Coupled systems mechanics

  • 제9권5호
  • /
  • Pages.397-410
  • /
  • 2020
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Thermomechanical interactions in a non local thermoelastic model with two temperature and memory dependent derivatives

  • Lata, Parveen (Department of Basic and applied Sciences, Punjabi University Patiala) ;
  • Singh, Sukhveer (Punjabi University APS Neighbourhood Campus)
  • 투고 : 2020.03.03
  • 심사 : 2020.04.14
  • 발행 : 2020.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present investigation is concerned with two-dimensional deformation in a homogeneous isotropic non local thermoelastic solid with two temperatures due to thermomechanical sources. The theory of memory dependent derivatives has been used for the study. The bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The Laplace and Fourier transforms have been used for obtaining the solution to the problem in the transformed domain. The analytical expressions for displacement components, stress components and conductive temperature are obtained in the transformed domain. For obtaining the results in the physical domain, numerical inversion technique has been applied. Numerical simulated results have been depicted graphically for explaining the effects of nonlocal parameter on the components of displacements, stresses and conductive temperature. Some special cases have also been deduced from the present study. The results obtained in the investigation should be useful for new material designers, researchers and physicists working in the field of nonlocal material sciences.

키워드

참고문헌

  1. Abbas, I.A. (2014), "A GN model based upon two temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity", Appl. Math. Comput., 245, 108-115. https://doi.org/10.1016/j.amc.2014.07.059.
  2. Abbas, I.A. (2014), "Eigenvalue approach for an unbounded medium with a spherical cavity based upon two-temperature generalized thermoelastic theory", J. Mech. Sci. Technol., 28, 4193-4198. https://doi.org/10.1007/s12206-014-0932-6.
  3. Abbas, I.A. (2014), "Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties", Meccanica, 49, 1697-1708. https://doi.org/10.1007/s11012-014-9948-3.
  4. Abbas, I.A. and Youssef, H.M. (2012), "A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method", Int. J. Thermophys., 33, 1302-1313. https://doi.org/10.1007/s10765-012-1272-3.
  5. Abbas, I.A. and Zenkour, A.M. (2014), "Two temperature generalized thermoelastic interaction in an infinite fibre- reinforced anisotropic plate containing a circular cavity with two relaxation times", J. Comput. Theor. Nanosci., 11(1), 1-7. https://doi.org/10.1166/jctn.2014.3309.
  6. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  7. Alzahrani, F.S. and Abbas, I. A. (2016), "The effect of magnetic field on a thermoelastic fiber-reinforced material under GN-III theory", Steel Compos. Struct., 22(2), 369-386. https://doi.org/10.12989/scs.2016.22.2.369.
  8. Artan, R. (1996), "Nonlocal elastic half plane loaded by a concentrated force", Int. J. Eng. Sci., 34(8), 943-950. https://doi.org/10.1016/0020-7225(95)00132-8.
  9. Asghar, S., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133.
  10. Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized thermo-microstretch elastic solid", Int. J. Thermophys., 35(1), 175-193. https://doi.org/10.1007/s10765-013-1541-9.
  11. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  12. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.
  13. Belkorissat, I., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new non-local refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063.
  14. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  15. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  16. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircraft Spacecraft Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001.
  17. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.
  18. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  19. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", J. Appl. Math. Phys. (ZAMP), 19, 614-627. https://doi.org/10.1007/BF01594969.
  20. Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publisher Corporation, New Delhi, India.
  21. Ebrahimi, F. and Shafiei, N. (2016), "Application of eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837.
  22. Edelen, D.G.B, Green, A.E. and Laws, N. (1971), "Nonlocal continuum mechanics", Arch. Rat. Mech. Anal., 43, 36-44. https://doi.org/10.1007/BF00251543.
  23. Edelen, D.G.B. and Laws, N. (1971), "On the thermodynamics of systems with nonlocality", Arch. Rat. Mech. Anal., 43, 24-35. https://doi.org/10.1007/BF00251543.
  24. Eringen, A.C. (2002), Nonlocal Continum Field Theories, Springer, New York, USA.
  25. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A. (2014), "Generalized thermo-viscoelasticity with memory-dependent derivatives", Int. J. Mech. Sci., 89, 470-475. https:/doi.org/10.1016/j.ijmecsci.2014.10.006.
  26. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A. (2016), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23, 545-553. https:/doi.org/10.1080/15376494.2015.1007189.
  27. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of laplace transform", J. Comput. Appl. Math., 10, 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.
  28. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  29. Jahangir, A., Tanvir, F. and Zenkour, A. (2020), "Reflection of photothermoelastic waves in a semiconductor material with different relaxations", Ind. J. Phys., 1-9. https://doi.org/10.1007/s12648-020-01690-x.
  30. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  31. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysus of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.
