Deformation of a three-layer circular plate under creep conditions

E. I. Starovoitov ; Yu. M. Pleskatshevsky ; A. V. Yarovaya

Problemy fiziki, matematiki i tehniki, no. 2 (2021), pp. 57-63.

Résumé

The analytical solution of the boundary value problem of axisymmetric bending of a circular three-layer plate under creep conditions is obtained using the experimental-theoretical Ilyushin method. The physical equations of state of the hereditary theory of linear viscoelasticity are used. The similarity of the creep cores of the layer materials was assumed. The polyline hypothesis is used to describe the kinematics of a plate package that is not symmetric in thickness. In the bearing layers, the Kirchhoff hypotheses are valid. In a relatively thick placeholder, the Timoshenko hypothesis is accepted. The well-known solution of a similar problem in the theory of elasticity for such a three-layer plate is taken as the initial one. Numerical approbation of the obtained solution is carried out.

Détail

Keywords: three-layer plate, bending, similarity of creep nuclei, experimental-theoretical method.

Bibliographie

[1] A.G. Gorshkov, E.I. Starovoitov, A.V. Yarovaya, Mekhanika sloistykh vyazkouprugoplasticheskikh elementov konstruktsii, Fizmatlit, M., 2005, 576 pp.

[2] M.A. Zhuravkov, E.I. Starovoitov, Mekhanika sploshnykh sred. Teoriya uprugosti i plastichnosti, BGU, Minsk, 2011, 540 pp.

[3] E.I. Starovoitov, M.A. Zhuravkov, D.V. Leonenko, Trekhsloinye sterzhni v termoradiatsionnykh polyakh, Belaruskaya navuka, Minsk, 2017, 276 pp.

[4] K.G. Golovko, P.Z. Lugovoi, V.F. Meish, Dinamika neodnorodnykh obolochek pri nestatsionarnykh nagruzkakh, Kievskii un-t, Kiev, 2012, 541 pp.

[5] Yu.M. Pleskachevskii, E.I. Starovoitov, A.V. Yarovaya, Dinamika metallopolimernykh sistem, Bel. navuka, Minsk, 2004, 386 pp.

[6] D.V. Tarlakovskii, G.V. Fedotenkov, “Two-Dimensional Nonstationary Contact of Elastic Cylindrical or Spherical Shells”, Journal of Machinery Manufacture and Reliability, 43:2 (2014), 145–152 | DOI | MR

[7] A.G. Gorshkov, E.I. Starovoitov, A.V. Yarovaya, “Garmonicheskie kolebaniya trekhsloinoi tsilindricheskoi vyazkouprugoplasticheskoi obolochki”, Prikladnaya mekhanika, 2001, no. 9, 100–107

[8] V.N. Paimushin, “Theory of moderately large deflections of sandwich shells having a transversely soft core and reinforced along their contour”, Mechanics of Composite Materials, 53:1 (2017), 3–26 | DOI

[9] E.I. Starovoitov, D.V. Leonenko, D.V. Tarlakovskii, “Rezonansnye kolebaniya krugovykh kompozitnykh plastin na uprugom osnovanii”, Mekhanika kompozitnykh materialov, 51:5 (2015), 793–806

[10] V.S. Deshpande, N.A. Fleck, “Dynamic Response of a Clamped Circular Sandwich Plate Subject to Shock Loading”, J. Appl. Mech., 71:5 (2004), 637–645 | DOI | Zbl

[11] E.I. Starovoitov, A.V. Yarovaya, D.V. Leonenko, “Deformirovanie uprugogo trekhsloinogo sterzhnya lokalnymi nagruzkami”, Problemy mashinostroeniya i avtomatizatsii, 2001, no. 4, 37–40

[12] L. Škec, G. Jelenić, “Analysis of a geometrically exact multi-layer beam with a rigid interlayer connection”, Acta Mechanica, 225:2 (2014), 523–541 | DOI | MR

[13] J. Belinha, L.M. Dints, “Nonlinear Analysis of Plates and Laminates Using the Element Free Galerkin Method”, Composite Structures, 78:3 (2007), 337–350 | DOI

[14] D. Julien, S. Karam, “Limit analysis of multi-layered plates. Part II: The Homogenesized Love-Kirchhoff Model”, Journal of the Mechanics and Physics of Solids, 56:2 (2008), 561–580 | DOI | MR | Zbl

[15] V.V. Moskvitin, E.I. Starovoitov, “Deformatsiya i peremennye nagruzheniya dvukhsloinykh metallopolimernykh plastin”, Mekhanika kompozitnykh materialov, 1985, no. 3, 409–416

