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IssuesArchive of Issues2009-5pp.769-775

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V.A. Postnov, "Constructive Symmetry in the Stability Problem for a Cylindrical Shell Reinforced by Stiffening Rings under Hydrostatic Pressure," Mech. Solids. 44 (5), 769-775 (2009)
Year 2009 Volume 44 Number 5 Pages 769-775
DOI 10.3103/S0025654409050148
Title Constructive Symmetry in the Stability Problem for a Cylindrical Shell Reinforced by Stiffening Rings under Hydrostatic Pressure
Author(s) V.A. Postnov (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, St. Petersburg, 199178 Russia)
Abstract We use the solution of the problem under study which was earlier obtained by the author [1-3] and which is based on a decomposition of the reinforced shell into separate constructive elements (the ribs and the shell itself) and then on deriving the equilibrium equations and consistency conditions for their strains. Under the assumption that the shell precritical state is momentless, this is a sufficiently exact solution. Its drawback is the significant complexity of the computational algorithm. In the present paper, we show that the laboriousness of the algorithm can be reduced dramatically if the shell under study has elements of design symmetry (identical ribs, their uniform spacing, or both). In addition, we present dependencies determining the stiffening rib rigidity needed to ensure that the shell remains stable for a given critical value of the external hydrostatic pressure.
Keywords cylindrical shell, stability, stiffening element, bending
References
1.  V. A. Postnov, "Stability of Circular Cylindrical Shell Reinforced by Stiffening Rings under the Action of Transverse and Longitudinal Loads," in Strength of Ship Constructions, No. 46 (Tr. LKI, Leningrad, 1964), pp. 49-58 [in Russian].
2.  V. A. Postnov, "Stability of a Circular Cylindrical Shell Reinforced by Ribs of Different Rigidity," in Proc. Sci.-Techn. Conf. in Structural Mechanics, No. 74 (Sudpromgiz, Leningrad, 1966), pp. 105-110 [in Russian].
3.  V. M. Kurnaev and V. A. Postnov, "Stability of Orthotropic Circular Cylindrical Shells Reinforced by Ring Frames under External Pressure," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 129-137 (1972) [Mech. Solids (Engl. Transl.)].
4.  P. A. Sokolov, "Stability of a Thin Cylindrical Shell Reinforced by Elastic Rings of Rigidity under the Action of Transverse and Longitudinal Loads," Prikl. Mat. Mekh. 1 (2), 256-281 (1933).
5.  W. A. Nash, "Buckling of Multiple-Bay of Ring Cylindrical Shells Subject to External Hydrostatic Pressure," Trans. ASME. J. Appl. Mech. 20 (4), 469-474 (1953).
6.  N. A. Alfutov, "Stability of Cylindrical Shells Reinforced by a Set of Transverse Forces and Loaded by an External Pressure," Inzh. Sb., No. 23, 36-46 (1956).
7.  Y. Yoshiyuki and N. Matsubara, "Buckling Strength of Metal Lining of a Cylindrical Pressure Vessel," Bull. JSME 12 (51), 421-429 (1969).
8.  J. Tian, C. M. Wang, and S. Swaddiwudhipong, "Elastic Buckling Analysis of Ring-Stiffened Cylindrical Shells under General Pressure Loading via the Ritz Method," Thin-Walled Struct. 35, 1-24 (1999).
9.  V. M. Ryabov, "Stability of a Cylindrical Shell Reinforced a Transverse Set under External Pressure and Axial Compression," Rasch. Prostr. Konstr., No. 12, 150-167 (1969).
10.  I. S. Malyutin, "Stability of Cylindrical Shell Reinforced by Ring Frame under External Pressure and Axial Forces," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 65-68 (1971) [Mech. Solids (Engl. Transl)].
11.  V. M. Darevskii, "Determining the Critical Pressure for Cylindrical Shell Reinforced by Arbitrarily Located Rings of Different Rigidity," Izv. Akad. Nauk SSSR. OTN. Mekh. Mashinostr., No. 3, 72-82 (1963).
12.  I. S. Malyutin, "Stability of Cylindrical Shell Reinforced by a Regular System of Rings of Different Rigidity," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 185-188 (1976) [Mech. Solids (Engl. Transl)].
13.  V. A. Postnov, G. A. Tumashik, and I. V. Moskvina, "Stability of Circular Cylindrical Shell Reinforced by Stiffening Rings under Action of External Hydrostatic Pressure. Construction Mass Optimization," in Nonlinear Problems of Mechanics and Physics of a Deformable Rigid Body, No. 9 (SPbGU, 2005), pp. 10-21 [in Russian]
14.  V. A. Postnov, G. A. Tumashik, and I. V. Moskvina, "Stability of Circular Cylindrical Shells Reinforced by Ring Frames under External Hydrostatic Pressure," in Proc. 35th Intern. Summer School Conf. Advanc. Probl. Mech. St. Petersburg, 2007 (St. Petersburg, 2007), pp. 346-355 [in Russian].
Received 26 November 2007
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