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Interactions in a homogeneous isotropic modified couple stress thermoelastic solid with multi-dual-phase-lag heat transfer and two temperature

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Harpreet (Department of Basic and Applied Sciences, Punjabi University)
  • 투고 : 2019.04.18
  • 심사 : 2020.07.06
  • 발행 : 2021.01.25

초록

The objective of this paper is to study the deformation in a homogeneous isotropic thermoelastic solid using modified couple stress theory subjected to ramp-type thermal source with two temperature. The advantage of this theory is the involvement of only one material length scale parameter which can determine the size effects. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The components of displacement, conductive temperature, stress components and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effect of two temperature is depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the size effects of microstructures.

키워드

참고문헌

  1. Abbas, I. and Marin, M. (2017), "Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating", Physica E-Low-Dimensional Syst. Nanostruct., 87, 254-260. https://doi.org/10.1016/j.physe.2016.10.048.
  2. Abbas, I.A. (2006), "Natural frequencies of a poroelastic hollow cylinder", Acta Mechanica, 186(1-4), 229-237. https://doi.org/10.1007/s00707-006-0314-y.
  3. Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., 20(5), 1103-1117. https://doi.org/10.12989/scs.2016.20.5.1103.
  4. Abbas, I.A. and Youssef, H.M. (2012), "A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method", Int. J. Thermophysics, 33(7), 1302-1313. https://doi.org/10.1007/s10765-012-1272-3.
  5. Abbas, I.A. and Youssef, H.M. (2013), "Two-temperature generalized thermoelasticity under ramp-type heating by finite element method", Meccanica, 48(2), 331-339. https://doi.org/10.1007/s11012-012-9604-8.
  6. Abbas, I.A. and Zenkour, A.M. (2014), "Two-temperature generalized thermoelastic interaction in an infinite fiber-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.
  7. Abualnour, M., Chick, 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.
  8. Ajri, M., Fakhrabadi, M.M.S. and Rastgoo, A. (2018), "Analytic solution for nonlinear dynamic behavior of viscoelastic nano-plates modified by consistent couple stress theory", Latin Am. J. Solid. Struct., 15(9), e113. https://doi.org/10.1590/1679-78254918
  9. Akgoz, B. and Civalek, O. (2013), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020.
  10. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM:MSGT electro-magnatoelastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  11. 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.
  12. Arif, S.M., Biwi, M. and Jahangir, A. (2018), "Solution of algebraic lyapunov equation on positive-definite hermitian matrices by using extended Hamiltonian algorithm", Comput. Mater. Continua, 54, 181-195. https://doi.org/10.3970/cmc.2018.054.181
  13. Belbachir, N., Bourada, M., Draiche, K., Tounsi, A. Bourada, F., Bousahla, A.A. and Mahmoud, S.R. (2020) "Thermal flexure analysis of anti-symmetric cross ply laminated plates using a four variable refined theory", Smart Struct. Syst., 25(4), 409-422. http://dx.doi.org/10.12989/sss.2020.25.4.409.
  14. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019) "Bending analysis of antisymmetric 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.
  15. Bhatti, M.M., Marin, M., Zeeshan, A., Ellahi, R. and Abdelsalam, S.I. (2020), "Swimming of Motile Gyrotactic Microorganisms and Nanoparticles in Blood Flow Through Anisotropically Tapered Arteries", Frontiers in Physics, 8, 1-12, Art. No. 95. https://doi.org/10.3389/fphy.2020.00001
  16. Bhatti, MM, Khalique, C.M., Beg, T.A., Beg, O.A. and Kadir, A. (2020), "Numerical study of slip and radiative effects on magnetic Fe3O4-water-based nanofluid flow from a nonlinear stretching sheet in porous media with Soret and Dufour diffusion", Modern Phys. Lett. B, 34(2), 2050026. https://doi.org/10.1142/S0217984920500268.
  17. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2002), "A simple nth-order shear deformation 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.
  18. Chen, W. and Li, X. (2014), "A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model", Archive of Appl. Mech., 84(3), 323-341. https://doi.org/10.1007/s00419-013-0802-1
