The use of the hereditary theory for shells heterogeneous across their thickness is considered. A variational method is formulated for calculating thin anisotropic shells made of a material whose deformation behavior can be described by relations of the linear theory of viscoelasticity. In order to transform the corresponding functional into a form suitable for shells, some assumptions related to concepts of the theory of thin shells are introduced. In the capacity of Euler equations, physical relations, nonlinear equilibrium equations, and nonlinear boundary conditions are derived. The state equations are deduced for a multilayered shell.
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References
N. P. Abovskii, N. P. Andreev, and A. P. Deruga, Variational Principles of the Theory of Elasticity and the Theory of Shells [in Russian], Nauka, Moscow (1978).
A. S. Vol’mir, Stability of Deform able Systems [in Russian], Nauka, Moscow (1987).
K. Z. Galimov, Fundamentals of the Nonlinear Theory of Thin Shells [in Russian], Izdat. KGU (1975).
A. L. Gol’denveizer, Theory of Elastic Thin Shells [in Russian], Nauka, Moscow (1976).
R. Yu. Amenzadeh and E. T. Kiyasbeyli, Vestnik Yakovlev ChGPU, Ser. Mekh. Pred. Sost., No. 4, 57–63 (2008).
Yu. N. Rabotnov, Elements of the Hereditary Mechanics of Solids [in Russian], Nauka, Moscow (1977).
K. Vasidzu, Variational Methods in the Theory of Elasticity and Plasticity [in Russian], Mir, Moscow (1987).
R. Yu. Amenzadeh, A. N. Alizadeh, and Preobrazhenskii, “Variational principle of the theory of heterogeneous shells under irradiation,” Mekh. Tverd. Tela, No. 2, 151–155 (1988).
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 231–240, March–April, 2009.
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Amenzadeh, R.Y. A variational principle in a geometrically nonlinear theory of heterogeneous viscoelastic shells. Mech Compos Mater 45, 159–164 (2009). https://doi.org/10.1007/s11029-009-9075-8
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DOI: https://doi.org/10.1007/s11029-009-9075-8