Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Starovoitov E. I., Leonenko D. V. Bending of an elastic circular three-layer plate in a neutron flux by a local load. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 3, pp. 360-375. DOI: 10.18500/1816-9791-2022-22-3-360-375, EDN: DIDXGQ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2022
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Russian
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Article type: 
Article
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539.374
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DIDXGQ

Bending of an elastic circular three-layer plate in a neutron flux by a local load

Autors: 
Starovoitov Eduard Ivanovich, Belarusian State University of Transport
Leonenko Denis V., Belarusian State University of Transport
Abstract: 

The bending of an elastic circular three-layer plate asymmetric in thickness by local loads uniformly distributed in a circle in a neutron current is considered. Polyline hypotheses are used to describe the kinematics of the package. Kirchhoff's hypotheses are valid in thin load-bearing layers. In a relatively thick incompressible filler, Timoshenko's hypothesis about the straightness and incompressibility of the deformed normal is fulfilled. The work of the tangential stresses of the filler is taken into account. Deformations are small. It is assumed that, in a linear approximation, an additional change in the volume of materials in the layers can be considered directly proportional to the integral neutron flux. Attenuation of the intensity of the neutron flux when passing through the layers of the plate is assumed according to the exponential law. The effect of neutron irradiation on the elasticity parameters of materials is not taken into account. The formulation of the corresponding boundary value problem is given. The system of differential equations of equilibrium in forces is obtained by the Lagrange variational method. In the contour of the plate, the boundary conditions of the hinge support are assumed. In this case, the requirement of zero bending moment on the contour of the plate includes an integral neutron flux. The solution to the boundary value problem is reduced to finding three desired functions — deflection, shear, and radial displacement of the median plane of the filler. An inhomogeneous system of ordinary linear differential equations is written out for these functions. The solution to the boundary value problem is obtained in the final form. Numerical parametric analysis of the obtained solutions is carried out. The dependence of the stress-strain state of a three-layer metal polymer plate on the magnitude and type of load, layer thickness, and neutron flux intensity is investigated.

Acknowledgments: 
The work was supported by the Belarusian Republican Foundation for Fundamental Research (project No. T22UZB-015).
References: 
  1. Bolotin V. V., Novichkov Yu. N. Mekhanika mnogosloinykh konstruktsiy [Mechanics of Multilayer Structures]. Moscow, Mashinostroenie, 1980, 375 p. (in Russian).
  2. Leonenko D. V., Starovoitov E. I. Impulsive action on the three-layered circular cylindrical shells in elastic media. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 2, pp. 202–209 (in Russian). https://doi.org/10.18500/1816-9791-2015-15-2-202-209
  3. Belostochnyi G. N., Myltcina O. A. Dynamic stability of heated geometrically irregular cylindrical shell in supersonic gas flow. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2018, vol. 22, iss. 4, pp. 750–761 (in Russian). https://doi.org/10.14498/vsgtu1653
  4. Blinkov Yu. A., Mesyanzhin A. V., Mogilevich L. I. Wave occurrences mathematical modeling in two geometrically nonlinear elastic coaxial cylindrical shells, containing viscous incompressible liquid. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 184–197 (in Russian). https://doi.org/10.18500/1816-9791-2016-16-2-184-197
  5. Tarlakovskii D. V., Fedotenkov G. V. Nonstationary 3D motion of an elastic spherical shell. Mechanics of Solids, 2015, vol. 50. iss. 2, pp. 208–217. https://doi.org/10.3103/S0025654415020107, EDN: TPPBRR
