Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effect of microtemperatures for micropolar thermoelastic bodies

  • Marin, Marin (Department of Mathematics and Computer Science, Transilvania University of Brasov) ;
  • Baleanu, Dumitru (Department of Mathematics and Computer Science, Cankaya University) ;
  • Vlase, Sorin (Department of Mechanical Engineering, Transilvania University of Brasov)
  • Received : 2016.07.01
  • Accepted : 2016.11.14
  • Published : 2017.02.10
⟨ Previous Next ⟩

Abstract

In this paper we investigate the theory of micropolar thermoelastic bodies whose micro-particles possess microtemperatures. We transform the mixed initial boundary value problem into a temporally evolutionary equation on a Hilbert space and after that we prove the existence and uniqueness of the solution. We also approach the study of the continuous dependence of solution upon initial data and loads.

Keywords

References

  1. Adams, R.A. (1975), Sobolev Spaces, Academic Press, New York.
  2. Chirita, S, Ciarletta, M. and D'Apice, C. (2013), "On a theory of thermoelasticity with microtem-peratures", J. Math. Anal. Appl., 397, 349-361. https://doi.org/10.1016/j.jmaa.2012.07.061
  3. Chirita, S. and Ghiba, I.D. (2012), "Rayleigh waves in Cosserat elastic materials", Int. J. Eng. Sci., 51, 117-127. https://doi.org/10.1016/j.ijengsci.2011.10.011
  4. Dyszlewicz, J. (2004), "Micropolar Theory of Elasticity", Lect. Notes Appl. Com-put. Mech., Vol. 15, Springer, Berlin/Heidelberg/New York.
  5. Eringen, A.C. (1966), "Linear theory of micropolar elasticity", J. Math. Mech., 15, 909-924.
  6. Eringen, A.C. (1999), Microcontinuum Field Theories I: Foundations and Solids, Springer-Verlag, New York/Berlin/ Heidelber.
  7. Grot, R.A. (1969), "Thermodynamics of a continuum with microstructure, Int. J. Eng. Sci., 7, 801-814. https://doi.org/10.1016/0020-7225(69)90062-7
  8. Iesan, D. (2004), Thermoelastic Models of Continua, Kluwer Academic Publishers, Dordrecht.
  9. Iesan, D. and Nappa, L. (2005), "On the theory of heat for micromorphic bodies", Int. J. Eng. Sci., 43, 17-32. https://doi.org/10.1016/j.ijengsci.2004.09.003
  10. Iesan, D. and Quintanilla, R. (2000), "On a theory of thermoelasticity with mi-crotemperatures", J. Therm. Stress., 23, 199-215. https://doi.org/10.1080/014957300280407
  11. Kim, D.K., Yu, S.Y. and Choi, H.S. (2013), "Condition assessment of raking dam-aged bulk carriers under vertical bending moments", Struct. Eng. Mech., 46(5), 629-644. https://doi.org/10.12989/sem.2013.46.5.629
  12. 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
  13. Marin, M, Abbas, I. and Kumar, R. (2014), "Relaxed Saint-Venant principle for thermoelastic micropolar di usion", Struct. Eng. Mech., 51(4), 651-662. https://doi.org/10.12989/sem.2014.51.4.651
  14. Marin, M. (1995), "On existence and uniqueness in thermoelasticity of micropolar bodies", Comptes Rendus, Acad. Sci. Paris, Serie II, 321(12), 475-480.
  15. Marin, M. (2010), "A domain of in uence theorem for microstretch elastic materials", Nonlin. Anal. R.W.A., 11(5), 3446-3452. https://doi.org/10.1016/j.nonrwa.2009.12.005
  16. Marin, M. and Marinescu, C. (1998), "Thermo-elasticity of initially stressed bodies. Asymptotic equipartition of energies", Int. J. Eng. Sci., 36 (1), 73-86. https://doi.org/10.1016/S0020-7225(97)00019-0
  17. Othman, M.I., Tantawi, R.S. and Abd-Elaziz, E.M. (2016), "Effect of initial stress on a porous thermoelastic medium with microtemperatures", J. Porous Media, 19(2), 155-172. https://doi.org/10.1615/JPorMedia.v19.i2.40
  18. Othman, M.I., Tantawi, R.S. and Hilal, M.I. (2016), "Hall current and gravity effect on magneto-micropolar thermoelastic medium with microtempe-ratures", J. Therm. Stress., 39(7), 751-771. https://doi.org/10.1080/01495739.2016.1188635
  19. Othman, M.I., Tantawi, R.S. and Hilal, M.I. (2016), "Rotation and modified Ohm's law influence on magneto-thermoelastic micropolar material with microtemperatures", Appl. Math. Comput., 276(5), 468-480
  20. Pazy, A. (1983), Semigroups of Operators of Linear Operators and Applications, Springer, New York, Berlin.
  21. Scalia, A. and Svanadze, M. (2009), "Potential method in the linear theory of thermoelasticity with microtemperatures", J. Therm. Stress., 32, 1024-1042. https://doi.org/10.1080/01495730903103069
  22. Sharma, K. and Marin, M. (2014), "Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids", An. Sti. Univ. Ovidius Constanta, 22(2), 151-175.
  23. Straughan, B. (2011), Heat Waves, Applied Mathematical Sciences, Springer, New York.
  24. Takabatake, H. (2012), "Effects of dead loads on the static analysis of plates", Struct. Eng. Mech., 42(6), 761-781. https://doi.org/10.12989/sem.2012.42.6.761