  32. Kumar, R., Sharma, N. and Lata, P. (2016a), "Thermomechanical interactions in the transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Model., 40, 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061.
  33. Kumar, R., Sharma, N. and Lata, P. (2016b), "Effects of Hall current in a transversely isotropic magnetothermoelastic two temperature medium with rotation and with and without energy dissipation due to normal force", Struct. Eng. Mech., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091.
  34. Lata, P. (2018a), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66 (1), 113-124. https://doi.org/10.12989/sem.2018.66.1.113.
  35. Lata, P. (2018b), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(2), 439-451. https://doi.org/10.12989/scs.2018.27.4.439.
  36. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33 (1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.
  37. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177/1099636217727577.
  38. Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", Int. J. Eng. Sci., 32(8), 1229-1240. https://doi.org/10.1016/0020-7225(94)90034-5
  39. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlin. Anal.: Real World Appl., 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001.
  40. Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", J. Vib. Control, 16(1), 33-47. https://doi.org/10.1177%2F1077546309103419. https://doi.org/10.1177/1077546309103419
  41. Marin, M. (2014), "Lagrange identity method for microstretch thermoelastic materials", J. Math. Anal. Appl., 363(1), 275-286. https://doi.org/10.1016/j.jmaa.2009.08.045.
  42. Marin, M. and Florea, O. (2014), "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", Analele Universitatii "Ovidius" Constanta-Seria Matematica, 22(1), 169-188. https://doi.org/10.2478/auom-2014-0014.
  43. Marin, M. and Nicaise, S. (2016), "Existence and stability results for thermoelastic dipolar bodies with double porosity", Continuum. Mech. Thermodyn., 28(6), 1645-1657. https://doi.org/10.1007/s00161-016-0503-4.
  44. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Nonsimple material problems addressed by the Lagrange's identity", Bound. Value Prob., 2013, 1-14. https://doi.org/10.1186/1687-2770-2013-135.
  45. Marin, M., Craciun, E.M. and Pop, N. (2016), "Considerations on mixed initial-boundary value problems for micropolar porous bodies", Dyn. Syst. Appl., 25 (1-2), 175-196.
  46. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of saint-venant's problem for elastic dipolar bodies with voids", Carpath. J. Math., 33(2), 219-232. https://doi.org/10.37193/CJM.2017.02.09
  47. Marin, M., Vlase, S., Ellahi, R. and Bhatti, M.M. (2019), "On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure", Symmetry, 11(7), 1-16. https://doi.org/10.3390/sym11070863.
  48. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A, Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  49. Othman, M.I.A. and Abbas, I.A. (2012), "Generalized thermoelasticity of thermal-shock problem in a non-homogeneous isotropic hollow cylinder with energy dissipation", Int. J. Thermophys., 33, 913-923. https://doi.org/10.1007/s10765-012-1202-4.
  50. Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2015), "The effect of rotation on plane waves in generalized thermo-microstretch elastic solid for a mode-I crack under green naghdi theory", J. Comput. Theor. Nanosci., 12(11), 4987-4997. https://doi.org/10.1166/jctn.2015.4022.
  51. Press, W.H., Teukolshy, S.A., Vellerling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, Cambridge, UK.
  52. Said, S.M. and Othman, M.I.A. (2016), "Wave propagation in a two-temperature fibre-reinforced magneto-thermoelastic medium with three-phase-lag-model", Struct. Eng. Mech., 57(2), 201-220. https://doi.org/10.12989/sem.2016.57.2.201.
  53. Sarkar, N., Ghosh, D. and Lahiri, A. (2018), "A two-dimensional magnetothermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative", Mech. Adv. Mater. Struct., 1-10. https:/doi.org/10.1080/15376494.2018.1432784.
  54. Sharma, N., Kumar, R. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipiation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Model., 40, 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061.
  55. Soleimani, A., Dastani, K., Hadi, A. and Naei, M.H. (2019), "Effect of out of plane defects on the postbuckling behaviour of graphene sheets based on nonlocal elasticity theory", Steel Compos. Struct., 30(6), 517-534. https://doi.org/10.12989/scs.2019.30.6.517.
  56. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  57. Youssef, H.M. (2005), "Theory of two-temperature-generalized thermoelasticity", IMA J. Appl. Math., 71, 383-390. https://doi.org/10.1093/imamat/hxh101.
  58. Youssef, H.M. and Al-Lehaibi, E.A. (2007), "State space approach of two-temperature generalized thermoelasticity of one-dimensional problem", Int. J. Solid. Struct., 44, 1550-1562. https://doi.org/10.1016/j.ijsolstr.2006.06.035.
  59. Yu, Y.J., Hu, W. and Tian, X.G. (2014), "A novel generalized thermoelasticity model based on memory-dependent derivative", Int. J. Eng. Sci., 811, 23-134. https://doi.org/10.1016/j.ijengsci.2014.04.014.
  60. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.

피인용 문헌

  1. 2D Quasi-Static Accurate Solutions for Isotropic Thermoelastic Materials with Applications vol.2021, 2020, https://doi.org/10.1155/2021/8825226
  2. Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer vol.38, pp.2, 2020, https://doi.org/10.12989/scs.2021.38.2.141
  3. The effect of multi-phase-lag and Coriolis acceleration on a fiber-reinforced isotropic thermoelastic medium vol.39, pp.2, 2021, https://doi.org/10.12989/scs.2021.39.2.125