  6. Tarlakovskii D. V., Fedotenkov G. V. Two-dimensional nonstationary contact of elastic cylindrical or spherical shells. Journal of Machinery Manufacture and Reliability, 2014, vol. 43, iss. 2, pp. 145–152. https://doi.org/10.3103/S1052618814010178
  7. Belostochny G. N., Myltcina O. A. The geometrical irregular plates under the influence of the quick changed on the time coordinate forces and temperature effects. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, vol. 15, iss. 4, pp. 442–451 (in Russian). https://doi.org/10.18500/1816-9791-2015-15-4-442-451
  8. Ivanez I., Moure M. M., Garcia-Castillo S. K., Sanchez-Saez S. The oblique impact response of composite sandwich plates. Composite Structures, 2015, vol. 133, pp. 1127–1136. https://doi.org/10.1016/j.compstruct.2015.08.035
  9. Suvorov Ye. M., Tarlakovskii D. V., Fedotenkov G. V. The plane problem of the impact of a rigid body on a half-space modelled by a Cosserat medium. Journal of Applied Mathematics and Mechanics, 2012, vol. 76, iss. 5, pp. 511–518. https://doi.org/10.1016/j.jappmathmech.2012.11.015
  10. Paimushin V. N., Gazizullin R. K. Static and monoharmonic acoustic impact on a laminated plate. Mechanics of Composite Materials, 2017, vol. 53, iss. 3, pp. 283–304. https://doi.org/10.1007/s11029-017-9662-z
  11. Paimushin V. N., Firsov V. A., Shishkin V. M. Modeling the dynamic response of a carbon-fiber-reinforced plate at resonance vibrations considering the internal friction in the material and the external aerodynamic damping. Mechanics of Composite Materials, 2017, vol. 53, iss. 4, pp. 425–440. https://doi.org/10.1007/s11029-017-9673-9
  12. Starovoitov E. I., Leonenko D. V., Tarlakovsky D. V. Resonance vibrations of a circular composite plates on an elastic foundation. Mechanics of Composite Materials, 2015, vol. 51, iss. 5, pp. 561–570. https://doi.org/10.1007/s11029-015-9527-2
  13. Kondratov D. V., Mogilevich L. I., Popov V. S., Popova A. A. Hydroelastic oscillations of a circular plate, resting on Winkler foundation. Journal of Physics: Conference Series, 2018, vol. 944, Art. 012057. https://doi.org/10.1088/1742-6596/944/1/012057
  14. Mogilevich L. I., Popov V. S., Popova A. A., Christoforova A. V. Mathematical modeling of hydroelastic oscillations of the stamp and the plate, resting on Pasternak foundation. Journal of Physics: Conference Series, 2018, vol. 944, Art. 012081. https://doi.org/10.1088/1742-6596/944/1/012081
  15. Bykova T. V., Grushenkova E. D., Popov V. S., Popova A. A. Hydroelastic response of a sandwich plate possessing a compressible core and interacting with a rigid die via a viscous fluid layer. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 3, pp. 351–366 (in Russian). https://doi.org/10.18500/1816-9791-2020-20-3-351-366
  16. Ageev R. V., Mogilevich L. I., Popov V. S. Vibrations of the walls of a slot channel with a viscous fluid formed by three-layer and solid disks. Journal of Machinery Manufacture and Reliability, 2014, vol. 43, iss. 1, pp. 1–8. https://doi.org/10.3103/S1052618814010026
  17. Rabboh S., Bondok N., Mahmoud T., El Kholy H. The effect of functionally graded materials into the sandwich beam dynamic performance. Materials Sciences and Applications, 2013, vol. 4, no. 11, pp. 751–760. https://doi.org/10.4236/msa.2013.411095
  18. Starovoitov E. I. Variable loading of three-layer shallow viscoplastic shells. Moscow University Mechanics Bulletin, 1980, vol. 35, iss. 1–2, pp. 54–58. EDN: FUDNEE
  19. Starovoitov E. I., Leonenko D. V. Variable bending of a three-layer rod with a compressed filler in the neutron flux. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 2, pp. 196–208 (in Russian). https://doi.org/10.18500/1816-9791-2017-17-2-196-208
  20. Starovoitov E. I., Leonenko D. V. Repeated alternating loading of a elastoplastic three-layer plate in a temperature field. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 1, pp. 60–75 (in Russian). https://doi.org/10.18500/1816-9791-2021-21-1-60-75
  21. Moskvitin V. V. Tsiklicheskoe nagruzhenie elementov konstruktsiy [Cyclic Loading of Structural Elements]. Moscow, Nauka, 1981. 344 p. (in Russian).
