Computer simulation of local and global buckling of thin-walled shells
DOI:
https://doi.org/10.7242/1999-6691/2015.8.3.19Keywords:
shell, geometric nonlinearity, stability, local buckling, gradient method, orthotropy, best parameter continuation methodAbstract
Stability of thin-walled structures is investigated on the basis of the geometrically nonlinear theory of shells. This allows us to monitor a series of shell deformation processes under different load changes. The local and general loss of stability can be determined by observing changes in the shape of the shell curved surface before and after critical loads. The shell material can be isotropic or orthotropic, but linear-elastic. A mathematical model of deformation of a shell is the functional of total potential energy of deformation of the shell. Two methods are applied to minimize the total energy functional of deformation of the shell. One is based on the method of L-BFGS with discrete approximation of the unknown functions by NURBS-surfaces. This enables taking into account various forms of fixing of the shell contour and the complex shape of this circuit. The other employs the Ritz method and the best parameter continuation method in the continuous approximation of the unknown displacement functions and the angles of rotation of the normal. This technique allows us to find the upper and lower critical loads and the bifurcation point. A combination of these techniques makes it possible to study both the subcritical and supercritical behavior of the structure and to identify the local and global buckling of the shell and their relationship. On the curve of equilibrium states versus “load q - deflection W ” one can see all moments of buckling of the shell caused by “swatting” of some part of it. Thus, after each buckling a significant change in the shape of the curved surface is observed. For illustration purposes the changes in the shell shape at subcritical and supercritical stages are plotted against its three-dimensional surface. After the general loss of stability the shell deforms under loading without any significant change in its shape, i.e. it behaves as a plate.
Downloads
References
Krivosapko S.N. O vozmoznostah obolocecnyh sooruzenij v sovremennoj arhitekture i stroitel’stve // Stroitel’naa mehanika inzenernyh konstrukcij i sooruzenij. - 2013. - No 1. - S. 51-56.
2. Ventsel E., Krauthammer T. Thin plates and shells: Theory, analysis and applications. - New York: Dekker, 2001. - 666 p.
3. Suhinin S.N. Prikladnye zadaci ustojcivosti mnogoslojnyh kompozitnyh obolocek. - M.: Fizmatlit, 2010. - 248 s.
4. Pikul’ V.V. Sovremennoe sostoanie teorii ustojcivosti obolocek // Vestnik DVO RAN. - 2008. - No 3. - S. 3-9.
5. Akusev V.L. Nelinejnye deformacii i ustojcivost’ tonkih obolocek. - M.: Nauka, 2004. - 276 s.
6. Reddy J.N. Mechanics of laminated composite plates and shells: theory and analysis. CRC Press, Boca Raton, FL, 2004. - 856 p.
7. Artem’eva A.A., Bazenov V.G., Kibec A.I., Laptev P.V., Sosin D.V. Verifikacia konecno-elementnogo resenia trehmernyh nestacionarnyh zadac uprugoplasticeskogo deformirovania, ustojcivosti i zakriticeskogo povedenia obolocek // Vycisl. meh. splos. sred. - 2010. - T. 3, No 2. - S. 5-14. DOI
8. Andreev L.V., Obodan N.I., Lebedev A.G. Ustojcivost’ obolocek pri neosesimmetricnoj deformacii. - M.: Nauka, 1988. - 208 s.
9. Valisvili N.V. Metody rasceta obolocek vrasenia na ECVM. - M.: Masinostroenie, 1976. - 278 s.
10. Grigoluk E.I., Kabanov V.V. Ustojcivost’ obolocek. - M.: Nauka, 1978. - 360 s.
11. Petrov V.V. Metod posledovatel’nyh nagruzenij v nelinejnoj teorii plastinok i obolocek. - Saratov: Izd-vo Sarat. un-ta, 1975. - 119 s.
