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Elastodynamic problem for an infinite body having a spherical cavity in the theory of thermoelasticity with double porosity

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present investigation is concerned with homogeneous, isotropic infinite double porous thermoelastic body with a spherical cavity subjected to ramp type mechanical/thermal source in the context of Lord-Shulman theory of thermoelasticity [1] with one relaxation time. Laplace transform technique has been used to obtain the expressions for radial stress, hoop stress, equilibrated stresses and temperature distribution. A numerical inversion technique has been applied to recover the resulting quantities in the physical domain. The components of stress and temperature distribution are depicted graphically to show the effect of porosity and relaxation time parameters. Some particular cases are also deduced from the present investigation.
Rocznik
Strony
267--289
Opis fizyczny
Bibliogr. 32 poz., wykr.
Twórcy
autor
  • Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
autor
  • Department of Mathematics and Statistics, H.P. University, Shimla, HP, India
Bibliografia
  • [1] Lord, H. and Shulman, Y.: A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299-309, 1967.
  • [2] Biot, M. A.: General theory of three-dimensional consolidation, J. Appl. Phys., 12, 155-164, 1941.
  • [3] Barenblatt, G.I., Zheltov, I.P. and Kochina, I. N.: Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), J. Appl. Math. Mech., 24, 1286-1303, 1960.
  • [4] Aifantis, E. C.: Introducing a multi-porous medium, Developments in Mechanics, 8, 209-211, 1977.
  • [5] Aifantis, E. C.: On the response of fissured rocks, Developments in Mechanics, 10, 249-253, 1979.
  • [6] Aifantis, E. C.: The mechanics of diffusion in solids, T.A.M. Report No. 440, Dept. of Theor. Appl. Mech., University of Illinois, Urbana, Illinois, 1980.
  • [7] Aifantis, E. C.: On the Problem of Diffusion in Solids, Acta Mech., 37, 265-296, 1980.
  • [8] Wilson, R. K. and Aifantis, E. C.: On the theory of consolidation with double porosity, Int. J. Engg. Sci., 20, No.9, 1009-1035, 1984.
  • [9] Khaled, M. Y., Beskos, D. E. and Aifantis, E. C.: On the theory of consolidation with double porosity-III, Int. J. Numer. Analy. Meth. Geomech. 8, 101-123, 1984.
  • [10] Wilson, R. K. and Aifantis, E. C.: A double porosity model for acoustic wave propagation in fractured porous rock. Int. J. Engg. Sci., 22, (8-10), 1209-1227, 1984.
  • [11] Nunziato , J.W. and Cowin , S.C.: A nonlinear theory of elastic materials with voids. Arch. Rat. Mech. Anal., 72 , 175-201, 1979.
  • [12] Cowin, S.C. and Nunziato, J. W.: Linear elastic materials with voids, J. Elasticity, 13, 125-147, 1983.
  • [13] Beskos, D. E. and Aifantis, E. C.: On the theory of consolidation with Double Porosity-II, Int. J. Engg. Sci., 24, 1697-1716, 1986.
  • [14] Khalili, N. and Valliappan, S.: Unified theory of flow and deformation in double porous media. Eur. J. Mech. A, Solids, 15 , 321-336, 1996.
  • [15] Khalili, N. and Selvadurai, A. P. S.: A Fully Coupled Constitutive Model for Thermo-hydro -mechanical Analysis in Elastic Media with Double Porosity, Geophys. Res. Lett., 30 , 2268-2271, 2003.
  • [16] Svanadze, M.: Fundamental solution in the theory of consolidation with double porosity, J. Mech. Behav. Mater. , 16 , 123-130, 2005.
  • [17] Svanadze, M.: Dynamical problems on the theory of elasticity for solids with double porosity, Proc. Appl. Math. Mech. 10, 209-310, 2010.
  • [18] Svanadze, M.: Plane waves and boundary value problems in the theory of elasticity for solids with double porosity. Acta Appl. Math., 122, 461-470, 2012.
  • [19] Straughan, B.: Stability and uniqueness in double porosity elasticity, Int. J. Eng. Sci., 65, 1-8, 2013.
  • [20] Svanadze, M.: On the theory of viscoelasticity for materials with double porosity, Disc. and Cont. Dynam. Syst. Ser. B., 19 No.7, 2335-2352, 2014.
  • [21] Svanadze, M.: Uniqueness theorems in the theory of thermoelasticity for solids with double porosity, Meccanica, 49 , 2099-2108, 2014.
  • [22] Iesan, D. and Quintanilla, R.: On a theory of thermoelastic materials with a double porosity structure, J. Therm. Stress., 37, 1017-1036, 2014.
  • [23] Allam, M. N. Elsibai, K. A. and Abouelergal, A. E.: Thermal stresses in a harmonic field for an infinite body with a circular cylindrical hole without energy dissipation, J. Therm. Stresses, 25, 57-68, 2002.
  • [24] Youssef, H. M.: Generalized thermoelasticity of an infinite body with a cylindrical cavity and variable material properties, J. Therm. Stresses, 28, 521-532, 2005.
  • [25] Youssef, H. M.: State space approach on generalized thermoelasticity for an infinite material with a spherical cavity and variable thermal conductivity subjected to ramp-type heating, Canadian Applied Mathematics Quarterly, 13, No.4 , 369-390, 2005.
  • [26] Allam, M. N, Elsibai, K.A. and Abouelregal, A.E.: Magneto-thermoelasticity for an infinite body with a spherical cavity and variable material properties without energy dissipation, Int. J. Solids Struct., 47, 2631-2638, 2010.
  • [27] Abd-alla, A. M. and Abo-dahab, S. M.: Effect of rotation and initial stress on an infinite generalized magneto-thermoelastic diffusion body with a spherical cavity, J. of Thermal Stresses, 35, 892-912, 2012.
  • [28] Zenkour, A. M. and Abouelregal, A. E.: Effects of phase-lags in a thermoviscoelastic orthotropic continuum with a cylindrical hole and variable thermal conductivity, Arch. Mech., 67, No.6, 457-475, 2015.
  • [29] Abbas, I. A., Kumar, R. and Rani, L.: Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating, Appl. Math. Comp. 254, 360-369, 2015.
  • [30] Honig, G. and Hirdes, U.: A method for the numerical inversion of the Laplace transforms, J. Comp. Appl. Math., 10, 113-132, 1984.
  • [31] Sherief, H. and Saleh, H.: A half space problem in the theory of generalized thermoelastic diffusion, Int. J. Solid. Struct., 42, 4484-4493, 2005.
  • [32] Khalili, N.: Coupling effects in double porosity media with deformable matrix, Geophys. Res. Lett., 30, 22 , DOI 10.1029/2003GL018544, 2003.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ecdd2f8a-1b88-4f9c-b91f-814bec4f9539
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