[16] A.G. Kozel, “Peremescheniya v krugovoi trekhsloinoi plastine na dvukhparametricheskom osnovanii”, Mekhanika. Issledovaniya i innovatsii, 2017, no. 10, 90–95

[17] A.G. Kozel, “Matematicheskaya model deformirovaniya krugovoi trekhsloinoi plastiny na osnovanii Pasternaka”, Problemy fiziki, matematiki i tekhniki, 2017, no. 1 (30), 42–46

[18] A.G. Kozel, “Vliyanie sdvigovoi zhestkosti osnovaniya na napryazhennoe sostoyanie sendvich-plastiny”, Fundamentalnye i prikladnye problemy tekhniki i tekhnologii, 2018, no. 6 (332), 25–35

[19] Yu.V. Zakharchuk, “Deformirovanie krugovoi trekhsloinoi plastiny so szhimaemym zapolnitelem”, Problemy fiziki, matematiki i tekhniki, 2017, no. 4 (4), 53–57

[20] Yu.V. Zakharchuk, “Peremescheniya v krugovoi trekhsloinoi plastine so szhimaemym zapolnitelem”, Mekhanika. Issledovaniya i innovatsii, 2017, no. 10, 55–66

[21] Yu.V. Zakharchuk, “Trekhsloinaya krugovaya uprugoplasticheskaya plastina so szhimaemym zapolnitelem”, Problemy fiziki, matematiki i tekhniki, 2018, no. 4 (37), 72–79

[22] E.I. Starovoitov, “Termosilovoe nagruzhenie trekhsloinykh pologikh obolochek”, Izv. AN SSSR. Mekhanika tverdogo tela, 1989, no. 5, 114–119

[23] E.I. Starovoitov, D.V. Leonenko, D.V. Tarlakovskii, “Deformirovanie trekhsloinoi krugovoi tsilindricheskoi obolochki v temperaturnom pole”, Problemy mashinostroeniya i avtomatizatsii, 2016, no. 1, 91–97

[24] A.S. Zelenaya, “Napryazhenno-deformirovannoe sostoyanie termouprugoi trekhsloinoi pryamougolnoi plastiny so szhimaemym zapolnitelem”, Izvestiya Gomelskogo gos. un-ta im. F. Skoriny. Estestvennye nauki, 2018, no. 6 (111), 98–104

[25] M.A. Zenkour, N.A. Alghamdi, “Thermomechanical bending response of functionally graded nonsymmetric sandwich plates”, Journal of Sandwich Structures and Materials, 12:1 (2010), 7–46 | DOI

[26] A.M. Zenkour, N.A. Alghamdi, “Bending Analysis of Functionally Graded Sandwich Plates under the Effect of Mechanical and Thermal Loads”, Mechanics of Advanced Materials and Structures, 17:6 (2010), 419–432 | DOI

[27] A.V. Nesterovich, “Neosesimmetrichnoe termosilovoe deformirovanie krugovoi odnosloinoi plastiny”, Problemy fiziki, matematiki i tekhniki, 2016, no. 2 (27), 54–61

[28] A.V. Nesterovich, “Napryazheniya v krugovoi plastine tipa Timoshenko pri neosesimmetrichnom rastyazhenii-szhatii”, Mekhanika. Issledovaniya i innovatsii, 2018, no. 11, 195–203

[29] A.V. Nesterovich, “Napryazhennoe sostoyanie krugovoi trekhsloinoi plastiny pri osesimmetrichnom nagruzhenii v svoei ploskosti”, Mekhanika. Issledovaniya i innovatsii, 2019, no. 12, 152–157

[30] V.A. Nifagin, M.A. Bubich, “Metod asimptoticheskikh razlozhenii v teorii uprugoplasticheskikh treschin”, Vestsi Natsyyanalnai akademii navuk Belarusi. Seryya fizika-matematychnykh navuk, 2011, no. 4, 60–66

[31] M.A. Gundina, “Energeticheskie invarianty v teorii uprugoplasticheskikh treschin”, Nauka i tekhnika, 16:4 (2017), 355–362

[32] M.A. Gundina, “Opredelenie nachalnogo napravleniya razvitiya treschiny v moment stragivaniya”, Problemy fiziki, matematiki i tekhniki, 2019, no. 1 (38), 40–44

[33] A.A. Ilyushin, B.E. Pobedrya, Osnovy matematicheskoi teorii termovyazkouprugosti, Nauka, M., 1970, 280 pp.

[34] E. Yanke, F. Emde, F. Lesh, Spetsialnye funktsii, Nauka, M., 1979, 342 pp.