Deformation of the circular three-layer plate with a compressible filler

Yu. V. Zakharchuk

Problemy fiziki, matematiki i tehniki, no. 4 (2017), pp. 53-57.

Résumé

The problem of symmetric bending of a three-layer elastic plate with a compressible filler asymmetrical in thickness is сonsidered. Kirchhoff's hypotheses are accepted for thin bearing layers. In a relatively thick aggregate, the transverse shear, radial displacements and deflection, which vary linearly in thickness are taken into account. The differential equations of equilibrium in the effort are obtained using the Lagrange variational method. The setting of the boundary value problem in the displacements is given in the cylindrical coordinate system.

Détail

Keywords: circular three-layer plate, elasticity
Mots-clés : compressible filler.

Bibliographie

[1] V.V. Bolotin, Yu.N. Novichkov, Mekhanika mnogosloinykh konstruktsii, Mashinostroenie, M., 1980, 375 pp.

[2] A.G. Gorshkov, E.I. Starovoitov, D.V. Tarlakovskii, Teoriya uprugosti i plastichnosti, Fizmatlit, M., 2011, 416 pp.

[3] E.I. Starovoitov, Soprotivlenie materialov, Fizmatlit, M., 2008, 384 pp.

[4] Yu.M. Pleskachevskii, E.I. Starovoitov, D.V. Leonenko, Mekhanika trekhsloinykh sterzhnei i plastin, svyazannykh s uprugim osnovaniem, Fizmatlit, M., 2011, 560 pp.

[5] A.G. Gorshkov, E.I. Starovoitov, A.V. Yarovaya, “Garmonicheskoe nagruzhenie sloistykh vyazkouprugoplasticheskikh sistem”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tverdogo tela, 2000, no. 6, 91–98

[6] A.G. Gorshkov, E.I. Starovoitov, A.V. Yarovaya, “Cyclic loading of elasticplastic bodies in neutron flux”, Mechanics of Solids, 36:1 (2001), 64–69

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

[8] V.V. Moskvitin, E.I. Starovoitov, “K issledovaniyu napryazhenno-deformirovannogo sostoyaniya dvukhsloinykh metallopolimernykh plastin pri tsiklicheskikh nagruzheniyakh”, Izv. AN SSSR. Mekhanika tverdogo tela, 1986, no. 1, 116–121

[9] E.L. Kuznetsova, D.V. Leonenko, E.I. Starovoitov, “Natural vibrations of three-layer circular cylindrical shells in an elastic medium”, Mechanics of Solids, 5:3 (2015), 359–366 | DOI

[10] E.I. Starovoitov, V.D. Kubenko, D.V. Tarlakovskii, “Kolebaniya kruglykh trekhsloinykh plastin, svyazannykh s uprugim osnovaniem”, Izv. VUZov. Aviatsionnaya tekhnika, 2009, no. 2, 16–19

[11] D.V. Leonenko, E.I. Starovoitov, “Thermal impact on a circular sandwich plate on an elastic foundation”, Mechanics of Solids, 47:1 (2012), 111–118 | DOI | MR

[12] E.I. Starovoitov, D.V. Leonenko, A.V. Yarovaya, “Vibrations of round three-layer plates under the action of various types of surface loads”, Strength of Materials, 35:4 (2003), 346–352 | DOI

[13] E.I. Starovoitov, D.V. Leonenko, A.V. Yarovaya, “Circular sandwich plates under local impulsive loads”, International Applied Mechanics, 39:8 (2003), 945–952 | DOI | Zbl

[14] E.I. Starovoitov, D.V. Leonenko, “Deformation of a three-layer elastoplastic beam on an elastic foundation”, Mechanics of Solids, 46:2 (2011), 291–298 | DOI

[15] A.G. Gorshkov, E.I. Starovoitov, A.V. Yarovaya, D.V. Leonenko, “Deformirovanie krugovoi trekhsloinoi plastiny na uprugom osnovanii”, Ekologicheskii vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva, 2005, no. 1, 16–22

[16] E.I. Starovoitov, D.V. Leonenko, M. Suleiman, “Termouprugii izgib koltsevoi trekhsloinoi plastiny na uprugom osnovanii”, Ekologicheskii vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva, 2006, no. 4, 55–62

[17] E.I. Starovoitov, D.V. Leonenko, “Thermoplastic bending of a sandwich ring plate on an elastic foundation”, International Applied Mechanics, 44:9 (2008), 1032–1040 | DOI | MR

[18] D.V. Leonenko, E.I. Starovoitov, “Thermoplastic strain of circular sandwich plates on an elastic base”, Mechanics of Solids, 44:5 (2009), 744–755 | DOI | MR

[19] D.V. Leonenko, E.I. Starovoitov, “Termoplasticheskoe deformirovanie krugovykh trekhsloinykh plastin na uprugom osnovanii”, Izv. RAN. Mekhanika tverdogo tela, 2009, no. 5, 106–119