Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effect of length scale parameters on transversely isotropic thermoelastic medium using new modified couple stress theory

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kaur, Harpreet (Department of Basic and Applied Sciences, Punjabi University)
  • Received : 2019.04.30
  • Accepted : 2020.05.18
  • Published : 2020.10.10
⟨ Previous Next ⟩

Abstract

The objective of this paper is to study the deformation in transversely isotropic thermoelastic solid using new modified couple stress theory subjected to ramp-type thermal source and without energy dissipation. This theory contains three material length scale parameters which can determine the size effects. The couple stress constitutive relationships are introduced for transversely isotropic thermoelastic solid, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacement components, stress components, temperature change 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 effects of length scale parameters are depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the scale effects of microstructures.

Keywords

Acknowledgement

The corresponding author Harpreet Kaur duly acknowledges the Junior Research Fellowship (JRF) received from University Grants Commission (UGC), Delhi India for pursuing her PhD under the sanctioned no. 19/6/2016/(i) EU-V.

References

  1. Atanasov, M.S., Karlicic, D., Kozic, P. and Janevski, G. (2017), "Thermal effect on free vibration and buckling of a double-microbeam system", Facta universitatis, Series, Mech. Eng., 15(1), 45-62. https://doi.org/10.22190/FUME161115007S.
  2. Chen, W. and Li, X. (2014), "A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model", Arch. Appl. Mech., 84(3), 323-341. https://doi.org/10.1007/s00419-013-0802-1.
  3. Chen, W., Shengqi, Y. and Li, X. (2014), "A study of scale effect of composite laminated plates based on new modified couple stress theory by finite-element method", J. Multiscale Comput. Eng., 12(6), 507-527. https://doi.org/10.1615/IntJMultCompEng.2014011286.
  4. Cosserat, E. and Cosserat, F. (1909), Theory of Deformable Bodies, Hermann et Fils, Paris, France.
  5. El-Karamany, A.S. and Ezzat, M.A. (2011), "On the two-temperature Green-Naghdi thermoelasticity theories", J. Thermal Stresses, 34(12), 1207-1226. https://doi.org/10.1080/01495739.2011.608313.
  6. Ezzat, M.A. and Abd-Elaal, M.Z. (1997), "State space approach to viscoelastic fluid flow of hydromagnetic fluctuating boundary-layer through a porous medium", ZAMM-J. Appl. Math. Mech., 77(3), 197-207. https://doi.org/10.1002/zamm.19970770307.
  7. Ezzat, M.A. and Abd-Elaal, M.Z. (1997a) "Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium", J. Franklin Institute, 334(4), 685-706. https://doi.org/10.1016/S0016-0032(96)00095-6.
  8. Ezzat, M.A. and Ewad, S.A. (2010), "Constitutive relations, uniqueness of solution, and thermal shock application in the linear theory of micropolar generalized thermoelasticity involving two temperatures", J. Thermal Stresses, 33(3), 226-250. https://doi.org/10.1080/01495730903542829.
  9. Guo, J., Chen, J. and Pan, E. (2016), "Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory", Composites Part B Eng., 107, 84-96. https://doi.org/10.1016/j.compositesb.2016.09.044.
  10. Guo, J., Chen,J. and Pan. E. (2018), "A three-dimensional size-dependent layered model for simply-supported and functionally graded magnetoelectroelastic plates", Acta Mechanica Solida Sinica, 31(5), 652-671. https://doi.org/10.1007/s10338-018-0041-7.
  11. Hadjesfandiari, A.R. and Dargush, G.F. (2011), "Couple stress theory for solids", J. Solids Struct., 48(18), 2496-2510.https://doi.org/10.1016/j.ijsolstr.2011.05.002.
  12. Hadjesfandiari, A.R., Hadjesfandiari, A., Zhang, H. and Dargush, G.F. (2018), "Size-dependent couple stress Timoshenko beam theory", preprints 201811.0236.v1 or preprint arXiv:1712.08527. https://doi.org/ /1712/1712.08527.
  13. Honig, G., 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.
  14. Kaur, I. and Lata, P. (2019c), "Transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation in generalized thermoelasticity due to inclined load", SN Appl. Sci., 1(5), 426. https://doi.org/10.1007/s42452-019-0438-z.
  15. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", J. Eng. Sci., 50 (1), 256-267.https://doi.org/10.1016/j.ijengsci.2010.12.008.
  16. Khorshidi, M.A. (2018), "The material length scale parameter used in couple stress theories is not a material constant", J. Eng. Sci., 133, 15-25. https://doi.org/10.1016/j.ijengsci.2018.08.005.
  17. Li,X., Guo, J. and Sun, T. (2019),"Bending Deformation of Multilayered One-Dimensional Quasicrystal Nanoplates Based on the Modified Couple Stress Theory", Acta Mechanica Solida Sinica, 32, 785-802. https://doi.org/10.1007/s10338-019-00120-8.
  18. Khorshidi, M.A., Shariati, M. (2015), "A modified couple stress theory for postbuckling analysis of Timoshenko and Reddy-Levinson single-walled carbon nanobeams", J. Solid. Mech., 7(4), 364 -373.
  19. Koiter, W.T. (1964), "Couple stresses in the theory of elasticity, I and II", Nederl. Akad.Wetensch. Proc. Serial B, 67, 17-29.
