Abstract
The effect of cryogenic and elevated temperatures on the nonlinear straining processes of the oblate hemi-ellipsoidal shells with a clamped edge under external axisymmetric pressure has been numerically simulated. Herewith the limit loads buckling have been determined. Shells with different wall thickness have been considered. The analysis was via the linearization and orthogonal sweep methods, which allowed for both material and geometrical non-linearity. The temperature dependence of the material characteristics has been taken into account. It has been found that the largest critical loads for all the shells under considerations are observed at cryogenic temperatures and its values decrease considerably at elevated temperatures.
Similar content being viewed by others
REFERENCES
S. N. Kryvoshapko, ‘‘Research on general and axisymmetric ellipsoidal shells used as domes, pressure vessels, and tanks,’’ Appl. Mech. Rev. 60, 336–355 (2007).
J. Błachut, ‘‘Experimental perspective on the buckling of pressure vessel components,’’ Appl. Mech. Rev. 66, 010803 (2014).
J. Zheng, K. Li, S. Liu, H. Ge, Z. Zhang, C. Gu, H. Qian, and Z. Hua, ‘‘Effect of shape imperfection on the buckling of large-scale thin-walled ellipsoidal head in steel nuclear containment,’’ Thin Wall. Struct. 124, 514–522 (2018).
K. Li, J. Zheng, S. Liu, H. Ge, G. Sun, Z. Zhang, C. Gu, and P. Xu, ‘‘Buckling behavior of large-scale thin-walled ellipsoidal head under internal pressure,’’ Thin Wall. Struct. 141, 260–274 (2019).
S. Daghighi, M. Rouhi, G. Zucco, and P. M. Weaver, ‘‘Bend-free design of ellipsoids of revolution using variable stiffness composites,’’ Comput. Struct. 233, 111630 (2020).
J. Błachut and O. R. Jaiswal, ‘‘On the choice of initial geometric imperfections in externally pressurized shells,’’ J. Press. Vessel Technol. Trans. ASME 121, 71–76 (1999).
C. T. Ross, B. H. Huat, T. B. Chei, C. M. Chong, and M. D. Mackney, ‘‘The buckling of GRP hemi-ellipsoidal dome shells under external hydrostatic pressure,’’ Ocean Eng. 30, 691–705 (2003).
Y. Q. Ma, C. M. Wang, and K. K. Ang, ‘‘Buckling of super ellipsoidal shells under uniform pressure,’’ Thin Wall. Struct. 46, 584–591 (2008).
A. Muc, M. Chwał, and M. Barski, ‘‘Remarks on experimental and theoretical investigations of buckling loads for laminated plated and shell structures,’’ Comput. Struct. 203, 861–874 (2018).
C. Tangbanjongkij, S. Chucheepsakul, and W. Jiammeepreecha, ‘‘Analytical and numerical analyses for a variety of submerged hemi-ellipsoidal shells,’’ J. Eng. Mech. 146, 04020066 (2020).
A. D. Kovalenko, Basics of Thermoelasticity (Nauk. Dumka, Kiev, 1970) [in Russian].
E. A. Thornton, ‘‘Thermal buckling of plates and shells,’’ Appl. Mech. Rev. 46, 485–506 (1993).
M. S. Ganeeva, ‘‘Temperature problem in geometrically and physically nonlinear theory of non-thin and thin shells,’’ Available from VINITI No. 4459-85 (1985).
M. S. Ganeeva, V. E. Moiseeva, and Z. V. Skvortsova, ‘‘Large deflections and stability of spherical segment under thermal and force loading,’’ Lobahevskii J. Math. 40 (6), 734–739 (2019).
M. S. Ganeeva, V. E. Moiseeva, and Z. V. Skvortsova, ‘‘Numerical analysis of nonlinear bending of the safety bursting disks subjected to the pressure and temperature of the working medium,’’ Uch. Zap. Kazan. Unin. 4, 670–680 (2018).
M. S. Ganeeva, V. E. Moiseeva, and Z. V. Skvortsova, ‘‘Nonlinear bending and stability of ellipsoidal reverse buckling disks being under the liquid pressure and temperature,’’ Ekol. Vestn. Nauch. Tsentrov ChES 2, 211–227 (2017).
A. A. Il’yushin, Plasticity. Part I. Elastic-Plastic Deformation (Gostekhteorizdat, Moscow, 1948) [in Russian].
M. S. Ganeeva and L. A. Kosolapova, ‘‘On Hooke’s relations in the temperature problem of an elastic solid body,’’ in Proceedings of the 12th International Conference on the Theory of Shells and Plates (1996), pp. 33–37.
M. S. Ganeeva and V. E. Moiseeva, ‘‘Nonlinear bending of non-thin components shells of revolution made of thermosensitive elastic-plastic material,’’ in Proceedings of the Seminar on Studies on Shell Theory (KFTI KazNC RAS, Kazan, 1990), Vol. 25, pp. 4–20.
M. S. Ganeeva, V. E. Moiseeva, and Z. V. Skvortsova, ‘‘Nonlinear straining of shallow and non-shallow spherical shells under thermal and force loadings,’’ J. Phys.: Conf. Ser. 1158, 022043 (2019).
N. I. Bezukhov, V. L. Bazhanov, I. I. Gol’denblatt, N. A. Nikolaenko, and A. M. Sinyukov, The Calculations for Strength, Stability and Oscillations in High Temperature Conditions (Mashinostroenie, Moscow, 1965) [in Russian].
Yu. P. Solntsev, B. S. Ermakov, and O. I. Sleptsov, Materials for Low and Cryogenic Temperatures. Encyclopedic Reference Book (Khimizdat, St. Petersburg, 2008) [in Russian].
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by D. A. Gubaidullin)
Rights and permissions
About this article
Cite this article
Moiseeva, V.E., Skvortsova, Z.V. Stress-Strain State Analysis of Oblate Ellipsoidal Shells under External Pressure Loading and Temperature. Lobachevskii J Math 42, 2179–2185 (2021). https://doi.org/10.1134/S1995080221090195
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080221090195