Geomechanics and Engineering

  • 제27권1호
  • /
  • Pages.45-54
  • /
  • 2021
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Generalized magneto-thermo-microstretch elastic solid with finite element method under the effect of gravity via different theories

  • Othman, Mohamed I.A. (Department of Mathematics, Faculty of Science, Zagazig University) ;
  • Abbas, Ibrahim A. (Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University) ;
  • Abo-Dahab, S.M. (Department of Mathematics, Faculty of Science, South Valley University)
  • 투고 : 2021.02.10
  • 심사 : 2021.09.28
  • 발행 : 2021.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

The present paper is aimed at studying the effect of gravity on the general model of the equations of generalized magneto-thermo-micro-stretch for a homogeneous isotropic elastic half-space solid. The problem is in the context of the Green-Lindsay (G-L) theories, as well as the coupled theory (CT). Finite element method is used to obtain the expressions for the displacement components, the force stresses, the temperature, the couple stresses, and the micro-stress distribution. Comparisons are made with the results in the presence and absence of gravity and magnetic field of a particular case for the generalized micropolar thermo-elasticity elastic medium (without micro-stretch constants) between the three theories.

키워드

참고문헌

  1. Abbas, I.A. and Othman, M.I.A. (2012), "Plane waves in generalized thermo-microstretch elastic solid with thermal relaxation using finite element method", Int. J. Thermophys., 33(12), 2407-2423. https://doi.org/10.1007/s10765-012-1340-8.
  2. Abd-Elaziz, E.M., Marin, M. and Othman, M.I.A. (2019), "On the effect of Thomson and initial stress in a thermo-porous elastic solid under G-N electromagnetic theory", Symmetry, 11(3), 413-430. https://doi.org/10.3390/sym11030413.
  3. Anya, A.I. and Khan, A. (2019), "Reflection and propagation of plane waves at free surfaces of a rotating micropolar fiber-reinforced medium with voids", Geomech. Eng., 18(6), 605-614. https://doi.org/10.12989/gae.2019.18.6.605.
  4. Baghban, A., Sasanipour, J., Pourfayaz, F. and Ahmadi, M.H. (2019), "Towards experimental and modeling study of heat transfer performance of water-SiO2 nanofluid in quadrangular cross-section channels", Eng. Appl. Comput. Fluid Mech., 13(1), 453-469. https://doi.org/10.1080/19942060.2019.1599428.
  5. 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", Front. Phys., 8, 1-12. https://doi.org/10.3389/fphy.2020.00095.
  6. Biot, M. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27, 240-253. https://doi.org/10.1063/1.1722351.
  7. Bofill, F. and Quintanilla, R. (1995), "Some qualitative results for the linear theory of thermo-microstretch elastic solids", Int. J. Eng. Sci., 33, 2115-2125. https://doi.org/10.1016/0020-7225(95)00048-3
  8. De Cicco, S. and Nappa, L. (1999), "On the theory of thermosmicrostretch elastic solids", J. Therm. Stresses, 22, 565-580. https://doi.org/10.1080/014957399280751.
  9. De Cicco, S. and Nappa, L. (2000), "Some results in the linear theory of thermo-micro-stretch elastic solids", J. Math. Mech., 5(4), 467-482.
  10. Eftekhari, S.A. (2018), "A coupled Ritz-finite element method for free vibration of rectangular thin and thick plates with general boundary conditions", Steel Compos. Struct., 28(6), 655-670. http://doi.org/10.12989/scs.2018.28.6.655.
  11. Eringen, A.C. (1971), "Micropolar elastic solids with stretch",Technical Report, Ari Kitabevi Matbassi, Istanbul, Turkey.
  12. Eringen, A.C. (1999), Micro-continuum Field Theories I: Foundation and Solids, Springer-Verlag, New York, U.S.A., Berlin, Heidelberg, Germany.
  13. Eringen, A.C. (1990), "Theory of thermo-microstretch elastic solids", Int. J. Eng. Sci., 28(12), 1291-1301. https://doi.org/10.1016/0020-7225(90)90076-U.
  14. Elnagar, A.M., Abd-Alla, A.M. and Ahmed, S.M. (1994), "Rayleigh waves in a magneto-elastic initially stresses conducting medium with the gravity field", B. Cal. Math. Soc. 86, 51-56.
  15. Ghalndari, M., Bornassi, S., Shamshirband, S., Mosavi, A. and Chau, K.W. (2019), "Investigation of submerged structures' flexibility on sloshing frequency using a boundary element method and finite element analysis", Eng. Appl. Comput. Fluid Mech., 13(1), 519-528. https://doi.org/10.1080/19942060.2019.1619197
  16. Green, A.E. and Laws, N. "On the entropy production inequality", Arch. Rat. Mech. Anal., 45(1), 47-53. https://doi.org/10.1007/BF00253395
  17. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7. https://doi.org/10.1007/BF00045689.
  18. Hobiny, A.D. and Abbas, I.A. (2020), "Fractional order thermoelastic wave assessment in a two-dimension medium with voids", Geomech. Eng., 21(1), 85-93. https://doi.org/10.12989/gae.2020.21.1.085.
  19. Iesan, D. and Nappa, L. (2001), "On the plane strain of micro-stretch elastic solids", Int. J. Eng. Sci., 39, 1815-1835. https://doi.org/10.1016/S0020-7225(01)00017-9.
  20. Jain, K., Kalkal, K.K. and Deswal, S. (2018), "Effect of heat source and gravity buildings under parametric fires", Struct. Eng. Mech., 68(2), 215-226. http://doi.org/10.12989/sem.2018.68.2.215.
