Abstract
The exact solution is constructed to a nonlinear problem on subcritical and postcritical deformation of a flexible long cylindrical shell with a noncircular cross-section and fixed periphery under uniform loading. The solution is represented by two relations in terms of elementary functions. The graphs demonstrate how the deflection behaves depending on the laws of change in the curvature and load distribution
Similar content being viewed by others
REFERENCES
N. A. Alfutov, Fundamentals of the Stability Analysis of Elastic Systems [in Russian], Mashinostroenie, Moscow (1991).
V. Z. Vlasov, The General Theory of Shells and Its Applications in Engineering [in Russian], Gostekhizdat, Moscow-Leningrad (1949).
A. S. Vol'mir, Flexible Plates and Shells [in Russian], Gostekhizdat, Moscow (1956).
A. S. Vol'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).
É. I. Grigolyuk and V. V. Kabanov, Stability of Shells [in Russian], Nauka, Moscow (1978).
Ya. M. Grigorenko, “Solution of the problem on deformation of a flexible long cylindrical shell with variable parameters,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 417–421 (1977).
Ya. M. Grigorenko and L. V. Kharitonova, “Influence of boundary conditions on the stability and postcritical behavior of flexible noncircular long cylindrical panels,” Dokl. NANU, No. 7, 35–37 (1995).
Ya. M. Grigorenko and V. I. Gulyaev, “Nonlinear problems of the theory of shells and methods for their solution,” Prikl. Mekh., 27, No. 10, 3–23 (1991).
L. H. Donnel, Beams, Plates, and Shells, McGraw-Hill, New York (1976).
M. S. Kornishin and Kh. M. Mushtari, “Stability of an infinitely long flat cylindrical panel under normal uniform pressure,” Izv. Kazanskogo Filiala Akad. Nauk SSSR, Ser. Fiz. Mat. Tekhn. Nauk, 7, 36–50 (1955).
Kh. M. Mushtari, “Some generalizations of the theory of thin shells with application to the solution of elastic-equilibrium stability problems,” Prikl. Mat. Mekh., 2, No. 14, 439–456 (1939).
A. S. Vol'mir (ed.), The Theory of Flexible Circular Plates [Russian translation], Izd. Inostr. Lit., Moscow (1957).
V. I. Feodos'ev, Elastic Elements of Precision Instrument Making [in Russian], Oborongiz, Moscow (1949).
Ya. M. Grigorenko and L. I. Zakhariichenko, “Analysis of the stress-strain state of noncircular cylindrical shells subject to thickness variation and weight retention,” Int. Appl. Mech., 35, No. 6, 567–576 (1999).
Ya. M. Grigorenko and L. I. Zakhariichenko, “Design of corrugated cylindrical shells under different end conditions,” Int. Appl. Mech., 35, No. 9, 897–905 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grigorenko, Y.M., Kas'yan, Y.B. Deformation of a Flexible Noncircular Long Cylindrical Shell Under a Nonuniform Load. International Applied Mechanics 37, 346–351 (2001). https://doi.org/10.1023/A:1011375630146
Issue Date:
DOI: https://doi.org/10.1023/A:1011375630146