Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Thermomechanical interactions in transversely isotropic thick circular plate with axisymmetric heat supply

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Iqbal (Department of Basic and Applied Sciences, Punjabi University)
  • Received : 2018.09.10
  • Accepted : 2019.01.29
  • Published : 2019.03.25
⟨ Previous Next ⟩

Abstract

The present investigation has focus on the study of deformation due to thermomechanical sources in a thick circular plate. The thick circular plate is homogeneous, transversely isotropic with two temperatures and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of stresses, conductive temperature and displacement components are computed in the transformed domain. However, the resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are illustrated graphically. The effects of two temperatures by considering different values of temperature parameters are shown on the various components. Some particular cases are also figured out from the present investigation.

Keywords

References

  1. Akbas, S.D. (2017), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/CSM.2017.6.4.399
  2. Ali Houari, M.B., Bakora, A. and Tounsi, A. (2018), "Mechanical and thermal stability investigation of functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 65(4), 423-434. https://doi.org/10.12989/SEM.2018.65.4.423
  3. Chandrasekharaiah, D.S. (1998), "Hyperbolic thermoelasticity: A review of recent literature", Appl. Mech. Rev., 51(12), 705-729. https://doi.org/10.1115/1.3098984
  4. Chauthale, S. and Khobragade, N.W. (2017), "Thermoelastic response of a thick circular plate due to heat generation and its thermal stresses", Glob. J. Pure Appl. Math., 13(10), 7505-7527.
  5. Chen, P.J. and Gurtin, E.M. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift fur Angewandte Mathematik und Physik, 19(4), 614-627. https://doi.org/10.1007/BF01594969
  6. Chen, P.J., Gurtin, E.M. and Williams, O.W. (1969), "On the thermodynamics of non-simple elastic materials with two temperatures", Zeitschrift fur angewandte Mathematik und Physik, 20(1), 107-112. https://doi.org/10.1007/BF01591120
  7. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on non-simple heat conduction", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 19(6), 969-970. https://doi.org/10.1007/BF01602278
  8. Dhaliwal, R. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
  9. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2017), "Twotemperature theory in Green-Naghdi thermoelasticity with fractional phase-lag heat transfer", Microsyst. Technol.-Spring. Nat., 24(2), 951-961.
  10. Ezzat, M.A., El-Karamany, A.S. and Ezzat, S.M. (2012), "Twotemperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer", Nucl. Eng. Des., 252, 267-277. https://doi.org/10.1016/j.nucengdes.2012.06.012
  11. Ezzat, M. and AI-Bary, A. (2016), "Magneto-thermoelectric viscoelastic materials with memory dependent derivatives involving two temperature", Int. J. Appl. Electromagnet. Mech., 50(4), 549-567. https://doi.org/10.3233/JAE-150131
  12. Ezzat, M. and AI-Bary, A. (2017), "Fractional magnetothermoelastic materials with phase lag Green-Naghdi theories", Steel Compos. Struct., 24(3), 297-307. https://doi.org/10.12989/SCS.2017.24.3.297
  13. Ezzat, M., El-Karamany, A. and El-Bary, A. (2015), "Thermoviscoelastic materials with fractional relaxation operators", Appl. Math. Modell., 39(23), 7499-7512. https://doi.org/10.1016/j.apm.2015.03.018
  14. Ezzat, M., El-Karamany, A. and El-Bary, A. (2016), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23(5), 545-553. https://doi.org/10.1080/15376494.2015.1007189
  15. Honig, G.H. (1984), "A method for the inversion of Laplace transform", J. Comput. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X
  16. Heydari, A. (2018), "Size-dependent damped vibration and buckling analyses of bidirectional functionally graded solid circular nano-plate with arbitrary thickness variation", Struct. Eng. Mech., 68(2), 171-182. https://doi.org/10.12989/sem.2018.68.2.171
