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STAROVOITOV Eduard I., D. Sc. in Phys. and Math., Prof., Head of the Department “Structural Мechanics”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

NESTSIAROVICH Alina V., M. Sc. in Eng., Post-Graduate Student of the Department “Structural Mechanics”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

Year 2021
Issue 1
Pages 38–45
Type of article RAR
Index UDK 539.3
Abstract A statement is given for the boundary value problem of non-axisymmetric deformation of an elastic threelayer circular plate in its own plane. The plate contour is pinched. Physical equations of state in the plate layers are described using the linear theory of elasticity, taking into account temperature influence on the elastic characteristics of materials. Equilibrium equations are obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution of the boundary value problem is reduced to finding the radial and tangential displacements in the layers of the plate. These displacements satisfy an inhomogeneous system of ordinary linear differential equations. To solve it, the method of decomposition into trigonometric Fourier series is applied. After substituting the series into the original system of equilibrium equations and performing the corresponding transformations, a system of ordinary linear differential equations is obtained to determine the four radial functions in each term of the series. The analytical solution is written out in the final form in the case of cosine radial and sinusoidal circumferential loads that depend linearly on the radial coordinate. The load is applied in the middle plane of the filler. Numerical approbation of the solution is carried out. The dependence of radial and tangential displacements on polar coordinates and temperature is investigated. Graphs of changes in displacements along the radius of the plate for different values of the angular coordinate are given. The weak dependence of displacements on temperature is illustrated when the plate contour is fixed.
Keywords three-layer circular plate, elasticity, non-axisymmetric load, displacements, numerical results
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  1. Golovko K.G., Lugovoy P.Z., Meysh V.F. Dinamika neodnorodnykh obolochek pri nestatsionarnykh nagruzkakh [Dynamics of inhomogeneous shells under transient load conditions]. Kiev, Kievskiy universitet Publ., 2012. 541 p. (in Russ.).
  2. Aghalovyan L. Asymptotic theory of anisotropic plates and shells. Singapore, London, World Scientific Publishing, 2015. 376 p.
  3. Zhuravkov M.A., Starovoitov E.I. Mekhanika sploshnykh sred. Teoriya uprugosti i plasthichnosti [Continuum mechanics. The theory of elasticity and plasticity]. Minsk, Belorusskiy gosudarstvennyy universitet Publ., 2011. 543 p. (in Russ.).
  4. Starovoitov E.I., Zhuravkov M.A., Leonenko D.V. Trekhsloynye sterzhni v termoradiatsionnykh polyakh [Three-layer bars in thermoradiation fields]. Minsk, Belaruskaya navuka Publ., 2017. 275 p. (in Russ.).
  5. Starovoitov E.I., Leonenko D.V., Pleskatshevsky Yu.M. Kolebaniya trekhsloynykh tsilindricheskikh obolochek v uprugoy srede Vinklera pri rezonanse [Vibrations of the three-layered cylindrical shells in the elastic Winkler’s medium at resonance]. Mechanics of machines, mechanisms and materials, 2013, no. 4(25), pp. 70–73 (in Russ.).
  6. Starovoitov E.I., Leonenko D.V., Tarlakovskiy D.V. Deformirovanie trekhsloynoy krugovoy tsilindricheskoy obolochki v temperaturnom pole [Deformation of three-layer circular cylindrical shell in the thermal field]. Engineering and automation problems, 2016, no. 1, pp. 91–97 (in Russ.).
  7. Ivañez I., Moure M.M., Garcia-Castillo S.K., Sanchez-Saez S. The oblique impact response of composite sandwich plates. Composite structures, 2015, no. 133, pp. 1127–1136.
  8. Paimushin V.N., Ivanov V.I., Khusainov V.R Analiz svobodnykh i sobstvennykh kolebaniy trekhsloynoy plastiny na osnove uravneniy utochnennoy teorii [Study of free and eigen vibrations of a three-layer plate on the bases of equations of a refined theory]. Mechanics of composite materials and structures, 2002, vol. 8, no. 4, pp. 543–554 (in Russ.).