  22. 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. https://doi.org/10.1016/j.ast.2016.02.017
  23. Yankovskii A. P. A Study of steady creep of layered metal-composite beams of laminated-fibrous structures with account of their weakened resistance to the transverse shift. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2016, vol. 20, iss. 1, pp. 85–108 (in Russian). https://doi.org/10.14498/vsgtu1459
  24. Paimushin V. N. Theory of moderately large deflections of sandwich shells having a transversely soft core and reinforced along their contour. Mechanics of Composite Materials, 2017, vol. 53, iss. 1, pp. 1–16. http://dx.doi.org/10.1007/s11029-017-9636-1
  25. Wang Zh., Lu G., Zhu F., Zhao L. Load-carrying capacity of circular sandwich plates at large deflection. Journal of Engineering Mechanics. 2017, vol. 143, iss. 9. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001243
  26. Skec L., Jelenic G. Analysis of a geometrically exact multi-layer beam with a rigid interlayer connection. Acta Mechanica, 2014, vol. 225, iss. 2, pp. 523–541. https://doi.org/10.1007/s00707-013-0972-5
  27. Starovoitov E. I., Leonenko D. V. Bending of a sandwich beam by local loads in the temperature field. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 1, pp. 69–83. https://doi.org/10.18500/1816-9791-2018-18-1-69-83
  28. Starovoitov E. I., Leonenko D. V., Yarovaya A. V. Elastoplastic bending of a sandwich bar on an elastic foundation. International Applied Mechanics, 2007, vol. 43, iss. 4, pp. 451–459. https://doi.org/10.1007/s10778-007-0042-6
  29. Pradhan M., Dash P. R., Pradhan P. K. Static and dynamic stability analysis of an asymmetric sandwich beam resting on a variable Pasternak foundation subjected to thermal gradient. Meccanica, 2016, vol. 51, iss. 3, pp. 725–739. https://doi.org/10.1007/s11012-015-0229-6 
  30. Zadeh H. V., Tahani M. Analytical bending analysis of a circular sandwich plate under distributed load. International Journal of Recent Advances in Mechanical Engineering, 2017, vol. 6, no. 1. https://doi.org/10.14810/ijmech.2017.6101
  31. 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, iss. 8, pp. 471–477. https://doi.org/10.4236/msa.2013.48057
  32. Zakharchuk Yu. V. The circular three-layer elastic-plastic plate with a compressible filler. Problems of Physics, Mathematics and Techniques, 2018, no. 4 (37), pp. 72–79 (in Russian). EDN: YRXVAL
  33. Kozel A. G. Deformation of a circular three-layer plate based on Pasternak. Teoreticheskaia i prikladnaia mekhanika [Theoretical and Applied Mechanics], 2017, no. 32, pp. 235–240 (in Russian). EDN: QNSPKA
  34. Kudin A., Al-Omari M. A. V., Al-Athamneh B. G. M., Al-Athamneh H. K. M. Bending and buckling of circular sandwich plates with the nonlinear elastic core material. International Journal of Mechanical Engineering and Information Technology, 2015, vol. 3, no. 08, pp. 1487–1493. https://doi.org/10.18535/ijmeit/v2i8.02
  35. Nestsiarovich A. V. Deformation of a three-layer circular plate under cosine loading in its plane. Problems of Physics, Mathematics and Techniques, 2020, iss. 1 (42), pp. 85–90 (in Russian). EDN: JJPZWS
  36. Ilyushin A. A., Ogibalov P. M. Uprugoplasticheskie deformatsii polykh tsilindrov [Elastoplastic Deformations of Hollow Cylinders]. Moscow, Moscow University Press, 1960. 224 p. (in Russian).
  37. Platonov P. A. Deistvie oblucheniya na strukturu i svoistva metallov [Effect of Irradiation on the Structure and Properties of Metals]. Moscow, Mashinostroenie, 1971. 40 p. (in Russian).
  38. Kulikov I. S., Nesterenko V. B., Tverkovkin B. E. Prochnost’ elementov konstruktsiy pri obluchenii [Strength of Structural Elements Under Irradiation]. Minsk, Navuka i tekhnika, 1990. 144 p. (in Russian).
  39. Tratsevskaia E. Yu. On the question of the geological substantiation of the engineering protection of cities (on the example of the city of Gomel). Promyshlennoe i grazhdanskoe stroitel’stvo [Industrial and Civil Engineering], 2005, no. 3, pp. 46–47 (in Russian).
  40. Starovoitov E. I. Description of the thermomechanical properties of some structural materials. Strength of Materials, 1988, vol. 20, iss. 4, pp. 426–431. https://doi.org/10.1007/BF01530849
Received: 
21.11.2021
Accepted: 
28.02.2022
Published: 
31.08.2022