  19. Cosserat, E. and Cosserat, F. (1909), Theory of Deformable Bodies, Paris, France, Hermann et Fils.
  20. 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.
  21. Fahsi, A., Tounsi, A., Hebali, H., Chikh, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates", Geomech. Eng., 13(3), 385-410. http://dx.doi.org/10.12989/gae.2017.13.3.385.
  22. Farokhi, H. and Ghayesh, M.H. (2015), "Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory", Int. J. Mech. Sci., 90, 133-144. https://doi.org/10.1016/j.ijmecsci.2014.11.002.
  23. Farokhi, H., Ghayesh, M.H. and Amabili, M. (2013), "Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory", Int. J. Eng. Sci., 68, 11-23. https://doi.org/10.1016/j.ijengsci.2013.03.001.
  24. Ghasemi, A.R. and Mohandes, M. (2016), "Size-dependent Bending of Geometrically Nonlinear of Micro-Laminated Composite Beam based on Modified Couple Stress Theory", Mech. Adv. Compos. Struct., 3, 53-62. https://dx.doi.org/10.22075/macs.2016.434.
  25. Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", Int. J. Solid. Struct., 48(18), 2496-2510. https://doi.org/10.1016/j.ijsolstr.2011.05.002.
  26. Hassan, M., Marin M., Ellahi, R. and Alamri, S.Z. (2018), "Exploration of convective heat transfer and flow characteristics synthesis by Cu-Ag/water hybrid-nanofluids", Heat Transfer Res., 49(18), 1837-1848. https://doi.org/10.1615/HeatTransRes.2018025569.
  27. Honig, G. and Hirdes, U. (1984), "A method for the numerical inversion of the Laplace transform", J. Comput. Appl. Math., 10(1), 113-132. https://doi.org/10.1016/0377-0427(84)90075-X.
  28. Jouneghani, F.Z., Babamoradi, H., Dimitri, R. and Tornabene, F. (2020), "A modified couple stress elasticity for non-uniform composite laminated beams based on Ritz formulation", Molecules, 25(6), 1404. https://doi.org/10.3390/molecules25061404.
  29. Kahrobaiyan, M.H., Asghari, M. and Ahmadian, M.T. (2014), "A Timoshenko Beam Element Based on the Modified Couple Stress Theory", Int. J. Mech. Sci., 79, 75-83. https://doi.org/10.1016/j.ijmecsci.2013.11.014.
  30. Ke, L.L., Wang, Y.S. and Wang, Z.D. (2011), "Thermal effect on free vibration and buckling of size-dependent microbeams", Physica E: Low-dimensional Syst. Nanostruct., 43(7), 1387-1393. https://doi.org/10.1016/j.physe.2011.03.009.
  31. Ke, L.L., Yang, J., Kitipornchai, S. and Bradford, M.A. (2012), "Bending, buckling and vibration of size-dependent functionally graded annular microplates", Compos. Struct., 94, 3250-3257. https://doi.org/10.1016/j.compstruct.2012.04.037.
  32. Khorshidi, K. and Fallah, A. (2017), "Free Vibration Analysis of Size-Dependent, Functionally Graded, Rectangular Nano/Micro-plates based on Modified Nonlinear Couple Stress Shear Deformation Plate Theories", Mech. Adv. Compos. Struct., 4, 127-137. https://dx.doi.org/10.22075/macs.2017.1800.1094
  33. Koiter, W.T. (1964), "Couple stresses in the theory of elasticity, I and II", Philos. T. Roy. Soc. London B, 67, 17-29.
  34. Kumar, R. and Abbas, I.A. (2013), "Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures", J. Comput. Theor. Nanosci., 10(9), 2241-2247. https://doi.org/10.1166/jctn.2013.3193
  35. Kumar, R. and Devi, S. (2019), "Resonance of Nanoscale Beam due to Various Sources in Modified Couple Stress Thermoelastic Diffusion with Phase Lags", Mech. Mechanical Eng., 23, 36-49. https://doi.org/10.2478/mme-2019-0006.
  36. Lata, P. (2018), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66(1), 113-124. http://dx.doi.org/10.12989/sem.2018.66.1.113.
  37. Lata, P. (2018a), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(4), 439-451. https://doi.org/10.12989/scs.2018.27.4.439.
  38. Lata, P. and Kaur, H. (2019), "Axisymmetric deformation in transversely isotropic thermoelastic medium using new modified couple stress theory", Coupled Syst. Mech., 8(6), 501-522. https://doi.org/10.12989/csm.2019.8.6.501.
  39. Lata, P. and Kaur, H. (2019a), "Deformation in transversely isotropic thermoelastic medium using new modified couple stress theory in frequency domain", Geomech. Eng., 19(5), 369-381.https://doi.org/10.12989/gae.2019.19.5.369.
  40. Ma, H., Gao, X.L. and Reddy, J. (2008), "A microstructure-dependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solids, 56, 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  41. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A, Adda Bedia, E.A. and Mahmoud, S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., https://doi.org/10.1177%2F1099636217727577 https://doi.org/10.1177%2F1099636217727577
