Coupled systems mechanics

  • 제13권3호
  • /
  • Pages.231-245
  • /
  • 2024
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Axisymmetric deformation of thick circular plate in microelongated thermoelastic solid

  • Rajneesh Kumar (Department of Mathematics, Kurukshetra University) ;
  • Aseem Miglani (Department of Mathematics, Ch. Devi Lal University) ;
  • Ravinder Kumar (Department of Mathematics, Ch. Devi Lal University)
  • 투고 : 2023.07.28
  • 심사 : 2024.03.29
  • 발행 : 2024.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

In the present work, a microelogated thermoelastic model based on Lord-Shulman (1967) and Green-Lindsay (1972) theories of thermoelasticity has been constructed. The governing equations for the simulated model are converted into two-dimensional case and made dimensionless for further simplification. Laplace and Hankel transforms followed by eigen value approach has been employed to solve the problem. The use of eigen value approach hasthe advantage of finding the solution of governing equationsin matrix form notations. This approach is straight forward and convenient for numerical computation and avoids the complicate nature of the problem. The components of displacement,stress and temperature distribution are obtained in the transformed domain. Numerical inversion techniques have been used to invert the resulting quantities in the physical domain. Graphical representation of the resulting quantities for describing the effect of microelongation are presented. A special case is also deduced from the present investigation. The problem find application in many engineering problems like thick-walled pressure vesselsuch as a nuclear containment vessel, a cylindricalroller etc.