  9. Grover N., Singh B.N., Maiti D.K. An inverse trigonometric shear deformation theory for supersonic flutter characteristics of multilayered composite plates. Aerospace science and technology, 2016, no. 52, pp. 41–51.
  10. Starovoitov E.I., Leonenko D.V., Tarlakovsky D.V. Rezonansnye kolebaniya krugovykh kompozitnykh plastin na uprugom osnovanii [Resonance vibrations of circular composite plates on an elastic foundation]. Mekhanika kompozitnykh materialov, 2015, vol. 51, no. 5, pp. 793–806 (in Russ.).
  11. Starovoitov E.I., Leonenko D.V. Kolebaniya krugovykh kompozitnykh plastin na uprugom osnovanii pod deystviem lokalnykh nagruzok [Vibrations of circular composite plates on an elastic foundation under the action of local loads]. Mekhanika kompozitnykh materialov, 2016, vol. 52, no 5, pp. 943–954 (in Russ.).
  12. Vasilevich Yu.V., Neumerzhitskiy V.V. Metod rascheta effektivnosti vibroizolyatsii odnosloynogo i mnogosloynogo ograzhdeniy v tverdoy uprugoy srede [Calculating method of vibrating insulation efficiency of single and multi-layer enclosures in solid elastic medium]. Mechanics of machines, mechanisms and materials, 2009, no. 1(6), pp. 56–58 (in Russ.).
  13. Dzhagangirov A.A. Nesushchaya sposobnost trekhsloynoy voloknistoy kompozitnoy koltsevoy plastinki, zashchemlennoy po kromkam [Carrying capacity of a three-layer fibrous composite annular plate, clamped along the edges]. Mekhanika kompozitnykh materialov, 2016, vol. 52, no. 2, pp. 385–398 (in Russ.).
  14. Chigarev A.V., Borisov A.V. Issledovanie modeley mnogosloynykh kostey cheloveka na prochnost pri nagruzhenii [Strength models of multilayer human bones by loading]. Mechanics of machines, mechanisms and materials, 2009, no. 1(6), pp. 85–87 (in Russ.).
  15. Starovoitov E.I., Leonenko D.V. Deformirovanie trekhsloynogo sterzhnya v temperaturnom pole [Deformation of three-layer beam in a temperature field]. Mechanics of machines, mechanisms and materials, 2013, no. 1(22), pp. 31–35 (in Russ.).
  16. Moskvitin V.V., Starovoitov E.I. Deformatsiya i peremennye nagruzheniya dvukhsloynykh metallopolimernykh plastin [Deformation and variable loading of two-layer metal-polymer plates]. Mekhanika kompozitnykh materialov, 1985, no. 3, pp. 409–416 (in Russ.).
  17. Škec L., Jelenić G. Analysis of a geometrically exact multi-layer beam with a rigid interlayer connection. Acta mechanica, 2014, vol. 225, no. 2, pp. 523–541.
  18. Belinha J., Dints L.M.J.S. Nonlinear analysis of plates and laminates using the element free Galerkin method. Composite structures, 2007, vol. 78, no. 3. pp. 337–350.
  19. Yang L., Harrysson O., West H., Cormier D. A Comparison of Bending Properties for Cellular Core Sandwich Panels. Materials sciences and applications, 2013, vol. 4, no. 8, pp. 471–477.
  20. Lee C.R., Sun S.J., Каm Т.Y. System parameters evaluation of flexibly supported laminated composite sandwich plates. AIAA journal, 2007, vol. 45, no. 9, pp. 2312–2322.
  21. Thai C.H., Tran L.V., Tran D.T., Nguyen-Thoi T., Nguyen-Xuan U. Analysis of laminated composite plates using higher order shear deformation plate theory and modebased smoother discrete shear gap method. Applied mathematical modelling, 2012, vol. 36, no. 11, pp. 5657–5677.
  22. Zenkour A.M., Alghamdi N.A. Thermomechanical bending response of functionally graded nonsymmetric sandwich plates. Journal of sandwich structures and materials, 2010, vol. 12, no. 1, pp. 7–46.
  23. Zenkour A.M., Alghamdi N.A. Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads. Mechanics of advanced materials and structures, 2010, vol. 17, no. 6, pp. 419–432.