  42. Marin, M. (1996), "Some basic theorems in elastostatics of micropolar materials with voids", J. Comput. Appl. Math., 70(1), 115-126. https://doi.org/10.1016/0377-0427(95)00137-9
  43. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlinear Analysis: RWA, 10(3), 1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001
  44. Marin, M. (1995), "On existence and uniqueness in thermoelasticity of micropolar bodies", Comptes rendus de l'Academie des sciences Paris, Serie II, B, 321(12), 375-480.
  45. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Tounsi, A. and Tounsi, A. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  46. Mindlin, R.D. and Tiersten, H.F. (1962), "Effects of Couple-Stress in Linear Elasticity", Archive for Rational Mechanics and Analysis, 11 (1), 415-448.https://doi.org/10.1007/BF00253946.
  47. Mohammadimehr, M. and Mohandes, M. (2015), "The effect of modified couple stress theory on buckling and vibration analysis of functionally graded double-layer Boron Nitride piezoelectric plate based on CPT", J. Solid Mech., 7(3), 281-298.
  48. Nateghi, A. and Salamat-talab, M. (2013), "Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory", Compos. Struct., 96, 97-110. https://doi.org/10.1016/j.compstruct.2012.08.048.
  49. Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2013), "Generalized magneto-thermo-microstretch elastic solid under gravitational effect with energy dissipation", Multidiscipline Model. Mater. Struct., 9(2), 145-176. https://doi.org/10.1108/MMMS-01-2013-0005.
  50. Press W.H., Teukolsky S.A., Vellerling W. T. and Flannery B.P. (1986), Numerical Recipe, Cambridge University Press.
  51. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A. Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4),311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  52. Riaz, A., Ellahi, R., Bhatti, M.M. and Marin, M. (2019) "Study of heat and mass transfer in the Eyring-Powell model of fluid propagating peristaltically through a rectangular compliant channel", Heat Transfer Res., 50(16), 1539-1560. https://doi.org/10.1615/HeatTransRes.2019025622
  53. Saeed, T., Abbas, I.A. and Marin, M. (2020), "A GL Model on Thermo-Elastic Interaction in a Poroelastic Material Using Finite Element Method", Symmetry, 12(3), 488. https://doi.org/10.3390/sym12030488
  54. Sharma, N., Kumar, R. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation", Mater. Phys. Mech., 22, 107-117.
  55. Sherief, H.H. and Saleh H. (2005), "A half-space problem in the theory of generalized thermoelastic diffusion", International J. Solid. Struct., 42, 4484-4493. https://doi.org/10.1016/0377-0427(84)90075-X.
  56. Simsek, M. and Reddy, J. (2013), "A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory", Compos. Struct., 101, 47-58. https://doi.org/10.1016/j.compstruct.2013.01.017.
  57. Thai, H.T. and Choi, D.H. (2013), "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Compos. Struct., 95, 142-153. https://doi.org/10.1016/j.compstruct.2012.08.023.
  58. 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-thermomechanical 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.
  59. Vlase, S., Marin, M., Öchsner, A. and Scutaru, M.L(2019), "Motion equation for a flexible one- dimensional element used in dynamical analysis of a multibody system", Continuum Mech. Thermodynam., 31(3), 715-724. https://doi.org/10.1007/s00161-018-0722-y
  60. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solid. Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  61. 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.
  62. Zenkour, A.M. (2019), "Effect of thermal activation and diffusion on a photothermal semiconducting half-space", J. Phys. Chem. Solids, 132, 56-67. https://doi.org/10.1016/j.jpcs.2019.04.011.
  63. Zenkour, A.M. (2019a), "Refined multi-phase-lags theory for photothermal waves of a gravitated semiconducting half-space", Compos. Struct., 212, 346-364. https://doi.org/10.1016/j.compstruct.2019.01.015.
  64. Zhang, B., He, Y., Liu, D., Gan, Z. and Shen, L. (2013), "A nonclassical Mindlin plate finite element based on a modified couple stress theory", Eur. J. Mech.-A/Solids, 42, 63-80. https://doi.org/10.1016/j.euromechsol.2013.04.005.

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