Literature Cited
G. M. Altukher, D. E. Lipovskii, and V. M. Shun, “Stability of structurally orthotropic spherical shells with variable rigidities in the direction of the meridian,” in: Stability of Three-Dimensional Structures [in Russian], Inzh.-Stroit. Inst., Kiev (1978), pp. 31–34.
I. Ya. Amiro, “Determining the critical parameters of short-term external pressure for spherical shells,” Prikl. Mekh.,17, No. 9, 34–38 (1981).
I. Ya. Amiro, “Stability of ribbed spherical shell under static and dynamic external pressure,” Prikl. Mekh.,17, No. 10, 51–60 (1981).
I. Ya. Amiro and V. A. Zarutskii, Methods of Shell Calculation, Vol. 2, Theory of Ribbed Shells [in Russian], Naukova Dumka, Kiev (1980).
I. Ya. Amiro and V. A. Zarutskii, “Research into the dynamics of ribbed shells,” Prikl. Mekh.,17, No. 11, 3–20 (1981).
I. Ya. Amiro and V. A. Zarutskii, “Research on the stability of ribbed shells,” Prikl. Mekh.,19, No. 11, 3–20 (1983).
I. Ya. Amiro, V. A. Zarutskii, and V. G. Palamarchuk, Dynamics of Ribbed Shells [in Russian], Naukova Dumka, Kiev (1983).
V. I. Babenko and V. M. Prichko, “Stability loss of spherical shells under external pressure,” Dokl. Akad. Nauk SSSR,260, No. 4, 831–833 (1981).
V. V. Boronov, “Stability for ribbed spherical shells,” in: Calculation of Building Structures, Taking Account of Physical Nonlinearity of Materials under Static and Dynamic Loads [in Russian], Leningrad (1984), pp. 32–35.
V. V. Boronov, R. D. Stepanov, and V. N. Frolov, “Experimental investigation of the stability of ribbed hemispherical shells,” Khim. Mashinostr., No. 10, 30–34 (1978).
D. Bushnell, “Nonlinear axisymmetric buckling of shells of revolution,” Raket. Tekh. Kosmonavt.,5, No. 3, 58–67 (1967).
O. V. Volosovich and S. A. Timashev, “Stability of thin convex reinforced shells,” in: Fourth All-Union Conference on Stability Problems in Constructional Mechanics. Abstracts of Proceedings [in Russian], Moscow (1972), pp. 119–120.
A. S. Vol'mir, Stability of Deformed Systems [in Russian], Nauka, Moscow (1967).
I. V. Vorovich and N. I. Minakova, Results of Science and Technology, Mechanics of Solid Deformable Bodies, Vol. 7, Stability Problems and Numerical Methods in the Theory of Spherical Shells [in Russian], VINITI, Moscow (1974).
K. Z. Galimov and R. G. Surkin, “Work of Kazan' scientists on plate and shell theory,” Issled. Teor. Plast. Oboloch., No. 5, 3–55 (1967).
O. A. Grachev, “Influence of shear deformations on the critical external pressure of a spherical shell,” Prikl. Mekh.,16, No. 8, 119–122 (1980).
O. A. Grachev, “Stability of spherical ribbed shells, taking account of shear deformations and the discreteness of rib distribution,” in: Prediction and Calculation of the Individual Life and Reliability of Mechanical Systems [in Russian], UNTs AN SSSR, Sverdlovsk (1980), pp. 35–37.
O. A. Grachev, “Influence of reinforcement parameters on the stability of ribbed spherical shells,” Prikl. Mekh.,19, No. 5, 49–55 (1983).
O. A. Grachev, “Ribbed spherical shells of minimum weight under external pressure,” in: Three-Dimensional Structures in the Krasnoyarsk Region [in Russian], Krasnoyarskii Politekhnicheskii Institut, Krasnoyarsk (1983), pp. 116–123.