Cited by

  1. A mathematical model for three-phase-lag dipolar thermoelastic bodies vol.2017, pp.1, 2017, https://doi.org/10.1186/s13660-017-1380-5
  2. A dipolar structure in the heat-flux dependent thermoelasticity vol.8, pp.3, 2018, https://doi.org/10.1063/1.5029259
  3. Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system pp.1432-0959, 2019, https://doi.org/10.1007/s00161-018-0722-y
  4. Improved rigidity of composite circular plates through radial ribs pp.2041-3076, 2018, https://doi.org/10.1177/1464420718768049
  5. Hysteretically Symmetrical Evolution of Elastomers-Based Vibration Isolators within α-Fractional Nonlinear Computational Dynamics vol.11, pp.7, 2017, https://doi.org/10.3390/sym11070924
  6. Symmetry in Applied Continuous Mechanics vol.11, pp.10, 2017, https://doi.org/10.3390/sym11101286
  7. A Fractional-Order Predator-Prey Model with Ratio-Dependent Functional Response and Linear Harvesting vol.7, pp.11, 2017, https://doi.org/10.3390/math7111100
  8. Oscillation of Second Order Neutral Type Emden-Fowler Delay Difference Equations vol.5, pp.6, 2019, https://doi.org/10.1007/s40819-019-0751-7
  9. Nonlinear pre and post-buckled analysis of curved beams using differential quadrature element method vol.14, pp.1, 2017, https://doi.org/10.1186/s40712-019-0114-5
  10. Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations vol.7, pp.12, 2017, https://doi.org/10.3390/math7121158
  11. Axisymmetric deformation in transversely isotropic thermoelastic medium using new modified couple stress theory vol.8, pp.6, 2017, https://doi.org/10.12989/csm.2019.8.6.501
  12. Finite element analysis of an elbow tube in concrete anchor used in water supply networks vol.234, pp.1, 2017, https://doi.org/10.1177/1464420719871690
  13. Thermomechanical interactions in transversely isotropic magneto-thermoelastic medium with fractional order generalized heat transfer and hall current vol.27, pp.1, 2020, https://doi.org/10.1080/25765299.2019.1703494
  14. Deformation in transversely isotropic thermoelastic thin circular plate due to multi-dual-phase-lag heat transfer and time-harmonic sources vol.27, pp.1, 2020, https://doi.org/10.1080/25765299.2020.1781328
  15. Effects of nonlocality and two temperature in a nonlocal thermoelastic solid due to ramp type heat source vol.27, pp.1, 2020, https://doi.org/10.1080/25765299.2020.1825157
  16. Bioconvection in the Rheology of Magnetized Couple Stress Nanofluid Featuring Activation Energy and Wu’s Slip vol.45, pp.1, 2020, https://doi.org/10.1515/jnet-2019-0049
  17. Bioconvection in the Rheology of Magnetized Couple Stress Nanofluid Featuring Activation Energy and Wu’s Slip vol.45, pp.1, 2020, https://doi.org/10.1515/jnet-2019-0049
  18. Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition vol.8, pp.1, 2020, https://doi.org/10.3390/math8010094
  19. Some Backward in Time Results for Thermoelastic Dipolar Structures vol.8, pp.None, 2017, https://doi.org/10.3389/fphy.2020.00041
  20. Vibration analysis of FG porous rectangular plates reinforced by graphene platelets vol.34, pp.2, 2020, https://doi.org/10.12989/scs.2020.34.2.215
  21. Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures vol.34, pp.2, 2017, https://doi.org/10.12989/scs.2020.34.2.309