12. Trach V.M. Stability of conical shells made of composites with one plane of elastic symmetry // Int. Appl. Mech. - 2007. - Vol. 43, no. 6. - P. 662-669. DOI
13. Ahmed M.K. Elastic buckling behavior of a four-lobed cross section cylindrical shell with variable thickness under non-uniform axial loads // Math. Probl. Eng. - 2009. - 829703. DOI
14. Jabareen M., Sheinman I. Effect of the nonlinear pre-buckling state on the bifurcation point of conical shells // Int. J. Solids Struct. - 2006. - Vol. 43, no. 7-8. - P. 2146-2159. DOI
15. Shadmehri F., Hoa S.V., Hojjati M. Buckling of conical composite shells // Compos. Struct. - 2012. - Vol. 94, no. 2. - P. 787-792. DOI
16. Tresev A.A., Seresevskij M.B. Issledovanie NDS pramougol’noj v plane obolocki polozitel’noj gaussovoj krivizny iz ortotropnyh materialov s ucetom svojstv raznosoprotivlaemosti // Vestnik Volgogr. gos. arhit.-stroit. un-ta. Ser.: Str-vo i arhit. - 2013. - No 31-2 (50). - S. 414-421.
17. Blinov A.N. O niznej kriticeskoj nagruzke uprugoj cilindriceskoj obolocki pri osevom szatii // Vestnik Sibirskogo federal’nogo universiteta. Matematika i fizika. - 2012. - No 5 (3). - S. 359-362.
18. Kirakosan R.M. Ob odnoj utocnennoj teorii gladkih ortotropnyh obolocek peremennoj tolsiny // Doklady nacional’noj akademii nauk Armenii. - 2011. - No 2. - S. 148-156.
19. Trusin S.I., Ivanov S.A. Cislennoe issledovanie ustojcivosti pologoj cilindriceskoj obolocki s ucetom fiziceskoj i geometriceskoj nelinejnostej pri razlicnyh granicnyh usloviah // Stroitel’naa mehanika i rascet sooruzenij. - 2011. - No 5. - S. 43-46.
20. Karpov V.V. Procnost’ i ustojcivost’ podkreplennyh obolocek vrasenia: v 2-h castah. - M: Fizmatlit, 2011. - C. 2. - 248 s.
21. Karpov V.V., Ignat’ev O.V., Sal’nikov A.U. Nelinejnye matematiceskie modeli deformirovania obolocek peremennoj tolsiny i algoritmy ih issledovania. - M.: Izd-vo ASV; SPb.: SPbGASU, 2002. - 420 s.
22. Karpov V.V., Volynin A.L., Muhin D.E. Nesimmetricnye formy poteri ustojcivosti pologih rebristyh obolocek pri linejno i nelinejno-uprugom deformirovanii // Uspehi stroitel’noj mehaniki i teorii sooruzenij. - Saratov: SGTU, 2010. - S. 105-112.
23. Qatu M.S., Asadi E., Wang W. Review of recent literature on static analyses of composite shells: 2000-2010 // Open Journal of Composite Materials. - 2012. - Vol. 2. - P. 61-86. DOI
24. Alijani F., Amabili M. Non-linear vibrations of shells: A literature review from 2003 to 2013 // Int. J. Nonlinear Mech. - 2014. - Vol. 58. - P. 233-257. DOI
25. MacKay J.R., van Keulen F. A review of external pressure testing techniques for shells including a novel volume-control method // Exp. Mech. - 2010. - Vol. 50, no. 6. - P. 753-772. DOI
26. Zinov’ev P.A., Smerdov A.A. Optimal’noe proektirovanie kompozitnyh materialov: Uceb. posobie. - M.: Izd-vo MGTU im. N.E. Baumana, 2006. - C. 2. - 103 s.
27. Solomatov V.I., Bobrysev A.N., Himmler K.G. Polimernye kompozicionnye materialy v stroitel’stve. - M.: Strojizdat, 1988. - 312 s.