  21. Khan, A.A., Bukhari, S.R. and Marin, M. (2019), "Effects of chemical reaction on third-grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index", Heat Transfer Res., 50(11), 1061-1080. http://doi.org/10.1615/HeatTransRes.2018028397.
  22. Kumar, K.V., Saravanan, T.J., Sreekala, R., Gopalakrishnan, N. and Mini, K.M. (2017), "Structural damage detection through longitudinal wave propagation using spectral finite element method", Steel Compos. Struct., 12(1), 161-183. http://doi.org/10.12989/gae.2017.12.1.161.
  23. Kaur, I. and Lata, P. (2020) "Axisymmetric deformation in transversely isotropic magneto-thermo-elastic solid with Green-Naghdi III due to inclined load", Int. J. Mech. Mater. Eng., 15(3), 1-9. https://doi.org/10.1186/s40712-019-0111-8.
  24. Kaur, I., Lata, P. and Singh, K. (2020) "Memory-dependent derivative approach on magneto-thermoelastic transversely isotropic medium with two temperatures", Int. J. Mech. Mater. Eng., 15(10), 1-13. https://doi.org/10.1186/s40712-020-00122-2.
  25. Lata, P. and Kaur, H. (2020), "Effect of two temperature on isotropic modified couple stress thermoelastic medium with and without energy dissipation", Geomech. Eng., 21(5), 461-469. https://doi.org/10.12989/gae.2020.21.5.461.
  26. Lata, P. and Singh, S. (2020), "Deformation in a nonlocal magneto-thermoelastic solid with hall current due to normal force", Geomech. Eng., 22(2), 109-117. https://doi.org/10.12989/gae.2020.22.2.109.
  27. Lata, P. and Kaur, I. (2019) "Axisymmetric thermo-mechanical analysis of transversely isotropic magneto thermoelastic solid due to time-harmonic sources", Coupled. Syst. Mech., 8(5), 415-437. https://doi.org/10.12989/csm.2019.8.5.415.
  28. Lin, Y.H. and Jiang, Y. (2020), "Finite element simulationfor multiphase fluids with different densities using an energy-law-preserving method", Eng. Appl. Comput. Fluid Mech., 14(1), 642-654.https://doi.org/10.1080/19942060.2020.1756413.
  29. Lord, H. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid, 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  30. Marin, M., Vlase, S. and Paun, M. (2015), "Considerations on double porosity structure for micropolar bodies", AIP Advances, 5(3), 037113. https://doi.org/10.1063/1.4914912.
  31. Marin, M. (1999), "An evolutionary equation in thermo-elastic bodies", J. Math. Phys., 40(3), 1391-1399. https://doi.org/10.1063/1.532809.
  32. Othman, M.I.A. (2002), "Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermo- elasticity", J. Therm. Stresses, 25(11), 1027-1045. https://doi.org/10.1080/01495730290074621.
  33. Othman, M.I.A. and Song, Y.Q. (2009), "The effect of rotation on 2-D thermal shock problems for a generalized magneto-thermoelasticity half-space.under three theories", Multi. Model. Mater. Struct., 5(1), 43-48. https://doi.org/10.1108/15736105200900003.
  34. Othman, M.I.A. and Abbas, I.A. (2014), "Effect of rotation on plane waves in generalized thermo-microstretch elastic solid comparison of different theories using finite element method", Can. J. Phys., 92(10), 1269-1277. https://doi.org/10.1139/cjp-2013-0482.
  35. Othman, M.I.A., Khan, A., Jahangir, R. and Jahangir, A. (2019), "Analysis on plane waves through magneto-thermoelastic microstretch rotating medium with temperature dependent elastic properties", Appl. Math. Model., 65, 535-548. https://doi.org/10.1016/j.apm.2018.08.032
  36. Othman, M.I.A. and Abd-Elaziz, E.M. (2019), "Effect of initial stress and hall current on a magneto-thermoelastic porous medium with micro-temperatures", Ind. J. Phys., 93(4), 475-485. https://doi.org/10.1007/s12648-018-1313-2.
  37. Othman, M.I.A., Alharbi, A.M. and Al-Autabi, A.M.K. (2020), "Micropolar thermoelastic medium with voids under the effect of rotation concerned with 3PHL model", Geomech. Eng., 21(5), 447-459. https://doi.org/10.12989/gae.2020.21.5.447.
  38. Ramezanizadeh, M., Nazari, M.A., Ahmadi, M.H. and Chau, K.W. (2019), "Experimental and numerical analysis of a nanofluidic thermosyphon heat exchanger", Eng. Appl. Comput. Fluid Mech., 13(1), 40-47. https://doi.org/10.1080/19942060.2018.1518272.
  39. Salih, S.Q., Aldlemy, M.S., Rasani, M.R. and Ariffin, A.K. (2019), "Thin and sharp edges bodies-fluid interaction simulation using cut-cell immersed boundary method", Eng. Appl. Comput. Fluid Mech., 13(1), 860-877. https://doi.org/10.1080/19942060.2019.1652209.
  40. Toh, W., Tan, L.B., Tse, K.M., Raju, K., Lee, H.P. and Tan, V.B.C. (2018), "Numerical evaluation of buried composite and steel pipe structures under the effect of gravity", Steel Compos. Struct., 26(1), 55-66. http://doi.org/10.12989/scs.2018.26.1.055.
  41. Yu, R.L., Liang, R., Zhou, W., Wang, S., Yue, S. and Cui, B. (2020), "Stress analysis of a filter screen based on dimensional analysis and finite element analysis", Eng. Appl. Comput. Fluid Mech., 14(1), 168-179. https://doi.org/10.1080/19942060.2019.1665588.
  42. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. (2013), The Finite Element Method: Its Basis and Fundamentals, Seventh Edition, Elsevier.