Bending of a three-layer plate by a uniformly distributed load in the neutron flux

E. I. Starovoitov

Problemy fiziki, matematiki i tehniki, no. 3 (2021), pp. 56-62.

Résumé

The bending of a circular three-layer plate with an asymmetric thickness under neutron irradiation conditions is considered. The axisymmetric continuous load is perpendicular to the plate plane. The kinematics of the package is described using the polyline hypothesis. For load-bearing layers, the Kirchhoff hypotheses are accepted. The relatively thick filler obeys Timoshenko's hypothesis about the straightness and incompressibility of the deformed normal. The work of tangential stresses in the filler is taken into account. Differential equilibrium equations are obtained by the Lagrange variational method. The contour of the plate is pivotally supported. The statement of the boundary value problem for finding the three desired functions: deflection, shear and radial displacement of the median plane of the filler is given. The solution for a uniformly distributed load is obtained in the final form. Its numerical parametric analysis is carried out.

Détail

Keywords: three-layer circular plate, bending, distributed axisymmetric load, elasticity
Mots-clés : neutron irradiation.

Bibliographie

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

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

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

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

[5] A.G. Gorshkov, É.I. Starovoitov, Yarovaya A. V., “Harmonic Vibrations of a Viscoelastoplastic Sandwich Cylindrical Shell”, International applied mechanics, 37:9 (2001), 1196–1203 | DOI | Zbl

[6] E.I. Starovoitov, D.V. Leonenko, D.V. Tarlakovsky, “Resonance vibrations of circular composite plates on an elastic foundation”, Mechanics of Composite Materials, 51:5 (2015), 561–570 | DOI

[7] 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

[8] 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

[9] 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

[10] 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

[11] 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 | Zbl

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

[13] V.V. Moskvitin, E.I. Starovoitov, “Deformation and variable loading of two-layer metal-polymer plates”, Mechanics of Composite Materials, 21:3 (1985), 267–273 | DOI

[14] E.I. Starovoitov, Yu.M. Pleskachevskii, A.V. Yarovaya, “Deformirovanie trekhsloinoi krugovoi plastiny v usloviyakh polzuchesti”, Problemy fiziki, matematiki i tekhniki, 2021, no. 2 (47), 57–63

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

[16] 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

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

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

[19] 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

[20] 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

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

[22] 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

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

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

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

[26] A.A. Ilyushin, P.M. Ogibalov, Uprugoplasticheskie deformatsii polykh tsilindrov, Izd-vo MGU, M., 1960, 224 pp.

[27] P.A. Platonov, Deistvie oblucheniya na strukturu i svoistva metallov, Mashinostroenie, M., 1971, 40 pp.

[28] I.S. Kulikov, V.B. Nesterenko, B.E. Tverkovkin, Prochnost elementov konstruktsii pri obluchenii, Navuka i tekhnika, Minsk, 1990, 144 pp.

[29] E.I. Starovoitov, D.V. Leonenko, “Deformation of a threelayer rod with a compressible core in a neutron flow”, International Applied Mechanics, 56:1 (2020), 81–91 | DOI

[30] E.I. Starovoitov, “Izmenenie neitronnogo potoka pri prokhozhdenii cherez trekhsloinuyu plastinu”, Mezhdunarodnyi sbornik nauchnykh trudov, Mekhanika. Issledovaniya i innovatsii, 13 (13), 2020, 141–146