O. A. Grachev, “Influence of rib eccentricity on the stability of spherical shells under external pressure,” Prikl. Mekh.,21, No. 1, 53–60 (1985).
O. A. Grachev, “Rational reinforcement of spherical shells under external pressure,” Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., No. 4, 78–81 (1985).
O. A. Grachev, “Stability of transversally isotropic reinforced spherical shells,” Strength and Stability of Shells. Proceedings of a Seminar [in Russian], Kazansk. Fiz.-Tekh. Inst., KF AN SSSR (1968), No. 19, Part 1, pp. 72–79.
O. A. Grachev and V. I. Ignatyuk, “Detemining the critical loads of shells of revolutior with eccentric reinforcing elements, taking account of shear deformations,” Prikl. Mekh.,22, No. 6, pp. 36–43 (1986).
O. A. Grachev and V. I. Ignatyuk, “Influence of the properties of the material of shells of revolution with eccentric reinforcing elements on the critical loads,” Mekh. Kompozit. Mater., No. 4, 665–671 (1986).
O. A. Grachev and V. I. Ignatyuk, “Stability of transversally isotropic ribbed shells of revolution,” Stroit. Mekhan. Rasch. Sooruzh., No. 3, 61–64 (1986).
O. A. Grachev and A. S. Pal'chevskii, “Experimental results on the stress-strain state of domes with meridional-annular reinforcement,” Research on the Calculation of Plates and Shells [in Russian], Rostov. Inzh.-Stroit. Inst., Rostov-on-Don (1982), pp. 59–62.
O. A. Grachev and A. S. Pal'chevskii, “Experimental investigation of the stability of ribbed spherical shells under external pressure,” Prikl. Mekh.,19, No. 2, 52–57 (1983).
E. I. Grigolyuka and V. I. Mamai, Mechanics of the Deformation of Spherical Shells [in Russian], Mosk. Univ., Moscow (1983).
P. A. Zhilin and G. A. Kizima, “Spherical strip with meridional reinforcing elements,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 97–105 (1969).
Ya. M. Zil'ber and S. A. Timashev, “Experimental investigation of the stability of domes with radial-annular reinforcement,” in: Abstracts of Proceedings and Reports from the Third All-Union Conference on the Experimental Investigation of Engineering Structures [in Russian], NIISK, Ural'skii Promstroiniiproekt, Sverdlovsk (1973), pp. 16–17.
V. F. Zipalova and A. S. Yudin, “Comparison of schemes for taking account of reinforcement in investigating the stability of a nonsloping spherical dome,” in: Proceeding of the Tenth All-Union Conference on the Theory of Shells and Plates, Kutaisi, 1975 [in Russian], Vol. 1, Metsniereba, Tbilisi (1975), pp. 610–618.
B. Ya. Kavlerchik, A. A. Kozhevnikov, and B. E. Kuznetsov, “Optimal design of reinforced spherical shell,” Prikl. Mekh.,9, No. 10, 119–122 (1973).
R. Crawford and D. Schwarts, “General instability and optimal design of spherical bottoms with waffle reinforcement,” Raket. Tekh. Kosmonavt.,3, No. 3, 164–170 (1965).
V. T. Lizin and V. A. Pyatkin, Design of Thin-Walled Structures [in Russian], Mashinostroenie, Moscow (1985).
M. E. Lipnitskii, Dome Coverings for Buildings in a Dry Climate [in Russian], Stroiizdat Leningrad (1981).
A. I. Manevich, Stability and Optimal Design of Reinforced Shells [in Russian], Vishcha Shkola, Kiev-Donetsk (1979).
A. I. Manevich and M. E. Kaganov, “Stability and weight optimization of reinforced spherical shells under external pressure,” Prikl. Mekh.,9, No. 1, 20–26 (1973).
Yu. M. Mauergauz, “General-tangent method in problems of optimizing reinforced shells,” in: Thirteenth All-Union Conference on the Theory of Plates and Shells, Tallin, 1983 [in Russian], Tallin. Politekhn. Inst., Tallin (1983), pp. 13–18.
