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Effect of inclined load on a functionally graded fiber-reinforced thermoelastic medium with temperature-dependent properties

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Abstract

The present research work is concerned with the solution of a problem on thermoelastic interactions in a functionally graded (non-homogeneous), fiber-reinforced, transversely isotropic half-space with temperature-dependent properties under the application of an inclined load in the context of Green-Naghdi theory of type III. Material properties are supposed to be temperature-dependent and are graded along x-direction. Normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement, and stress components. These are computed numerically and limned graphically to observe the disturbances induced in the medium due to fiber reinforcement, non-homogeneity parameter, temperature-dependent properties, and inclination angle of the load and time. Certain particular cases of interest have been deduced from the current investigation.

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References

  1. Duhamel, J.M.C.: Une memoire sur les phenomenes thermo-mecaniques. J. de L’ Ecole Polytech. 15, 1–57 (1837)

    Google Scholar 

  2. Biot, M.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240–253 (1956)

    Article  MathSciNet  Google Scholar 

  3. Lessen, M.: Thermoelasticty and thermal shock. J. Mech. Phys. Solid. 5, 57 (1956)

    Article  MathSciNet  Google Scholar 

  4. Weiner, J.H.: A uniqueness problem for coupled thermoelastic problems. Quart. Appl. Math. 15, 102–105 (1957)

    Article  MathSciNet  Google Scholar 

  5. Lord, H.W., Shulman, Y.A.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solid. 15, 299–309 (1967)

    Article  Google Scholar 

  6. Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)

    Article  Google Scholar 

  7. Green, A.E., Naghdi, P.M.: A re-examination of basic postulates of thermomechanics. Proc. R. Soc. Lond. Ser. A 432, 171–194 (1991)

    Article  MathSciNet  Google Scholar 

  8. Green, A.E., Naghdi, P.M.: On undamped heat waves in an elastic solid. J. Therm. Stress. 432, 253–264 (1992)

    Article  MathSciNet  Google Scholar 

  9. Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elast. 31, 189–208 (1993)

    Article  MathSciNet  Google Scholar 

  10. Hetnarski, R.B., Ignaczak, J.: Generalized thermoelasticity. J. Therm. Stress. 22, 451–476 (1999). https://doi.org/10.1080/014957399280832

    Article  MathSciNet  MATH  Google Scholar 

  11. Awrejcewicz, J., Pyryev, Y.: Dynamic damper of vibrations with thermo-elastic contact. Arch. Appl. Mech. 77, 281–291 (2007)

    Article  Google Scholar 

  12. Krysko, V.A., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Papkova, I.V., Serebryakov, A.V., Krysko, A.V.: Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena. Phys. Lett. A 377, 2058–2061 (2013)

    Article  MathSciNet  Google Scholar 

  13. Awrejcewicz, J., Krysko, V.A.: Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members (Applications of the Bubnov-Galerkin and Finite Difference Methods). Springer Nature, Switzerland AG (2020) https://doi.org/10.1007/978-3-030-37663-5

  14. Krysko-jr, V.A., Awrejcewicz, J., Krylova, E.Y., Papkova, I.V.: Mathematical modeling of nonlinear thermodynamics of nanoplates. Chaos Solitons Fract. (2022). https://doi.org/10.1016/j.chaos.2022.112027

    Article  MathSciNet  MATH  Google Scholar 

  15. Reddy, J.N., Chin, C.D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Therm. Stress. 21, 593–626 (1998)

    Article  Google Scholar 

  16. Krysko, V.A., Awrejcewicz, J., Bruk, V.M.: On the solution of a coupled thermo-mechanical problem for non-homogeneous Timoshenko-type shells. J. Math. Anal. Appl. 273, 409–416 (2002)

    Article  MathSciNet  Google Scholar 

  17. Wang, B.L., Mai, Y.W.: Transient one-dimensional heat conduction problems solved by finite element method. Int. J. Mech. Sci. 47, 303–317 (2005)

    Article  Google Scholar 

  18. Abbas, I.A., Zenkour, A.M.: LS model on electro-magneto-thermo-elastic response of an infinite functionally graded cylinder. Compos. Struct. 96, 89–96 (2013)

    Article  Google Scholar 

  19. Kirichenko, V.F., Awrejcewicz, J., Kirichenko, A.V., Krysko, A.V., Krysko, V.A.: On the non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer shallow shells with initial imperfections. Int. J. Non-Linear Mech. 74, 51–72 (2015)

    Article  Google Scholar 

  20. Pal, P., Das, P., Kanoria, M.: Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source. Acta. Mech. 226, 2103–2120 (2015). https://doi.org/10.1007/s00707-015-1301-y

    Article  MathSciNet  MATH  Google Scholar 

  21. Mishra, K.C., Sharma, J.N., Sharma, P.K.: Analysis of vibrations in a non-homogeneous thermoelastic thin annular disk under dynamic pressure. Mech. Based Design Struct. Machin. 45, 207–218 (2017)

    Article  Google Scholar 

  22. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Bodyagina, K.S., Krysko, V.A.: Topological optimization of thermoelastic composites with maximized stiffness and heat transfer. Compos. Part B Engineering 158, 319–327 (2019)

    Article  Google Scholar 

  23. Awrejcewicz, J., Krysko, A.V., Zhigalov, M.V., Krysko, V.A.: Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields. Springer Nature, Switzerland AG (2021) https://doi.org/10.1007/978-3-030-55993-9

