.2017.10.034
12. Wang B., Yang M., Zeng D., Hao P., Li G., Li Y., Tian K. Post-buckling behavior of stiffened cylindrical shell and experimental validation under non-uniform external pressure and axial compression. Thin-Walled Structures. 2021. No. 161. P. 1-12. DOI: 10.1016/j.tws.2021.107481
13. Hilburger M.W. Developing the next generation shell buckling design factors and technologies. Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Honolulu. 2012. DOI: 10.2514/6.2012-1686
14. Almroth B.O., Holmes A.M., Brush D.O. An experimental study of the buckling of cylinders under axial compression. Experimental Mechanics. 1964. Vol. 4, No. 9. P. 263-270. DOI: 10.1007/BF02323088
15. Tennyson R.C. A note on the classical buckling load of circular cylindrical shells under axial compression. AIAA Journal. 1963. Vol. 1, No. 2. P. 475-476.
16. Konokh V.I., Krasovskii V.L. About influence of the isolated local dimple on buckling of smooth thin-walled cylinders at axial compression. Soprotivlenie materialov i teoriya sooruzhenii. 1973. No. 21. P. 114–121. (In Russ.)
17. Evkin A.YU., Krasovskii V.L., Manevich L.I. Buckling of axial compressed cylindrical shells at local quasistatic influences. Izvestiya AN SSSR. Mekhanika tverdogo tela. 1978. No. 6. P. 96-100. (In Russ.)
18. Krasovsky V., Marchenko V., Schmidt R. Deforming and buckling of axially compressed cylindrical shells with local loads in numerical simulations and experiments. Thin-Walled Structures. 2011. Vol. 49, P. 576-580. DOI: 10.1016/j.tws.2010.09.009
19. Hilburger M.W., Waters W.A.J., Haynie W.T. Buckling Test Results from the 8-Foot-Diameter Orthogrid-Stiffened Cylinder Test Article TA01, 2015 [Test Dates: 19-21 November 2008], NASA/TP-2015-218785, L-20490, NF1676L-20067.
20. Hilburger M, Lindell MC, Waters WA, Gardner NW. Test and Analysis of Buckling Critical Stiffened Metallic Launch Vehicle Cylinders. In: 2018 AIAA/ASCE/AHS/ ASC Structures, Structural Dynamics, and Materials Conference. January 2018. DOI: 10.2514/6.2018-1697
21. Rudd M.T., Hilburger M.W., Lovejoy A.E., Lindell M.C., Gardner N.W., Schultz M.R. Buckling response of a large-scale, seamless, orthogrid-stiffened metallic cylinder. In: 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. January 2018. DOI: 10.2514/6.2018-1987
22. Anisimov S.A. Pavlov V.F., Sazanov V.P. On the applicability limits of the structurally orthotropic shell model in problems of calculating the buckling under axial compression of waffle cylindrical shells. Dinamika i vibroakustika. 2024. Vol. 10, No. 2. C. 49-58. (In Russ.). DOI: 10.18287/2409-4579-2024-10-2-49-58
Download