28. Tyskevic V.N. Vybor kriteria procnosti dla trub iz armirovannyh plastikov // Izvestia VolgGTU. - 2011. - No 5 (78). - S. 76-79.
29. Ankovskij A.P. Rascet naprazenno-deformirovannogo sostoania slozno armirovannyh metallokompozitnyh obolocek v usloviah ustanovivsejsa polzucesti // Vycisl. meh. splos. sred. - 2011. - T. 4, No 1. - S. 109-123. DOI
30. Maksimyuk V.A., Storozhuk E.A., Chernyshenko I.S. Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review) // Int. Appl. Mech. - 2012. - Vol. 48, no. 6. - P. 613-687. DOI
31. Golovanov A.I., Ivanov V.A., Paimushin V.N. Numerical analysis method for studying local forms of stability loss of bearing layers of three-layered shells using mixed forms // Mech. Compos. Mater. - 1995. - Vol. 31, no. 1. - P. 69-79. DOI
32. Smerdov A.A. Vozmoznosti povysenia mestnoj ustojcivosti podkreplennyh i integral’nyh kompozitnyh konstrukcij // Izvestia vyssih ucebnyh zavedenij. Masinostroenie. - 2014. - No 10. - S. 70-79.
33. Wang X.-T., Qin Z.-B., Gao L.-Z., Liang X.-X. The effect of frame torsion on the local stability of a ring-stiffened cylindrical shell // Journal of Marine Science and Application. - 2004. - Vol. 3, no. 2. - P. 12-16. DOI
34. Manevic A.I. K teorii svazannoj poteri ustojcivosti podkreplennyh tonkostennyh konstrukcij // PMM. - 1982. - T. 42, No 2. - S. 337-345.
35. Tovstik P.E. Ustojcivost’ tonkih obolocek. - M: Nauka, Fizmatlit, 1995. - 320 s.
36. Il’in V.P., Karpov V.V. Svazannost’ form poteri ustojcivosti rebristyh obolocek // Trudy XIV Vsesouznoj konferencii po teorii plastin i obolocek. - Kutaisi: Mecnierba 1987. - S. 615-619.
37. Novozilov V.V. Teoria tonkih obolocek. - L.: Sudpromizdat, 1962. - 431 s.
38. Ambarcuman S.A. Teoria anizotropnyh obolocek. - M.: Fizmatlit, 1961. - 384 s.
39. Vol’mir A.S. Nelinejnaa dinamika plastinok i obolocek. - M.: Nauka, 1972. - 432 s.
40. Karpov V.V., Semenov A.A. Matematiceskaa model’ deformirovania podkreplennyh ortotropnyh obolocek vrasenia // Inzenerno-stroitel’nyj zurnal. - 2013. - No 5. - S. 100-106. DOI
41. Baranova D.A. Algoritm issledovania ustojcivosti podkreplennyh obolocek vrasenia na osnove metoda L-BFGS // Promyslennoe i grazdanskoe stroitel’stvo. - 2012. - No 3. - S. 58-59.
42. Kuznecov E.B. Metod prodolzenia resenia i nailucsaa parametrizacia. - M.: Izd-vo MAI-PRINT, 2010. - 160 s.
43. Semenov A.A. Algoritmy issledovania procnosti i ustojcivosti podkreplennyh ortotropnyh obolocek // Stroitel’naa mehanika inzenernyh konstrukcij i sooruzenij. - 2014. - No 1. - S. 49-63.
44. Wang X. Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method // Comput. Method. Appl. M. - 2007. - Vol. 196, no. 17-20. - P. 2242-2251. DOI
45. Van Campen D.H., Bouwman V.P., Zhang G.Q., Zhang J., Ter Weeme B.J.W. Semi-analytical stability analysis of doubly-curved orthotropic shallow panels - considering the effects of boundary conditions // Int. J. Nonlinear Mech. - 2002. - Vol. 37, no. 4-5. - P. 659-667. DOI
Downloads
Published
Issue
Section
License
Copyright (c) 2015 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.