Literature Cited
J. Alberg, E. Nilson, and J. Walsh, Theory of Coefficients and Its Applications [Russian translation], Mir, Moscow (1972).
R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York (1966).
I. G. Bubnov, Works on Plate Theory [in Russian], Gostekhizdat, Moscow (1953).
E. F. Burmistrov, “Calculation of hollow orthotropic shells, taking into account finite deformations,” Inzh. Sb.,22, 83–97 (1955).
N. V. Valishvili and V. B. Silkin, “Calculation of annular plates with large displacements,” in: Strength Calculations. Collected Papers [in Russian], No. 16 (1975), pp. 50–65.
A. S. Vol'mir, Flexible Plates and Shells [in Russian], Gostekhizdat, Moscow (1956).
I. I. Vorovich and V. R. Zipalova, “Solution of nonlinear boundary-value problems of elasticity theory by transforming to a Cauchy problem” Prikl. Mat. Mekh.,29, No. 5, 894–901 (1965).
S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk,16, No. 3, 171–174 (1961).
É. I. Grigolyuk, “Behavior of circular plate after stability loss,” Vestn. Inzh. Tekh., No. 3, 103–106 (1949).
B. Ya. Kantor, Nonlinear Problems of the Theory of Inhomogeneous Hollow Shells [in Russian], Naukova Dumka, Kiev (1971).
M. A. Koltunov, “Taking into account the finiteness of displacements in problems on the flexure and stability of plates and hollow shells,” Vestn. Mosk. Univ., No. 5, 13–29 (1952).
M. S. Kornishin, Nonlinear Problems of the Theory of Plates and Hollow Shells and Methods of Solution [in Russian], Nauka, Moscow (1964).
V. V. Novozhilov, Principles of Nonlinear Elasticity Theory [in Russian], Gostekhizdat, Moscow (1948).
P. F. Pankovich, Marine Structural Mechanics [in Russian], Sudpromgiz, Leningrad (1941).
A. V. Karmishin, V. I. Myachenkov, V. A. Leskovets, and A. N. Frolov, Statics and Dynamics of Thin-Walled Shell Structures [in Russian], Mashinostroenie, Moscow (1975).
A. S. Vol'mir (editor), Theory of Flexible Circular Plates [in Russian], IL, Moscow (1957).
S. P. Timoshenko and S. Woinowsky-Krieger, Plates and Shells [in Russian], Fizmatgiz, Moscow (1963).
V. I. Feodos'ev, “Geometrically nonlinear problems of plate and shell theory,” in: Proceedings of the Fourth All-Union Conference on Plate Theory [in Russian], Nauka, Moscow (1966), pp. 971–976.
Additional information
Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 14, No. 4, pp. 63–70, April, 1978.
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Grigorenko, Y.M., Ovlyakuliev, O. Numerical solution of boundary-value problems on the deformation of flexible annular plates of variable rigidity. Soviet Applied Mechanics 14, 385–391 (1978). https://doi.org/10.1007/BF00883915
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DOI: https://doi.org/10.1007/BF00883915