키워드

참고문헌

  1. Abo-Dhab, S.M., Abouelregl, A.E. and Marin, M. (2020), "Generalized thermoelastic functionally graded on a thin slim strip non-gaussian laser beam", Symmetry, 12(7), 1094. http://doi.org/10.3390/sym12071094. 
  2. Ailawalia, P., Sachdeva, S.K. and Pathania, D.S. (2015), "Plane strain deformation in a thermoelastic microelongated solid with internal heat source", Int. J. Appl. Mech. Eng., 20(4), 717-731.  https://doi.org/10.1515/ijame-2015-0047
  3. Boley, B.A. and Weiner J.H. (1960), Theory of Thermal Stresses, John Wiley and Sons, New York. 
  4. Dhaliwal, R.S. and Singh, A. (1980), Dynamical Coupled Thermoelasticity, Hindustan Publishers, Delhi. 
  5. El-Sapa, S., Alhejaili, W., Lotfy, Kh. and El-Bary, A.A. (2023), "Excited non-local microelongated semiconductor layer thermal-optical mechanical waves affected by rotational field", Crystal., 13(1), 116. https://doi.org/10.3390/cryst13010116. 
  6. Eringen, A.C. (1966), "Linear theory of micropolar elasticity", J. Math. Mech., 15(6), 909-923.  https://doi.org/10.1512/iumj.1966.15.15060
  7. Eringen, A.C. (1971), "Micropolar elastic solids with stretch", Ari Kitabevi Matbaasi, 24, 1-18.
  8. Eringen, A.C. (1984), "Plane waves in nonlocal micropolar elasticity", Int. J. Eng. Sci., 22(8-10), 1113-1121. https://doi.org/10.1016/0020-7225(84)90112-5. 
  9. Eringen, A.C. (1990a), "Theory of thermo-microstretch elastic solids", Int. J. Eng. Sci., 28(12), 1291-1301. https://doi.org/10.1016/0020-7225(90)90076-U. 
  10. Eringen, A.C. (1990b), "Theory of thermo-microstretch fluids and bubbly liquids", Int. J. Eng. Sci., 28, 133-143. https://doi.org/10.1016/0020-7225(90)90063-O. 
  11. Eringen, A.C. (1999), Microcontinuum Field Theories, I, Foundations and Solids, Springer-Verlag, New York. 
  12. Green, A.E. and Lindsay, K. (1972), "Thermoelasticity", J. Elast., 2(1), 1-7.  https://doi.org/10.1007/BF00045689
  13. Honing, G. and Hirdes, U. (1984), "A method for the numerical inversion of Laplace transform", J. Comput. And Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X. 
  14. Ismail, G.M., Gepreel, K., Lotfy, Kh., Mahdy, A.M.S., El-Bary, A. and Saeed, A.M. (2022), "Influence of variable thermal conductivity on thermal-plasma-elastic waves of excited microelongated semiconductor", Alex. Eng. J., 61(12), 12271-12282. https://doi.org/10.1016/j.aej.2022.06.024. 
  15. Kiris, A. and Inan, E. (2005), "Eshelby tensors for a spherical inclusion in microelongated elastic fields", Int. J. Eng. Sci., 43(1-2), 49-58. https://doi.org/10.1016/j.ijengsci.2004.06.002. 
  16. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5. 
  17. Lotfy, Kh. (2022), "Thermo-mechanical waves of excited microelongated semiconductor layer during photothermal transport processes", Wave. Random Complex Media, 1-17. https://doi.org/10.1080/17455030.2022.2157067. 
  18. Marin, M., Florea, O. and Mahmoud, S.R. (2015), "A result regarding the seismic dislocations in microstretch thermoelastic bodies", Math. Prob. Eng., 2015, Article ID 850261. https://doi.org/10.1155/2015/850261. 
  19. Othman, M.I., Atwa, S.Y., Eraki, E.E.M. and Ismail, M.F. (2022), "Dual-phase-lag model on microelongated thermoelastic rotating medium", J. Eng. Therm. Sci., 2(1), 13-26.  https://doi.org/10.21595/jets.2022.22597
  20. Othman, M.I., Fekry, M. and Marin, M. (2020), "Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating", Struct. Eng. Mech., 73(6), 621-629. https://doi.org/10.12989/sem.2020.73.6.621. 
  21. Press, W.H., Teukolsky, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes, Cambridge University Press. 
  22. Raddadi, M.H., El-Sapa, S., Elamin, M.A., Chtioui, H., Chteoui, R., El-Bary, Alaa, A. and Lotfy, Kh. (2024), "Optoelectronic-thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity", Open Phys., 22, 20230145. https://doi.org/10.1515/phys-2023-0145. 
  23. Sachdeva, S.K. and Ailawalia, P. (2015), "Plane strain deformation in thermoelastic microelogated solid", Civil Environ. Res., 7(2), 92-98. 
  24. Sharma, S., Sharma, K. and Bhargava, R.R. (2014). "Plane waves and fundamental solution in an electromicrostretch elastic solids", Afrika Matematika, 25, 483-497.  https://doi.org/10.1007/s13370-013-0161-7
  25. Sharma, S. and Khator, S. (2021), "Power generation planning with reserve dispatch and weather uncertainties including penetration of renewable sources", Int. J. Smart Grid Clean Energy, 10(4), 292-303. https://doi.org/10.12720/sgce.10.4.292-303. 
  26. Sharma, S. and Khator, S. (2022), "Micro-Grid planning with aggregator's role in the renewable inclusive prosumer market", J. Power Energy Eng., 10(4), 47-62. https://doi.org/10.4236/jpee.2022.104004. 
  27. Sharma, S., Sharma, K. and Bhargava, R.R. (2013a with 2013), "Wave motion and representation of fundamental solution in electro-microstretch viscoelastic solids", Mater. Phys. Mech., 17(2), 93-110. 
  28. Shaw, S. and Mukhopadhyay, B. (2012), "Periodically varying heat source response in a functionally graded microelongated medium", Appl. Math. Comput., 218(11), 6304-6313. https://doi.org/10.1016/j.amc.2011.11.109. 
  29. Shaw, S. and Mukhopadhyay, B. (2013), "Moving heat source response in a thermoelastic microelongated solid", J. Eng. Phys. Thermophys., 86(3), 716-722. https://doi.org/10.1007/s10891-013-0887-y. 
  30. Tayel, I.M., Lotfy, Kh., El-Bary, A.A., Alebraheem, J. and Mohammed, M.A. (2023), "Microelongated thermo-elastodiffusive waves of excited semiconductor material under laser pulses impact", Math., 11(7), 1627. https://doi.org/10.3390/math11071627.