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Stress concentration at the circular hole of cyclically bent layered composite plate within the framework of a moment theory of thermoviscoelasticity. (English) Zbl 07249560

Summary: In the continuum mechanics there is a class of problems that cannot be solved directly or the solutions of these problems are affected by large errors when the classical equations of thermoviscoelasticity are considered. The paper discusses a special case of such problems – the cyclic bending of a composite plate with a circular hole subjected to the stationary self-heating, which was solved within the framework of a moment theory of thermoviscoelasticity.

MSC:

80A99 Thermodynamics and heat transfer
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[1] Savin, G. N.; Nemish, Y. N., Investigations into stress concentration in the moment theory of elasticity (a survey), Appl. Mech., 4, 1-17 (1968)
[2] Altenbach, J.; Altenbach, H.; Eremeyev, V. A., On generalized Cosserat-type theories of plates and shells: a short review and bibliography, Arch. Appl. Mech., 80, 73-92 (2010) · Zbl 1184.74042
[3] Cosserat, E. F.; Cosserat, F. F., Théorie des corps deformables (1909) · JFM 40.0862.02
[4] Kubenko, V. D.; Shul’ga, N. A., A dynamic plane problem of the moment theory of elasticity and viscoelasticity, Appl. Mech., 3, 50-53 (1967)
[5] Lomakin, V. A.; Savova, L. N., Problems of straining of microinhomogeneous viscoelastic bodies and the moment theory of viscoelasticity, Polym. Mech., 2, 213-220 (1967)
[6] Savova, L. N., Two-dimensional problem in the moment theory of viscoelasticity concerning stress concentration near a circular hole, Appl. Mech., 4, 6-13 (1968)
[7] Bykov, D. L.; Il’yushin, A. A.; Ogibalov, P. M.; Pobedrya, B. E., Some fundamental problems of the theory of thermoviscoelasticity, Polym. Mech., 1, 41-58 (1971)
[8] Kolokol’chikov, V. V., Microrelaxation model for describing the moment effects in viscoelastic polymers, Polym. Mech., 13, 501-506 (1977)
[9] Pobedrya, B. E.; Rodriguez, A., Modelling of structures in the mechanics of composites, Mech. Compos. Mater., 37, 459-474 (2001)
[10] Omarov, S. E., Effective characteristics of layered composites with allowance for structural changes, Mech. Solids, 42, 463-470 (2007)
[11] Pobedrya, B. E.; Omarov, S. E., Determination of material functions for the linear moment theory of viscoelasticity, Mosc. Univ. Mech. Bull., 62, 117-122 (2007) · Zbl 1164.74060
[12] Pobedrya, B. E.; Omarov, S. E., Constitutive relations of the moment theory of elasticity, Mosc. Univ. Mech. Bull., 62, 84-86 (2007) · Zbl 1164.74348
[13] Omarov, S. E., Determining the material constant in the equilibrium problem for an infinite elastic plane weakened by a circular hole, Mech. Solids, 44, 776-780 (2007)
[14] Omarov, S. E., A method of determining the material functions in the linear moment theory of elasticity, Mosc. Univ. Mech. Bull., 64, 110-113 (2009)
[15] Altenbach, H., Eine direkt formulierte lineare Theorie für viskoelastische Platten und Schalen, Ingeneur Archiv, 58, 215-228 (1988) · Zbl 0661.73032
[16] Altenbach, H.; Eremeyev, V. A., On the bending of viscoelastic plates made of polymer foams, Acta Mech., 204, 137-154 (2009) · Zbl 1165.74030
[17] Katunin, A.; Fidali, M., Self-heating of polymeric laminated composite plates under the resonant vibrations: theoretical and experimental study, Polym. Compos., 33, 138-146 (2012)
[18] Katunin, A.; Fidali, M., Fatigue and thermal failure of polymeric composites subjected to cyclic loading, Adv. Compos. Lett., 21, 64-69 (2012)
[19] Katunin, A.; Gnatowski, A., Influence of heating rate on evolution of dynamic properties of polymeric laminates, Plast. Rubber Compos., 41, 233-239 (2012)
[20] Gevorkyan, G. A., Equations of plate bending in the moment theory of elasticity, Appl. Mech., 2, 74-79 (1966)
[21] Bouyge, F.; Jasiuk, I.; Boccara, S.; Ostoja-Staszewski, M., A micromechanically based couplestress model of an elastic orthotropic two-phase composite, Eur. J. Mech. A-Solids, 21, 465-481 (2002) · Zbl 1100.74538
[22] Hayrapetyan, G. S.; Sargsyan, S. H., Theory of micropolar orthotropic elastic thin plates, Comm. Acad. Sci., 65, 22-33 (2012)
[23] Tsiatas, G. C.; Yiotis, A. J., A modified couple stress theory for bending (2013) · Zbl 1297.74159
[24] Trovalusci, P.; Masiani, R., Non-linear micropolar and classical continua for anisotropic discontinuous materials, Int. J. Solids Struct., 40, 1281-1297 (2003) · Zbl 1062.74514
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