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A general study of fundamental solutions in aniotropicthermoelastic media with mass diffusion and voids

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.
Rocznik
Strony
22--41
Opis fizyczny
Bibliogr. 29 poz., rys.
Twórcy
autor
  • Department of Mathematics, Maharaja Agrasen Mahavidyalya Jagadhri-135003 Haryana, INDIA
  • Department of Mathematics, Mukand Lal National College Yamuna Nagar-135001 Haryana, INDIA
Bibliografia
  • [1] Ding H.J., Chen B. and Liang J. (1996): General solutions for coupled equations in piezoelectric media. − Int. J. Solids Struct., vol.33, pp.2283-2298.
  • [2] Dunn M.L. and Wienecke H.A. (1999): Half space Green’s functions for transversely isotropic piezoelectric solids. − Journal of Applied Mechanics, vol.66, pp.675-699.
  • [3] Pan E. and Tanon F. (2000): Three dimensional Green’s functions in anisotropic piezoelectric solids. − Int. J. Solids Struct., vol.37, pp. 943-958.
  • [4] Chen W.Q. (2000): On the general solution for piezothermoelasticity for transverse isotropy with applications. − ASME J. Appl. Mech., vol.67, pp.705-711.
  • [5] Chen W.Q., Lim C.W. and Ding H.J. (2005): Point temperature solution for a penny- shaped crack in an infinite transversely isotropic thermo-piezo-elastic medium. − Eng. Anal. with Bound. Elem., vol29, pp524-532.
  • [6] Sharma B. (1958): Thermal stresses in transversely isotropic semi-infinite elastic solids. − ASME J. Appl. Mech., vol.23, pp.86-88.
  • [7] Ciarletta M., Scalia A. and Svanadze M. (2007): Fundamental solution in the theory of micropolar thermoelastic for materials with voids. − J. Therm. Stress, vol.30, pp.213-229.
  • [8] Hou P.F., Leung A.Y.T. and He Y.J. (2008): Three-dimensional Green’s functions for transversely isotropic thermoelastic biomaterials. − Int. J. Solids Struct., vol.45, pp.6100-6113.
  • [9] Hou P.F., Wang L. and Yi T. (2009): 2D Green’s functions for semi-infinite orthotropic thermoelastic plane. − Appl. Math. Model., vol.33, pp.1674-1682.
  • [10] Xiong S.M., Hou P.F. and Yang S.Y. (2010): 2D Green's functions for semi-infinite orthotropic piezothermoelastic plane. − IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol.57, pp.1003-1010.
  • [11] Aouadi M. (2010): A theory of thermoelastic diffusion materials with voids. − Z. Angew. Math. Phys., vol.61, pp.357-379.
  • [12] Hou P.F., Sha H. and Chen C.P. (2011): 2D general solution and fundamental solution for orthotropic thermoelastic materials. − Engineering Analysis with Boundary Elements, vol.35, pp.56-60.
  • [13] Seremet V. (2011): Deriving exact Green’s functions and integral formulas for a thermoelastic wedge. − Engng. Anal. with Bound. Elements., vol.35, pp.527-532.
  • [14] Seremet V. (2012): New closed form Green’s function and integral formula for a thermoelastic quadrant. − Appl. Math. Model., vol.36, pp.799-812.
  • [15] Kumar R. and Kansal T. (2012): Plane waves and fundamental solution in the generalized theories of thermoelastic diffusion. − Int. J. Appl. Math. Mech., vol.8, pp1-20.
  • [16] Kumar R. and Chawla V. (2011): A study of fundamental solution in orthotropic thermodiffusive elastic media. − International Communication in Heat and Mass Transfer, vol.27, pp.456-462.
  • [17] Kumar R. and Chawla V. (2012): Green’s functions in orthotropic thermoelstic diffusion media. − Engineering Analysis with Boundary Elements, vol.36, pp.1272-1277.
  • [18] Kumar R. and Chawla V. (2012): General steady-state solution and green’s function in orthotropic piezothermoelastic diffusion medium. − Archives of Mechanics, vol.64, pp.555-579.
  • [19] Kumar R. and Chawla V. (2013): Fundamental solution for two-dimensional problem in orthotropic piezothermoelastic diffusion media. − Material Physics and Mechanics, vol.16, pp.159-174.
  • [20] Kumar R. and Chawla V. (2013): Reflection and refraction of plane wave at the interface between elastic and thermoelastic media with three-phase-lag. − International Communication in Heat and Mass Transfer, vol48, pp.53-60.
  • [21] Kumar R. and Gupta V. (2014): Green’s function for transversely isotropic thermoelastic diffusion bimaterials. − Journal of Thermal Stresses, vol.37, pp.1201-1229.
  • [22] Kumar R. and Chawla V. (2015): General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids. − Journal of Advanced Mathematics and Applications, American Scientific Publishers, vol.3, pp.1-8.
  • [23] Şeremet V. (2016): A method to derive thermoelastic Green’s functions for bounded domains (on examples of twodimensional problems for parallelepipeds). − Acta Mechanica, vol.227, pp.3603-3620.
  • [24] Pan L.H, Hou P.F and Chen J.Y. (2016): 2D steady-state general solution and fundamental solution for fluidsaturated. − Z. Angew. Math. Phys ZAMP, pp.67-84.
  • [25] Chawla V., Ahuja S. and Rani V. (2017): Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media. − Multidiscipline Modeling in Materials and Structures, vol.13, pp.409-423.
  • [26] Dang H.Y., Zhao M.H., Fan C.Y. and Chen Z.T. (2018): Analysis of arbitrarily shaped planar cracks in threedimensional isotropic hygrothermoelastic media. − J. Therm. Stress.,vol.6, pp.1-28.
  • [27] Zhao M.H., Dang H.Y., Fan C.Y. and Chen Z.T. (2018): Three dimensional steady-state general solution for isotropic hygrothermoelastic media. − Journal of Thermal Stresses, vol.41, pp.951-972.
  • [28] Tomar T., Goyal N. and Szekeres A. (2019): Plane waves in thermo-viscoelastic material with voids under different theories of thermoelasticity. − Int. J. of Applied Mechanics and Engineering, vol.24, pp.691-708.
  • [29] Biswas S. (2020): Fundamental solution of steady oscillations equations in nonlocal thermoelastic medium with voids. − Journal of Thermal Stresses, vol.43, pp.284-304.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bc622546-d397-4338-9433-526a28c77ae0
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