  22. A Study of Deformations in a Thermoelastic Dipolar Body with Voids vol.12, pp.2, 2017, https://doi.org/10.3390/sym12020267
  23. Criteria of Existence for a q Fractional p-Laplacian Boundary Value Problem vol.6, pp.None, 2020, https://doi.org/10.3389/fams.2020.00007
  24. Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating vol.73, pp.6, 2017, https://doi.org/10.12989/sem.2020.73.6.621
  25. Time harmonic interactions in an orthotropic media in the context of fractional order theory of thermoelasticity vol.73, pp.6, 2017, https://doi.org/10.12989/sem.2020.73.6.725
  26. Radar seeker performance evaluation based on information fusion method vol.2, pp.4, 2017, https://doi.org/10.1007/s42452-020-2510-0
  27. Numerical solution of Korteweg-de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves vol.95, pp.4, 2017, https://doi.org/10.1088/1402-4896/ab6070
  28. Influence of porosity distribution on vibration analysis of GPLs-reinforcement sectorial plate vol.35, pp.1, 2017, https://doi.org/10.12989/scs.2020.35.1.111
  29. Vibrational characteristic of FG porous conical shells using Donnell's shell theory vol.35, pp.2, 2017, https://doi.org/10.12989/scs.2020.35.2.249
  30. Time harmonic interactions in non local thermoelastic solid with two temperatures vol.74, pp.3, 2017, https://doi.org/10.12989/sem.2020.74.3.341
  31. The effect of gravity and hydrostatic initial stress with variable thermal conductivity on a magneto-fiber-reinforced vol.74, pp.3, 2017, https://doi.org/10.12989/sem.2020.74.3.425
  32. Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux vol.41, pp.6, 2017, https://doi.org/10.1007/s10483-020-2612-8
  33. Effect of two-temperature on the energy ratio at the boundary surface of inviscid fluid and piezothermoelastic medium vol.18, pp.6, 2017, https://doi.org/10.12989/eas.2020.18.6.743
  34. On a free boundary value problem for the anisotropic N-Laplace operator on an N−dimensional ring domain vol.28, pp.2, 2020, https://doi.org/10.2478/auom-2020-0027
  35. Thermomechanical response in a two-dimension porous medium subjected to thermal loading vol.30, pp.8, 2020, https://doi.org/10.1108/hff-11-2019-0803
  36. Influence of Geometric Equations in Mixed Problem of Porous Micromorphic Bodies with Microtemperature vol.8, pp.8, 2020, https://doi.org/10.3390/math8081386
  37. Memory response in elasto-thermoelectric spherical cavity vol.9, pp.4, 2020, https://doi.org/10.12989/csm.2020.9.4.325
  38. Reflection of coupled dilatational and shear waves in the generalized micropolar thermoelastic materials vol.26, pp.21, 2017, https://doi.org/10.1177/1077546320908705
  39. Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model vol.30, pp.11, 2017, https://doi.org/10.1108/hff-12-2019-0917
  40. Fractional order GL model on thermoelastic interaction in porous media due to pulse heat flux vol.23, pp.3, 2017, https://doi.org/10.12989/gae.2020.23.3.217
  41. Three-phase lag model of thermo-elastic interaction in a 2D porous material due to pulse heat flux vol.30, pp.12, 2017, https://doi.org/10.1108/hff-03-2020-0122
  42. Dual-phase-lag model on thermo-microstretch elastic solid Under the effect of initial stress and temperature-dependent vol.38, pp.4, 2021, https://doi.org/10.12989/scs.2021.38.4.355
  43. Composite Structures with Symmetry vol.13, pp.5, 2021, https://doi.org/10.3390/sym13050792