  20. Kumar, R. and Devi, S. (2015), "Interaction due to Hall current and rotation in a modified couple stress elastic half-Space due to ramp-type loading", Comput. Method. Sci. Technol., 21(4), 229-240. https://doi.org/10.12921/cmst.2015.21.04.007.
  21. Kumar, R., Sharma, N. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperature", Appl. Math. Modell., 40(13-14), 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061
  22. Lata, P. and Kaur, I. (2019a), "Transversely isotropic thick plate with two temperature and GN type-III in frequency domain", Coupl. Syst. Mech., 8(1), 55-70. http://dx.doi.org/10.12989/csm.2019.8.1.055.
  23. Lata, P. and Kaur, I. (2019b), "Thermomechanical Interactions in transversely isotropic thick circular plate with axisymmetric heat supply", Struct. Eng. Mech., 69(6), 607- 614.http://dx.doi.org/10.12989/sem.2019.69.6.60.
  24. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22(3), 567-587. http://dx.doi.org/10.12989/scs.2016.22.3.567.
  25. Marin, M. (1997), "On weak solutions in elasticity of dipolar bodies with voids", J. Comput. Appl. Math., 82(1-2), 291-297. https://doi.org/10.1016/S0377-0427(97)00047-2.
  26. Marin, M. (1998), "Contributions on uniqueness in thermoelastodynamics on bodies with voids", Revista Ciencias Matematicas (Havana),16(2), 101-109.
  27. Marin, M. (2008), "Weak solutions in elasticity of dipolar porous materials", Math. Problem. Eng., 2008, 1-8. http://dx.doi.org/10.1155/2008/158908.
  28. Marin, M. (2009), "On the minimum principle for dipolar materials with stretch", Nonlinear Analysis: Real World Appl., 10(3),1572-1578. https://doi.org/10.1016/j.nonrwa.2008.02.001.
  29. Marin, M. (2010), "A partition of energy in thermoelasticity of microstretch bodies", Nonlinear Analysis: Real World Appl., 11(4),2436-2447. https://doi.org/10.1016/j.nonrwa.2009.07.014
  30. Marin, M. and Baleanu, D. (2016), "On vibrations in thermoelasticity without energy dissipation for micropolar bodies", Boundary Value Problem, Berlin, 2016, 111-129. https://doi.org/10.1186/s13661-016-0620-9.
  31. Marin, M. and Stan, G. (2013), "Weak solutions in Elasticity of dipolar bodies with stretch", Carpathian J. Math.,29(1), 33-40. https://doi.org/10.37193/CJM.2013.01.12
  32. Mindlin, R.D., and Tiersten, H.F. (1962), "Effects of Couple-Stress in Linear Elasticity", Arch. Rational Mech. Anal., 11(1), 415-448.https://doi.org/10.1007/BF00253946.
  33. Najafi, M., Rezazadeh, G. and Shabani, R. (2012b), "Thermo-elastic damping in a capacitive micro-beam resonator considering hyperbolic heat conduction model and modified couple stress theory", J. Solid. Mech., 4(4), 386-401.
  34. Press W. H., Teukolsky S.A., Vellerling W. T., Flannery B.P. (1986), Numerical Recipe, Cambridge University Press, Cambridge, United Kingdom.
  35. Reddy, J.N., Romanoff, J. and Loya, J.A. (2016), "Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory", Europe J. Mech. A/Solids,56, 92-104. https://doi.org/10.1016/j.euromechsol.2015.11.001.
  36. Roque, C.M.C., Ferreira, A.J.M. and Reddy, J.N. (2013), "Analysis of Mindlin micro plates with a modified couple stress theory and a meshless method", Appl. Math. Modell., 37(7), 4626-4633.https://doi.org/10.1016/j.apm.2012.09.063.
  37. Shaat, M., Mahmoud, F.F., Gao, X.L. and Faheem, A.F.(2014), "Size dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects", J. Mech. Sci., 79, 31-37.https://doi.org/10.1016/j.ijmecsci.2013.11.022.
  38. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016), "Nonlinear vibration of axially functionally graded tapered microbeams", J. Eng. Sci., 102, 12-26. https://doi.org/10.1016/j.ijengsci.2016.02.007.
  39. 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.
  40. Slaughter W.S. (2002), The Linearised Theory of Elasticity, Birkhauser Boston, Cambridge, USA.
  41. Tiwari, G. (1971), "Effect of couple-stresses in a semi-infinite elastic medium due to impulsive twist over the surface", Pure Appl. Geophys., 91(1), 71-75. https://doi.org/10.1007/BF00877889.
  42. Togun, N., Bagdatli, S.M. (2017), "Investigation of the size effect in Euler-Bernoulli nanobeam using the modified couple stress theory", Celal Bayar University J. Sci., 13(4), 893-899.https://doi.org/10.18466/cbayarfbe.370362.
  43. Tsiatas, G.C. and Yiotis, A.J. (2010), "A microstructure-dependent orthotropic plate model based on a modified couple stress theory", WIT Transactions on State of the Art in Sci. Eng., 43, 295-307.https://doi.org/10.2495/978-1-84564-492-5/22.
  44. Wang, L., Xu, Y. and Ni, Q. (2013), "Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: A unified treatment", J. Eng. Sci., 68, 1-10. https://doi.org/10.1016/j.ijengsci.2013.03.004.
  45. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress-based strain gradient theory for elasticity", J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  46. Zenkour, A.M. (2018), "Modified couple stress theory for micro-machined beam resonators with linearly varying thickness and various boundary conditions", Arch. Mech. Eng., 65(1), 41-64. https://doi.org/10.24425/119409.
  47. Zhang, Z. and Li, S. (2020), "Thermoelastic Damping of Functionally Graded Material Micro-Beam Resonators Based on the Modified Couple Stress Theory", Acta Mechanica Solida Sinica, 46.