Bending a circular five-layer plate by local load

V. S. Salicki

Problemy fiziki, matematiki i tehniki, no. 3 (2024), pp. 27-31.

Résumé

The bending of an elastic circular five-layer plate under the action of a local transverse load distributed in a circle was studied. The plate, symmetrical in thickness, has three thin load-bearing layers (two external and one internal), the deformation of which obeys Kirchhoff’s hypotheses. In two relatively thick fillers, the normal remains straight and does not change its length, but rotates through some additional angle. The system of differential equations for the equilibrium of the plate was obtained by the Lagrange variational method. The analytical solution of the problem is written in Bessel functions in final form. Numerical results of the study of deflections and relative shifts are presented depending on the radius of the force circle, the thickness of the internal load-bearing layer, and the materials of the external load-bearing layers.

Détail

Keywords: five-layer plate, circular load, analytical solution, numerical investigations.

Bibliographie

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

[2] L. Aghalovyan, Asymptotic theory of anisotropic plates and shells, World Scientific Publishing, Singapore–London, 2015, 376 pp.

[3] M.A. Zhuravkov, E.I. Starovoitov, Matematicheskie modeli mekhaniki tverdogo tela, BGU, Minsk, 2021, 535 pp.

[4] M.A. Zhuravkov, Lyu Yongtao, E.I. Starovoitov, Mechanics of Solid Deformable Body, Springer, Singapore, 2022, 317 pp. | MR

[5] A. Abdusattarov, E.I. Starovoitov, N.B. Ruzieva, Deformirovanie i povrezhdaemost uprugoplasticheskikh elementov konstruktsii pri tsiklicheskikh nagruzheniyakh, «IDEAL PRESS», Tashkent, 2023, 381 pp.

[6] E.A. Lachugina, “Poperechnye kolebaniya pyatisloinoi uprugoi krugovoi plastiny s zhestkimi zapolnitelyami”, Mekhanika. Issledovaniya i innovatsii, 2022, no. 15, 212-219

[7] E.A. Lachugina, “Chastoty sobstvennykh kolebanii pyatisloinoi krugovoi plastiny”, Teoreticheskaya i prikladnaya mekhanika, 38, BNTU, Minsk, 2023, 227-233

[8] A.G. Gorshkov, E.I. Starovoitov, A.V. Yarovaya, “Harmonic vibrations of a viscoelastoplastic sandwich cylindrical shell”, International Applied Mechanics, 37:9 (2001), 1196-1203 | DOI | Zbl

[9] E.I. Starovoitov, D.V. Leonenko, “Issledovanie spektra chastot trekhsloinoi tsilindricheskoi obolochki s uprugim napolnitelem”, Mekhanika kompozitsionnykh materialov i konstruktsii, 21:2 (2015), 162-169

[10] E.I. Starovoitov, Yu.M. Pleskachevskii, D.V. Leonenko, D.V. Tarlakovskii, “Deformirovanie stupenchatoi kompozitnoi balki v temperaturnom pole”, Inzhenerno-fizicheskii zhurnal, 88:4 (2015), 987-993

[11] E.I. Starovoitov, D.V. Leonenko, “Deformirovanie trekhsloinogo sterzhnya v temperaturnom pole”, Mekhanika mashin, mekhanizmov i materialov, 2013, no. 1 (22), 31-35

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

[13] E.I. Starovoitov, Y.V. Zakharchuk, E.L. Kuznetsova, “Elastic circular sandwich plate with compressible filler under axially symmetrical thermal force load”, Journal of the Balkan Tribological Association, 27:2 (2021), 175-188

[14] E.I. Starovoitov, “Izgib trekhsloinoi plastiny ravnomerno raspredelennoi nagruzkoi v neitronnom potoke”, Problemy fiziki, matematiki i tekhniki, 2021, no. 3 (48), 56-62 | DOI

[15] E.I. Starovoitov, A.G. Kozel, “Izgib uprugoi krugovoi trekhsloinoi plastiny na osnovanii Pasternaka”, Mekhanika kompozitsionnykh materialov i konstruktsii, 24:3 (2018), 392-406 | DOI

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

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

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

[19] V.S. Salitskii, “Uravneniya ravnovesiya krugovoi pyatisloinoi plastiny v usiliyakh”, Materialy XXVII Mezhdunar. simpoziuma «Dinamicheskie i tekhnologicheskie problemy mekhaniki konstruktsii i sploshnykh sred» im. A.G. Gorshkova, v. 1, 2021, 199-201

[20] V.S. Salitskii, “Izgib zaschemlennoi po konturu krugovoi pyatisloinoi plastiny”, Mekhanika. Issledovaniya i innovatsii, 15, Gomel, 2022, 209-213

[21] V.S. Salitskii, “Izgib krugovoi pyatisloinoi plastiny”, Teoreticheskaya i prikladnaya mekhanika, 38, Minsk, 2023, 234-239