The problem of the mechanical behavior of metal-composite plates of regular layered structure in bending under conditions of steady-state creep of all phase materials is formulated. Equations describing, with various degrees of accuracy, the stress and viscous creep states of such plates with account of their weakened resistance to transverse shears are obtained. The relations of the classical Kirkhoff theory, the nonclassical Reissner theory results, and the second variant of Timoshenko theory result as special cases of these equations. For asymmetrically loaded annular plates with one edge clamped and statically loaded other one, a simplified variant of the refined theory, whose complexity in practical realization is comparable to that of the Reissner theory, is developed. The bending deformations of such annular plates at different levels of thermal actions are calculated. It is shown that, with increasing temperature, the accuracy of calculations within the framework of the traditional theories decreases sharply and neither of them provides an accuracy for the calculated compliance of the structure even within 20%.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. N. Andreev and Yu. V. Nemiroskii, Multilayered Anisotropic Shells and Plates. Bending, Stability, and Vibrations [in Russian], Nauka, Novosibirsk (2001).
V. V. Pikul’, Mechanics of Shells [in Russian], Vladivistok, Dal’nauka (2009).
M. A. Kanibolotskii and Yu. S. Urzhumtsev, Optimum Design of Laminated Structures [in Russian], Nauka, Novosibirsk (1989).
Yu. P. Trykov, E. P. Pokataev, V. G. Shmorgun, A. A. Khrapov, Residual Stresses in Laminated Composites [in Russian], Metallurgizdat, Moscow (2010).
S. K. Godunov, S. P. Kiselev, I. M. Kulikov, and V. I. Mali, Modeling of Shock-Wave Processes in Elastoplastic Materials on Various (Nuclear, Meso, and Thermodynamic) Structural Levels [in Russian], Institute of Computer Researche, Moscow-Izhevsk (2014).
L. M. Kachanov, Theory of Creep [in Russian], Fizmatgiz, Moscow (1960).
Yu. N. Rabotnov, Creep of Elements of Structures [in Russian], Nauka, Moscow (1966).
O. V. Sosnin, B. V. Gorev, and A. F. Nikitenko, Energy Variant of Creep Theory [in Russian], IGiL Siberian branch of the USSR Academy of Sciences, Novosibirsk (1986).
A. F. Nikitenko, Creep and Long-Term Strength of Metal Materials [in Russian], NGASU, Novosibirsk (1997).
G. M. Khazhinskii, Models of Deformation and Fracture of Metals [in Russian], Nauchnyi Mir, Moscow (2011).
A. P. Yankovskii, “Calculation of the steady-state creep of shallow metal-composite shells of layered-fibrous structure,” Vest. Samara Gos. Tekhn. Univ., Series of Physical and Mathematical Sci., 1, No. 20 (2010).
Yu. V. Nemirovskii, “Creep of clamped plates with various structures of reinforcement,” Prikl. Mekh. Tekhn. Fizika, 55, No. 1 (2014).
A. P. Yankovskii, “Analysis of the secondary anisotropic creep of layered metal-composite plates with account of their weakened resistance to the transverse shear. 2. Model of deformation,” Mech. Compos. Mater., 48, No. 2, 193-208 (2012).
E. Reissner, “On bending of elastic plates,” Quarterly of Appl. Mathematics, 5, No. 1, 55-68 (1947).
A. S. Yudin, “Stability and Vibrations of Structurally Anisotropic and Artificial Shells of Revolution [in Russian], Publishing House of the South Federal University, Rostov-on-Don (2011).
V. O. Kaledin, S. M. Aul’chenko, A. B. Mitkevich, E. V. Reshetnikova, E. A. Sedova, and Yu. V. Shpakova, Modeling the Statics and Dynamics of Shell Structures from Composite Materials [in Russian], Fizmatgiz, Moscow (2014).
A. K. Malmeister, V. P. Tamuzh, and G. A. Teters, Strength of Polymer and Composite Materials [in Russian], Zinatne, Riga (1980).
S. A. Ambartsumyan, Theory of Anisotropic Plates. Strength, Stability, and Vibrations, Nauka, Moscow (1987).
V. G. Bazhenov, E. V. Pavlenkova, and A. A. Artemyev, “Numerical solution of generalized axisymmetric problems of the dynamics of elastoplastic shells of revolution at large deformations,” Komput. Mekh. Splosh. Sred, 5, No. 4, 427-434 (2012).
A. P. Yankovskii, “Analysis of the secondary anisotropic creep of layered metal–composite plates with account of their weakened resistance to the transverse shear. 1. Structural models,” Mech. Compos. Mater., 48, No. 1, 1-14 (2012).
V. L. Biderman, Mechanics of Thin-Walled Structures. Statics [in Russian], Mashinostorenie, Moscow (1977).
S. P. Demidov, Theory of Elasticity [in Russian], Vyssha Shkola, Moscow (1979).
G. Hall and G. Watt, Modern Numerical Methods for Ordinary Differential Equations, Publishing of Oxford University press, USA (1976).
K. Dekker and J. Verver, Stability of Runge–Kutta Methods for Stiff Nonlinear Differential Equations. North-Holland, Amsterdam (1984).
G. S. Pisarenko and N. S. Mozharskii, Equations and Boundary-Value Problems of the Theory of Plasticity and Creep. Handbook [in Russian], Naukova Dumka, Kiev (1981).
Composite Materials. Handbook [in Russian], Ed. D. M. Karpinos. Naukova Dumka, Kiev (1985).
Acknowledgements
This work was carried out at a financial support of the Russian Fund for Basic Research (Project No. 14-01-00102-á).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Mekhanika Kompozitnykh Materialov, Vol. 52, No. 6, pp. 1017-1042, November-December, 2016.
Rights and permissions
About this article
Cite this article
Yankovskii, A.P. Refined Deformation Model for Metal-Composite Plates of Regular Layered Structure in Bending Under Conditions of Steady-State Creep. Mech Compos Mater 52, 715–732 (2017). https://doi.org/10.1007/s11029-017-9622-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11029-017-9622-7