  17. Tripathi, J.J., Kedar, G.D. and Deshmukh, K.C. (2016), "Generalized thermoelastic diffusion in a thick circular plate including heat source", Alexandr. Eng. J., 55(3), 2241-2249. https://doi.org/10.1016/j.aej.2016.06.003
  18. Kant, S. and Mukhopadhyay, S. (2017), "A detailed comparative study on responses of four heat conductionmodels for an axisymmetric problem of coupled thermoelasticinteractions inside a thick plate", Int. J. Therm. Sci., 117, 196-211. https://doi.org/10.1016/j.ijthermalsci.2017.03.018
  19. Kumar, R., Manthena, V.R., Lamba, N.K. and Kedar, G.D. (2017), "Generalized thermoelastic axi-symmetric deformation problem in a thick circular plate with dual phase lags and two temperatures", Mater. Phys. Mech., Russ. Acad. Sci., 32, 123-132.
  20. Kumar, R., Sharma, N. and Lata, P. (2016), "Effect of two temperatures and thermal phase-lags in a thick plate due to a ring load with axisymmetric heat supply", Comput. Meth. Sci. Technol., 22(3), 153-162. https://doi.org/10.12921/cmst.2016.0000005
  21. Kumar, R., Sharma, N. and Lata, P. (2016), "Effects of thermal and diffusion phase-lags in a plate with axisymmetric heat supply", Multidiscipl. Model. Mater. Struct., 12(2), 275-290. https://doi.org/10.1108/MMMS-08-2015-0042
  22. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (2017), "Rayleigh waves in anisotropic magnetothermoelastic medium", Coupled Syst. Mech., 6(3), 317-333. https://doi.org/10.12989/CSM.2017.6.3.317
  23. Liu, J., Cao, L. and Chen, Y.F. (2019), "Analytical solution for free vibration of multi-span continuous anisotropic plates by the perturbation method", Struct. Eng. Mech., 69(3), 283-291. https://doi.org/10.12989/SEM.2019.69.3.283
  24. Lord, H. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Sol., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  25. Marin, M. (1997), "Cesaro means in thermoelasticity of dipolar bodies", Acta Mech., 122(1-4), 155-168. https://doi.org/10.1007/BF01181996
  26. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Math., 16(2), 101-109.
  27. Marin, M. and Oechsner, A. (2017), "The effect of a dipolar structure on the holder stability in green-naghdi thermoelasticity", Contin. Mech. Thermodyna., 29(6), 1365-1374. https://doi.org/10.1007/s00161-017-0585-7
  28. Marin, M. and Stan, G. (2013), "Weak solutions in elasticity of dipolar bodies with stretch", Carpath. J. Math., 29(1), 33-40. https://doi.org/10.37193/CJM.2013.01.12
  29. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a micro stretch thermoelastic body with two temperatures", Abstr. Appl. Analy., 583464.
  30. Ozdemir, Y.I. (2018), "Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation", Struct. Eng. Mech., 65(3), 213-222. https://doi.org/10.12989/SEM.2018.65.3.213
  31. Press, W.T. (1986), Numerical Recipes in Fortran, Cambridge University Press.
  32. Shahani, A.R. and Torki, H.S. (2018), "Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity", Contin. Mech. Thermodyn., 30(3), 509-527. https://doi.org/10.1007/s00161-017-0618-2
  33. Sharma, N., Kumar, R. and Lata, P. (2015), "Effect of two temperature and anisotropy in an axisymmetric problem in transversely isotropic thermoelastic solid without energy dissipation and with two temperature", Am. J. Eng. Res., 4(7), 176-187.
  34. Slaughter, W.S. (2002), The Linearized Theory of Elasticity, Birkhauser, Basel, Switzerland.
  35. Taleb, O., Houari, M.S., Bessaim, A., Tounsi, A. and Mahmoud, A.S. (2018), "A new plate model for vibration response of advanced composite plates in thermal environment", Struct. Eng. Mech., 67(4), 369-383. https://doi.org/10.12989/SEM.2018.67.4.369
  36. Tripathi, J., Kedar, G.D. and Deshmukh, K.C. (2015), "Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply", Acta Mech., 226(7), 2121-2134. https://doi.org/10.1007/s00707-015-1305-7
  37. Youssef, H. (2011), "Theory of two-temperature thermoelasticity without energy dissipation", J. Therm. Stress., 34(2), 138-146. https://doi.org/10.1080/01495739.2010.511941

Cited by

  1. Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures vol.34, pp.2, 2019, https://doi.org/10.12989/scs.2020.34.2.309
  2. Reflection of plane harmonic wave in rotating media with fractional order heat transfer vol.9, pp.4, 2019, https://doi.org/10.12989/amr.2020.9.4.289