Literature Cited
S. P. Timoshenko and S. A. Voinovskii-Kriger, Plates and Shells [in Russian], Nauka, Moscow (1963).
A. S. Vol'mir, Stability of Deformable Systems [in Russian], Nauka, Moscow (1967).
A. L. Gol'denveizer, "Construction of an approximate theory of bending of plates by the method of asymptotic integration of equations of elasticity theory," Prikl. Mat. Mekh.,26, No. 4, 668–686 (1962).
A. L. Gol'denveizer and A. V. Kolos, "Construction of two-dimensional equations of the theory of thin elastic plates," Prikl. Mat. Mekh.,29, No. 1, 141–155 (1965).
Ph. Ciarlet and P. Rabier, Karman Equations [Russian translation], Mir, Moscow (1983).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tsev, Linear and Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1967).
O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).
A. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York (1980).
A. S. Vol'mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).
Additional information
Translated from Vychislitel'nye Metody i Sistemy Obrabotki Dannykh na ÉVM, pp. 71–92, 1988.
Rights and permissions
About this article
Cite this article
Pronkin, Y.N. Rigorous construction of the dynamic equations of nonlinear theory of thin elastic plates. Comput Math Model 2, 153–166 (1991). https://doi.org/10.1007/BF01128926
Issue Date:
DOI: https://doi.org/10.1007/BF01128926