N. P. Mel'nikov, Metallic Structures Outside the USSR [in Russian], Stroiizdat, Moscow (1971).
F. A. Plotnikov, “Sloping spherical shell reinforced by annular ribs,” in: Research into the Theory and Method of Calculation of Building Structures [in Russian], Moscow (1984), pp. 119–130.
A. V. Pogorelov, Geometric Theory of Shell Stability [in Russian], Nauka, Moscow (1966).
T. V. Polonskaya, “Analysis of the influence of reinforcement schemes on the stress-strain state of a shell of revolution,” in: Spatial Structures in the Krasnoyarsk Region [in Russian], Krasnoyar. Politekhn. Inst., Krasnoyarsk (1983), pp. 147–151.
Yu. M. Pochtman, “Optimizing the design of spherical reinforced shells,” Izv. Vyssh. Uchebn. Zaved., Stroit. Arkhit., No. 3, 40–44 (1976).
G. I. Pshenichnov, Theory of Thin Elastic Grid Shells and Plates [in Russian], Nauka, Moscow (1982).
B. I. Sakharov, “Calculating a thin reinforced spherical shell under an internal uniform pressure,” Izv. Vyssh. Uchebn. Zaved., Mashinostr., No. 10, 86–93 (1965).
B. I. Sakharov, “Thin sloping spherical shells reinforced by rigid elements under an axisymmetric load,” Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., No. 4, 41–45 (1967).
B. I. Sakharov, “Thin reinforced spherical shells under internal or external pressure,” Tr. Mosk. Aviats. Inst., No. 180, 151–172 (1971).
R. D. Stepanov and V. V. Boronov, “Stability of hemispherical shells with a meridional reinforcing element,” Khim. Mashinostr., No. 10, 25–29 (1978).
R. D. Stepanov, V. N. Frolov, E. V. Vorob'ev, and V. V. Boronov, “Experimental investigation of the stability of smooth and ribbed spherical shells by the photoelasticity method,” in: Proceedings of the Seventh All-Union Conference on the Photoelasticity Method [in Russian], Vol. 4, Tallin (1979), pp. 191–193.
A. A. Syas'kii, “Welded orthotropic spherical shells with reinforcing elements,“ Prikl. Mekh.,21, No. 1, 66–73 (1985).
S. Tillman, “Influence of the distribution of reinforcing elements on the behavior of spherical shells in buckling,” in: International Conference on Three-Dimensional Shell Structures of Coverings for Buildings in Ordinary and Seismic Regions, Alma-Ata, 1977 [in Russian], Stroiizdat, Moscow (1977), pp. 197–198.
S. A. Timashev, Stability of Reinforced Shells [in Russian], Stroiizdat, Moscow (1974).
S. I. Trenin and E. S. Shimusyuk, “Stability of reinforced spherical shells,” in: Theory of Shells and Plates. Proceedings of the Eighth All-Union Conference on the Theory of Shells and Plates [in Russian], Nauka, Moscow (1973), pp. 348–351.
V. I. Tur, “Stability of a preliminarily loaded sloping metallic grid dome reinforced by a three-dimensional tie rod,” Izv. Vyssh. Uchebn. Zaved., Stroit. Arkhit., No. 2, 1–5 (1983).
V. I. Tur, “Stability of a preliminarily loaded sloping grid dome,” Issled. Prostranst. Konstr., No. 4, 116–124 (1983).
I. M. Fedotkin, V. V. Klyavlin, I. K. Koshevoi, et al., “Minimization of the weigth of a waffle spherical shell under a specified critical load,” Vestn. Kiev. Politekh. Inst., Khim. Mashinostr. Tekhnol., No. 22, 66–71 (1985).
V. F. Tsybulin, “Experimental investigation of stability loss of nonsloping spherical shells of variable thickness under the action of uniform external pressure,” Stroit. Mekhan., Gazoaérodin., Proizvod. Letatel. Apprat., No. 2, 207–211 (1974).
