Fundamental Solution in the Theory of Thermoelastic Diffusion Materials with Double Porosity
Subject Areas : Engineering
1 - Department of Mathematics, M.N.College, Shahabad, 136135, India
Keywords: Thermoelastic, Double porosity, Steady oscillations, Diffusion,
Abstract :
The main purpose of present article is to find the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity in case of steady oscillations in terms of elementary functions.
[1] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[2] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-I, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 55-64.
[3] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-II, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 205-211.
[4] Nowacki W., 1974, Dynamical problems of thermodiffusion in solids-III, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 257-266.
[5] Nowacki W., 1976, Dynamical problems of diffusion in solids, Engineering Fracture Mechanics 8: 261-266.
[6] Sherief H.H., Hamza F.A., Saleh H.A., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591-608.
[7] Iesan D., 1986, A theory of thermoelastic materials with voids, Acta Mechanica 60: 67-89.
[8] Aouadi M., 2010, A theory of thermoelastic diffusion materials with voids, Zeitschrift für Angewandte Mathematik und Physik 61: 357-379.
[9] Barenblatt G.I., Zheltov I.P., Kochina I.N., 1960, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics 24: 1286-1303.
[10] Warren J., Root P., 1963, The behavior of naturally fractured reservoirs, Society of Petroleum Engineers Journal 3: 245-255.
[11] Wilson R.K., Aifantis E.C., 1982, On the theory of consolidation with double porosity I, International Journal of Engineering Science 20: 1009-1035.
[12] Iesan D., Quintanilla R., 2014, On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses 37: 1017-1036.
[13] Kansal T., 2018, Generalized theory of thermoelastic diffusion with double porosity, Archives of Mechanics 70: 241-268.
[14] Svanadze M., 2005, Fundamental solution in the theory of consolidation with double Porosity, Journal of the Mechanical Behavior of Biomedical Materials 16: 123-130.
[15] Svanadze M., De Cicco S., 2013, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Archives of Mechanics 65: 367-390.
[16] Svanadze M., 2013, Fundamental Solution in the linear theory of consolidation for elastic solids with double porosity, Journal of Mathematical Sciences 195: 258-268.
[17] Scarpetta E., Svanadze M., Zampoli V., 2014, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, Journal of Thermal Stresses 37: 727-748.
[18] Kumar R., Vohra R., Gorla M.G., 2016, Some considerations of fundamental solution in micropolar thermoelastic materials with double porosity, Archives of Mechanics 68: 263-284.
[19] Kumar R., Kansal T., 2012, Plane waves and fundamental solution in the generalized theories of thermoelastic diffusion, International Journal of Applied Mathematics and Mechanics 8: 1-20.
[20] Kupradze V.D., Gegelia T.G., Basheleishvili M.O., Burchuladze T.V., 1979, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Company, Amsterdam, New York, Oxford.