  24. Dalot J., Sab K. Limit analysis of multi-layered plates. Part I: The homogenized Love–Kirchhoff model. Journal of the mechanics and physics of solids, 2008, vol. 56, no 2, pp. 561–580.
  25. Starovoitov E.I., Leonenko D.V. Termouprugoe deformirovanie trekhsloynoy krugloy plastiny poverkhnostnymi nagruzkami razlichnykh form [Thermoelastic deformation of three-layer circular plate by a surface loads of various forms]. Mekhanika kompozitnykh materialov, 2018, no. 1(42), pp. 81–88 (in Russ.).
  26. Starovoitov E.I., Leonenko D.V., Suleyman M. Deformirovanie lokalnymi nagruzkami kompozitnoy plastiny na uprugom osnovanii [Deformation of a composite plate on an elastic foundation by local loads]. Mekhanika kompozitnykh materialov, 2007, vol. 43, no. 1, pp. 109–120 (in Russ.).
  27. Kozel A.G. Uravneniya ravnovesiya uprugoplasticheskoy krugovoy plastiny na osnovanii Pasternaka [Equilibrium equations for an elastoplastic circular plate based on Pasternak]. Mechanics. Researches and Innovations, 2018, iss. 11, pp. 127–133 (in Russ.).
  28. Zakharchuk Yu.V. Deformirovanie krugovoy trekhsloynoy plastiny so szhimaemym zapolnitelem [Deformation of the circular three-layer plate with a compressible filler]. Problems of physics, mathematics and technics, 2017, vol. 33, no. 4, pp. 53–57 (in Russ.).
  29. Starovoitov E.I., Zakharchuk Yu.V. Nelineynoe deformirovanie trekhsloynoy plastiny so szhimaemym zapolnitelem [Nonlinear deformation of circular sandwich plates with compressible filler]. Mechanics of machines, mechanisms and materials, 2019, no. 3(48), pp. 26–33 (in Russ.).
  30. Zelenaya A.S. Napryazhenno-deformirovannoe sostoyanie uprugoy trekhsloynoy pryamougolnoy plastiny so szhimaemym zapolnitelem [Stress-strain state of the elastic three-layer plate with the compressible filler]. Mechanics. Researches and Innovations, 2017, iss. 10, pp. 67–74 (in Russ.).
  31. Timoshenko S.P., Voynorovskiy-Kriger S. Plastinki i obolochki [Plates and shells]. Moscow, Nauka Publ., 1966. 636 р. (in Russ.).
  32. Bosakov S.V. Raschet konstruktsiy na uprugom osnovanii metodom Rittsa. Chast 1. Osnovanie Vinklera [Calculation of structures on an elastic foundation by the Ritz method. Part 1. Winkler foundation]. Bulletin of Science and Research Center “Stroitelstvo”, 2012, no. 5, pp. 38–53 (in Russ.).
  33. Bosakov S.V. K resheniyu kontaktnoy zadachi dlya krugloy plastinki [To the solution of the contact problem for a circular plate]. Prikladnaya matematika i mekhanika, 2008, vol. 72, no. 1, pp. 99–102 (in Russ.).
  34. Nestsiarovich А.V. Napryazhennoe sostoyanie krugovoy trekhsloynoy plastiny pri osesimmetrichnom nagruzhenii v svoey ploskosti [Stressed state of a circular three-layer plate under axisymmetric loading in its plane]. Mechanics. Researches and Innovations, 2019, iss. 12, pp. 152–157 (in Russ.).
  35. Nestsiarovich А.V. Uravneniya ravnovesiya trekhsloynoy krugovoy plastiny pri neosesimmetrichnom nagruzhenii [Equilibrium equations for a three-layer circular plate under non-axisymmetric loading]. Teoreticheskaya i prikladnaya mekhanika, 2019, iss. 34, pp. 154–159 (in Russ.).
  36. Nestsiarovich А.V. Napryazheniya v krugovoy plastine tipa Timoshenko pri neosesimmetrichnom rastyazhenii-szhatii [Stresses in a Timoshenko-type circular plate under nonaxisymmetric tension-compression]. Mechanics. Researches and Innovations, 2018, iss. 11, pp. 195–203 (in Russ.).