The stability of equilibrium states of shells of revolution with nonzero Gaussian curvature under combined axisymmetric loads is analyzed. The analysis is based on a dynamic stability criterion and allows for the nonlinearity and inhomogeneity of subcritical state and mutual influence of the loads. The stability domains of shells with positive, negative, and alternating curvature at different combinations of distributed pressure and boundary forces and moments are constructed. Substantial differences in sizes and configurations of the stability domains and in buckling modes on the boundary of interaction of the loads are revealed depending on the sign of the curvature.
Similar content being viewed by others
References
N. A. Alfutov, Foundations of the Stability Design of Elastic Systems [in Russian], Mashinostroenie, Moscow (1991).
V. P. Belous, “Stability of reinforced cylindrical shells subject to axial compression and external pressure,” Prats. Odesk. Politekhn. Univ., 1, No. 38, 37–41 (2012).
B. M. Broude, “On boundary surfaces,” in: Proc. 6th All-Union Conf. on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1966). pp. 188–192.
Ya. M. Grigorenko, O. I. Bespalova, and N. P. Boreiko, “Stability of systems composed of shells of revolution with variable Gaussian curvature,” Mat. Met. Fiz. Mekh. Polya, 62, No. 1, 127–142 (2019).
Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar’, Free Vibrations of Elements of Shell Structures [in Russian], Naukova Dumka, Kyiv (1986).
V. Z. Grishchak, D. D. Grishchak, and N. N. D’yachenko, “Effective approximate analytic solution of a stability problem for a sandwich conical shell under combined loading,” Mat. Met. Fiz. Mekh. Polya, 61, No. 3, 63–77 (2018).
A. V. Karmishin, V. I. Myachenkov, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures [in Russian], Mashinostroenie, Moscow (1975).
P. F. Papkovich, Structural Mechanics of a Ship [in Russian], Part II, Sudpromgiz, Leningrad (1941).
E. I. Bespalova and N. P. Yaremchenko, “Stability of systems composed of shells of revolution,” Int. Appl. Mech., 53, No. 3, 545–555 (2017).
S. A. Bochkarev and S. V. Lekomtsev, “Stability of functionally graded circular cylindrical shells under combined loading,” Mech. Comp. Mater., No. 3, 349–362 (2019).
A. Evkin, M. Kolesnikov, and D. Prikazchikov, “Buckling of a spherical shell under external pressure and inward concentrated load: asymptotic solution,” Math. Mech. Solids, 22, No. 6, 1425–1437 (2016).
S. M. Hasheminejad and M. A. Motaaleghi, “Supersonic flatter control of an electrorheological fluid-based smart circular cylindrical shell,” Int. J. Struct. Stabil. Dynam., 14, No. 2, 1350064 (2014).
O. Ifayefunmi, “A survey of buckling of conical shells subjected to axial compression and external pressure,” J. Eng. Sci. Technol. Rev., 7, No. 2, 182–189 (2014).
P. Jasion, “Stabilty analysis of shells of revolution under pressure conditions,” Thin-Walled Struct., 47, 311–317 (2009).
C. Li, Y. Miao, H. Wang, and Q. Feng, “Thermal buckling of thin spherical shells under uniform external pressure and non-linear temperature,” Thin-Walled Struct., 119, 782–794 (2017).
H. Lin, D. Cao, and C. Shao, “An admissible function for vibration and flutter studies of FG cylindrical shells with arbitrary edge conditions using characteristic orthogonal polynomials,” Comp. Struct., 185, 748–763 (2018).
R. Mohammadzadeh, M. M. Najafizadeh, and M. Nejati, “Buckling of 2D-FG cylindrical shells under combined external pressure and axial compression,” Adv. Appl. Math. Mech., 5, No. 3, 391–406 (2013).
N. P. Semenyuk, V. M. Trach, and A. V. Podvornyi, “Spatial stability of layered anisotropic cylindrical shells under compressive loads,” Int. Appl. Mech., 55, No. 2, 211–221 (2019).
N. P. Semenyuk, V. M. Trach, and N. B. Zhukova, “Stability and initial post-buckling behavior of orthotropic cylindrical sandwich shells with unidirectional elastic filler,” Int. Appl. Mech., 55, No. 6, 636–647 (2019).
N. P. Semenyuk and N. B. Zhukova, “Stability of a sandwich cylindrical shell with core subject to external pressure and pressure in the inner cylinder,” Int. Appl. Mech., 56, No. 1, 52–66 (2020).
A. H. Sofiev, “The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure,” Comp. Struct., 92, No. 2, 488–498 (2010).
A. H. Sofiev, N. Alizada, O. Akin, and S. Adiguzel, “On stability of FGM shells subjected to combined loads with different edge conditions and resting on elastic foundations,” Acta Mech., 223, No. 1, 189–204 (2012).
P. T. Smith, C. T. F. Ross, and A. P. F. Little, “Composite tubing collapse under uniform external hydrostatic pressure,” in: Proc. of the Int. Conf. on Computing in Civil and Building Engineering (ICCCBE), University Press, Nottinghem (2010), pp. 1–7.
A. Tafreshi and C. Bailey, “Instability of imperfect composite cylindrical shells under combined loading,” Comp. Struct., 80, No. 1, 49–64 (2007).
Th. A. Winterstetter and H. Schmidt, “Stability of circular cylindrical steel shells under combined loading,” Thin-Walled Struct., 40, 893–909 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 57, No. 4, pp. 35–46, July–August 2021.
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Rights and permissions
About this article
Cite this article
Bespalova, O.I., Boreiko, N.P. Stability of Shells of Revolution with Different Gaussian Curvature in the Field of Combined Static Loads. Int Appl Mech 57, 405–413 (2021). https://doi.org/10.1007/s10778-021-01092-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-021-01092-4