We describe a technique for determining the axially symmetric geometrically nonlinear thermoviscoelastoplastic state of layered shells of revolution with regard for the damageability of the material. This procedure is based on the geometrically nonlinear relations of the theory of thin shells taking into account the transverse shear strains. We use the relations of thermoviscoplasticity, describing the deformation of an element of the body along small-curvature trajectories, as equations of state. The equivalent stress in the kinetic equations of damageability and creep is determined by the criterion of long-term strength taking into account the influence of the kind of stressed state. The procedure is illustrated by numerical results.
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A. V. Belov, “Fracture of a nonuniformly heated rotating conic shell of variable rigidity under conditions of creep,” in: Proceedings of the XIV Conference of Young Scientists of the Institute of Mechanics, Ukr. SSR Academy of Sciences [in Russian], Part 2, Kiev (1989), pp. 226–230, Deposited at VINITI 2.08.89, No. 5165-V89 DEP.
A. V. Belov, Elastoplastic Stress-Strain State of Shells of Revolution under Axially Symmetric Loading with Regard for the Damageability of the Material in Creep [in Russian], Construction Engineering Institute, Kiev (1989), Deposited at UkrNIINTI, No. 1456-UK89.
A. V. Burlakov, G. I. L’vov, and O. K. Morachkovskii, Long-Term Strength of Shells [in Russian], Vyshcha Shkola, Kharkov (1981).
A. Z. Galishin, “A procedure of determining the parameters of creep and long-term strength of isotropic materials under nonisothermal loading,” Probl. Prochn., No. 4, 21–30 (2004).
A. Z. Galishin, “Determination of the axially symmetric geometrically nonlinear thermoviscoelastoplastic state of layered shells based on the theory of processes of small-curvature deformation,” Prikl. Mekh., 39, No. 7, 114–122 (2003).
A. Z. Galishin, “Determination of the thermoviscoplastic state of shells of revolution with regard for the damageability of the material in creep,” Prikl. Mekh., 40, No. 5, 71–79 (2004).
A. Z. Galishin, V. A. Merzlyakov, and Yu. N. Shevchenko, “Application of the Newton method to calculation of the axially symmetric thermoelastoplastic state of flexible layered branched shells based on the shear model,” Mekh. Kompoz. Mater., 37, No. 3, 307–322 (2001).
M. S. Ganeeva, Strength and Stability of Shells of Revolution [in Russian], Nauka, Moscow (1992).
Ya. M. Grigorenko and A. T. Vasilenko, Problems of the Statics of Anisotropic Inhomogeneous Shells [in Russian], Nauka, Moscow (1992).
Sh. N. Kats, “A study of the long-term strength of carbon pipes,” Teploénergetika, No. 11, 37–40 (1955).
V. V. Novozhilov, Theory of Elasticity [in Russian], Sudpromgiz, Leningrad (1958).
Yu. N. Rabotnov, Creep of Structural Elements [in Russian], Nauka, Moscow (1966).
N. I. Bezukhov, V. L. Bazhanov, I. I. Gol’denblat, et al., Strength Analysis, Stability, and Vibrations under Conditions of High Temperatures [in Russian], Mashinostroenie, Moscow (1965).
Yu. N. Shevchenko and R. G. Terekhov, Physical Equations of Thermoviscoplasticity [in Russian], Naukova Dumka, Kiev (1982).
Yu. N. Shevchenko, R. G. Terekhov, N. S. Braikovskaya, and S. M. Zakharov, “An investigation into the processes of fracture of elements of a body as a result of the damageability of the material in creep,” Prikl. Mekh., 30, No. 4, 21–30 (1994).
Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, “Defining equations for the description of the processes of deformation of elements of a body along small-curvature trajectories with regard for the type of stressed state of the material,” Prikl. Mekh., 42, No. 4, 62–72 (2006).
H. Altenbach, “Topical problems and applications of creep theory,” Int. Appl. Mech., 39, No. 6, 631–655 (2003).
H. Altenbach, O. Morachkovsky, K. Naumenko, and A. Sychov, “Geometrically nonlinear bending of thin-walled shells and plates under creep-damage conditions,” Arch. Appl. Mech., 67, 339–352 (1997).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 2, pp. 175–187, April–June, 2008.
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Shevchenko, Y.N., Galishin, A.Z. Determination of the axially symmetric geometrically nonlinear thermoviscoelastoplastic state of thin layered shells with regard for the damageability of the material. J Math Sci 162, 216–230 (2009). https://doi.org/10.1007/s10958-009-9633-6
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DOI: https://doi.org/10.1007/s10958-009-9633-6