Thermal elastic bending of a circular three-layer plate, associated with the Pasternak foundation
Problemy fiziki, matematiki i tehniki, no. 2 (2022), pp. 31-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

An axisymmetric bending of an elastic three-layer circular plate connected to the Pasternak foundation is considered. The effect of the temperature field is taken into account. To describe the kinematics of a plate package asymmetric in thickness, the hypothesis of a broken normal is accepted. The statement of the problem and its solution are carried out in a cylindrical coordinate system. The system of equilibrium equations was obtained using the Lagrange variational method. Its general analytical solution is written out in displacements. A numerical parametric analysis of the stress-strain state of a three-layer metal-polymer plate under a uniformly distributed load has been carried out. The significant influence of temperature on the stresses in the layers is shown.
Keywords: thermoelasticity, Pasternak foundation, three-layer plate.
@article{PFMT_2022_2_a5,
     author = {A. G. Kozel},
     title = {Thermal elastic bending of a circular three-layer plate, associated with the {Pasternak} foundation},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {31--37},
     publisher = {mathdoc},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2022_2_a5/}
}
TY  - JOUR
AU  - A. G. Kozel
TI  - Thermal elastic bending of a circular three-layer plate, associated with the Pasternak foundation
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2022
SP  - 31
EP  - 37
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2022_2_a5/
LA  - ru
ID  - PFMT_2022_2_a5
ER  - 
%0 Journal Article
%A A. G. Kozel
%T Thermal elastic bending of a circular three-layer plate, associated with the Pasternak foundation
%J Problemy fiziki, matematiki i tehniki
%D 2022
%P 31-37
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2022_2_a5/
%G ru
%F PFMT_2022_2_a5
A. G. Kozel. Thermal elastic bending of a circular three-layer plate, associated with the Pasternak foundation. Problemy fiziki, matematiki i tehniki, no. 2 (2022), pp. 31-37. http://geodesic.mathdoc.fr/item/PFMT_2022_2_a5/

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

[2] V.V. Mozharovskii, V.E. Starzhinskii, Prikladnaya mekhanika sloistykh tel iz kompozitov, Navuka i tekhnika, Minsk, 1988, 271 pp.

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

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

[5] E. Carrera, F.A. Fazzolari, M. Cinefra, Thermal Stress Analysis of Composite Beams, Plates and Shells: Computational Modelling and Applications, Academic Press, 2016, 410 pp.

[6] M.A. Zhuravkov, E.I. Starovoitov, Mekhanika sploshnykh sred. Teoriya uprugosti i plastichnosti, BGU, Minsk, 2011, 543 pp.

[7] E.I. Starovoitov, M.A. Zhuravkov, D.V. Leonenko, Trekhsloinye sterzhni v termoradiatsionnykh polyakh, Bel. navuka, Minsk, 2017, 275 pp.

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

[9] V.N. Paimushin, R.A. Kayumov, S.A. Kholmogorov, “Ob odnom metode resheniya zadach o neuprugom deformirovanii sloistogo kompozita”, Izvestiya vysshikh uchebnykh zavedenii. Matematika, 2021, no. 6, 55–66

[10] E.I. Starovoitov, Yu.V. Zakharchuk, “Izgib uprugoplasticheskoi krugovoi trekhsloinoi plastiny so szhimaemym zapolnitelem”, Mekhanika kompozitsionnykh materialov i konstruktsii, 26:1 (2020), 58–73 | Zbl

[11] Yu.V. Zakharchuk, “Deformirovanie krugovoi trekhsloinoi plastiny so szhimaemym zapolnitelem”, Problemy fiziki, matematiki i tekhniki, 2017, no. 4 (33), 53–57

[12] A.S. Zelenaya, “Tsilindricheskii izgib uprugoplasticheskoi pryamougolnoi trekhsloinoi plastiny so szhimaemym zapolnitelem v temperaturnom pole”, Problemy fiziki, matematiki i tekhniki, 2019, no. 1 (38), 45–49

[13] A.S. Zelenaya, “Termouprugii izgib trekhsloinoi pryamougolnoi plastiny so szhimaemym zapolnitelem”, mezhdunar. sb. nauch. tr., Mekhanika. Issledovaniya i innovatsii, 11, BelGUT, Gomel, 2018, 93–100

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

[15] A.V. Nesterovich, “Osesimmetrichnoe nagruzhenie krugloi fizicheski nelineinoi trekhsloinoi plastiny v svoei ploskosti”, Problemy fiziki, matematiki i tekhniki, 2021, no. 3 (48), 24–29

[16] 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

[17] 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

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

[19] E.I. Starovoitov, D.V. Leonenko, M. Suleyman, “Deformation of a composite plate on an elastic foundation by local loads”, Mechanics of Composite Materials, 43:1 (2007), 75–84 | DOI

[20] A.V. Yarovaya, “Termouprugoplasticheskoe deformirovanie krugovoi trekhsloinoi plastiny na uprugom osnovanii”, Matematicheskoe modelirovanie, kompyuternyi i naturnyi eksperiment v estestvennykh naukakh, 2017, no. 1 (Data dostupa: 12.01.2022) http://mathmod.esrae.ru/11-31

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

[22] T.F. Fwa, X.P. Shi, S.A. Tan, “Use of Pasternak foundation model in concrete pavement analysis”, Journal of transportation engineering, 122:4 (1996), 323–328 | DOI

[23] J.T. Katsikadelis, L.F. Kallivokas, “Clamped plates on Pasternak-type elastic foundation by the boundary element method”, Journal of Applied Mechanics, 53 (1986), 909–917 | DOI | Zbl

[24] M. Arefi, M.N.M. Allam, “Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation”, Smart Structures and Sestems, 16:1 (2015), 81–100 | DOI

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

[26] A.G. Kozel, “Deformirovanie krugovoi trekhsloinoi plastiny na osnovanii Pasternaka”, mezhdunar. nauch.-tekhn. sb., Teoreticheskaya i prikladnaya mekhanika, 32, BNTU, Minsk, 2017, 235–240

[27] A.G. Kozel, “Deformirovanie fizicheski nelineinoi trekhsloinoi plastiny na osnovanii Pasternaka”, mezhdunar. sb. nauch. tr., Mekhanika. Issledovaniya i innovatsii, 12, BelGUT, Gomel, 2019, 105–112

[28] E.I. Starovoitov, A.G. Kozel, “Izgib uprugoi trekhsloinoi krugovoi plastiny na osnovanii Pasternaka”, Mekhanika kompozitsionnykh materialov i konstruktsii, 24:1 (2018), 392–406

[29] A.G. Kozel, “Nelineinyi izgib sendvich-plastiny na osnovanii Pasternaka”, mezhdunar. nauch.-tekhn. sb., Teoreticheskaya i prikladnaya mekhanika, 35, BNTU, Minsk, 2020, 106–113

[30] A.G. Kozel, “Sravnenie reshenii zadach izgiba trekhsloinykh plastin na osnovaniyakh Vinklera i Pasternaka”, Mekhanika mashin, mekhanizmov i materialov. - Minsk, 2021, no. 1 (54), 30–37

[31] P.L. Pasternak, Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoschi dvukh koeffitsientov posteli, Gosstroiizdat, M., 1954, 56 pp.