  24. Saeed, A.M., Lotfy, Kh., El-Bary, A., Ahmed, M.H.: Functionally graded (FG) magneto-photothermoelastic semiconductor material with hyperbolic two-temperature theory. J. Appl. Phys. 131, 1–13 (2022). https://doi.org/10.1063/5.0072237

    Article  Google Scholar 

  25. Thi, H.N.: Thermal vibration analysis of functionally graded porous plates with variable thickness resting on elastic foundations using finite element method. Mech. Based Design Struct. Machin. (2022). https://doi.org/10.1080/15397734.2022.2047719

    Article  Google Scholar 

  26. Lomakin, V.A.: The Theory of Elasticity of Non-Homogeneous Bodies. Moscow (1976)

  27. Ezzat, M.A., Othman, M.I.A., El-Karamany, A.S.: The dependence of the modulus of elasticity on the reference temperature in generalized thermoelasticity. J. Therm. Stress. 24, 1159–1176 (2001)

    Article  Google Scholar 

  28. Aouadi, M.: Temperature dependence of an elastic modulus in generalized linear micropolar thermoelasticity. Z. Angew. Math. Phys. 57, 1057–1074 (2006)

    Article  MathSciNet  Google Scholar 

  29. Othman, M.I.A., Said, S.M.: 2D problem of magneto-thermoelasticity fiber-reinforced medium under temperature dependent properties with three-phase-lag model. Meccanica 49, 1225–1241 (2014)

    Article  MathSciNet  Google Scholar 

  30. Sheoran, D., Kumar, R., Thakran, S., Kalkal, K.K. Thermo-mechanical disturbances in a nonlocal rotating elastic material with temperature dependent properties. Int. J. Numer. Method. Heat and Fluid Flow 31, 3597-3620 (2021). https://doi.org/10.1108/HFF-12-2020-0794

  31. Hashin, Z., Rosen, W.B.: The elastic moduli of fiber-reinforced materials. J. Appl. Mech. 31, 223–232 (1964)

    Article  Google Scholar 

  32. Rogers, T.G.: Anisotropic elastic and plastic materials, In: Thoft- Christensen, P. (ed): Continuum Mechanics Aspects of Geodynamics and Rock Fracture, pp. 177-200. Mechanics Reidel, Dordrecht (1975)

  33. Belfield, A.J., Rogers, T.G., Spencer, A.J.M.: Stress in elastic plates reinforced by fiber lying in concentric circles. J. Mech. Phys. Solid. 31, 25–54 (1983)

    Article  Google Scholar 

  34. Abbas, I.A., Othman, M.I.A.: Generalized magneto-thermoelasticity in a fiber-reinforced anisotropic half-space. Int. J. Thermophys. 32, 1071–1085 (2011). https://doi.org/10.1007/s10765-011-0957-3

    Article  Google Scholar 

  35. Kalkal, K.K., Sheokand, S.K., Deswal, S.: Reflection and transmission between thermoelastic and initially stressed fiber-reinforced thermoelastic half-spaces under dual-phase-lag model. Acta. Mech. 230, 87–104 (2019). https://doi.org/10.1007/s00707-018-2302-4

    Article  MathSciNet  MATH  Google Scholar 

  36. Deswal, S., Poonia, R., Kalkal, K.K.: Disturbances in an initially stressed fiber-reinforced orthotropic thermoelastic medium due to inclined load. J. Braz. Soc. Mech. Sci. Eng. 42, 1–15 (2020)

    Article  Google Scholar 

  37. Hobiny, A., Abbas, A.: A study on thermoelastic interactions in fiber-reinforced mediums containing spherical cavities. Wave. Rand. Compl. Media (2021). https://doi.org/10.1080/17455030.2021.1976879

    Article  Google Scholar 

  38. Deswal, S., Kumar, S., Jain, K.: Plane wave propagation in a fiber-reinforced diffusive magneto-thermoelastic half space with two-temperature. Wave. Rand. Comp. Media 32, 43–65 (2022)

    Article  MathSciNet  Google Scholar 

  39. Spencer, A.J.M.: Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer-Verlag Wien, New York (1984)

    Book  Google Scholar 

  40. Said, S.M., Othman, M.I.A.: Gravitational effect on a fiber-reinforced thermoelastic medium with temperature-dependent properties for two different theories. Iran. J. Sci. Technol. Trans. Mech. Eng. 40, 223–232 (2016). https://doi.org/10.1007/s40997-016-0014-8

    Article  Google Scholar 

  41. Gunghas, A., Kumar, R., Deswal, S., Kalkal, K.K.: Influence of rotation and magnetic fields on a functionally graded thermoelastic solid subjected to a mechanical load. J. Math. 19, 1–16 (2019). https://doi.org/10.1155/2019/1016981

    Article  MathSciNet  MATH  Google Scholar 

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  1. Department of Mathematics, Indira Gandhi University, Meerpur (Rewari), Haryana, 122502, India

    M. S. Barak & Priti Dhankhar

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  1. M. S. Barak
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Barak, M.S., Dhankhar, P. Effect of inclined load on a functionally graded fiber-reinforced thermoelastic medium with temperature-dependent properties. Acta Mech 233, 3645–3662 (2022). https://doi.org/10.1007/s00707-022-03293-5

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