V. F. Chizhov, “Stability of a spherical shell with a significantly inhomogeneous stress state,” in: Fourth All-Union Conference on Stability Problems in Constructurional Mechanics. Abstracts of Proceedings [in Russian], Moscow (1972), p. 106.
A. S. Yudin, “Stability of a spherical shell of stepwise-varying rigidity,” Fiz.-Mat. Issled., Rostov. Univ., Rostov-on-Don (1972), pp. 46–51.
K. P. Buchert, “Zur Stabilität grosser doppert dekrummeter and versteifter Schalen,” Stahlbau,34, No. 2, 55–62 (1965).
J. O. Crooker and K. P. Buchert, “Reticular space structures,” J. Struct. Div., Proc. Am. Soc. Civil, Engin.,96, No. 3, 697–700 (1970).
A. R. Jefts, S. Gyha-Majumdar, and M. K. Wanchoo, “Instability behavior of stiffened dome liners under construction conditions,” in: Transcripts of Fourth International Conference on the structural Mechanics of Reactor Technology, San Francisco, California, 1977, Vol. J(a), Amsterdam (1977), j. 5.10, pp. 1–11.
K. Klöppel and O. Jungbluth, “Beitrag zum Durchschlagproblem dünnwandiger Kügelschalen. Versuche und Bemessungsformeln,” Stahlbau,22, No. 6, 121–123 (1953).
K. Klöppel and E. Roos, “Beitrag zum Durchschlagproblem dünnwandiger versteifter und unversteifter Kügelschalen für voll und halbseitige Belastung,” Stahlbaum25, No. 3, 49–60 (1956).
L. Kollar, “Buckling of complete spherical shells and spherical caps,” in: Buckling of Shells, Proceeding of State-of-the-Art Colloquium, University of Stuttgart, May 6–7, 1982, Berlin (1982), pp. 401–425.
G. J. Simitses and C. M. Blackmon, “Shape through buckling of eccentrically stiffened shallow spherical caps,” Int. J. Sol. Struct.,11, No. 9, 1035–1040 (1975).
J. Singer, “Buckling experiments on shells—a review of recent developments,” Sol. Mech. Arch.,7, No. 3, 273–313 (1982).
K. Simino, K. Mitsui, and Y. Ozawa, “An elastic stability analysis for spherical shells,” Bull. JSME,27, No. 224, 153–158 (1984).
S. C. Tillman, “Some effects of rib-reinforcement arrangement on spherical-dome buckling,” Exp. Mech.,18, No. 10, 396–400 (1978).
K. Uchiyama and M. Yamada, “Buckling of orthogonally stiffened and framed spherical shells under external pressure,” in: Shell and Spatial Structural Engineering International symposium, Proceedings of International Symposium on Shell and Spatial Structure, Rio de Janeiro, 19–21 September 1983, London-Plymouth (1984), pp. 220–239.
M. Yamada, “An approximation on the buckling analysis of orthogonally stiffened and framed spherical shells under external pressure,” Shell and Spatial Structure Structural Engineering. Proceedings of an International Symposium on Shell and Spatial Structure, Rio de Janeiro, 19–21 September, 1983.
Ye Zhiming, “The nonlinear stability problem of thin spherical cap with variable thickness,” Acta Mech. Sin.,16, No. 6, 634–638 (1984).
M. S. Zarghame and F. J. Heger, “Buckling of thin concrete domes,” J. Amer. Concr. Inst., No. 6, 487–500 (1983); Proc.,80, 487–500.
Additional information
Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 22, No. 11, pp. 3–17, November, 1986.
Rights and permissions
About this article
Cite this article
Amiro, I.Y., Grachev, O.A. Stability of spherical reinforced shells. Soviet Applied Mechanics 22, 1015–1026 (1986). https://doi.org/10.1007/BF01272864
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01272864