每年出版 12 期
ISSN 打印: 1091-028X
ISSN 在线: 1934-0508
Indexed in
DYNAMIC PROBLEM OF SATURATED SOIL UNDER THE FRACTIONAL ORDER THEORY OF THERMOELASTICITY
摘要
In this article, we consider the thermo-hydro-mechanical (THM) problem of a poroelastic half-space soil medium subjected to time harmonic loads consisting of both normal and thermal loads in the context of the fractional order theory of thermoelasticity with one relaxation time. The foundation material is a uniform, fully saturated, poroelastic half-space medium. Normal mode analysis was used to obtain expressions for the nondimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution on the poroelastic half-space medium, and the expressions were represented graphically. The effects of the fractional order parameters and time parameters on all physical variables were analyzed in the numerical results.
-
Abbas, I.A. and Youssef, H.M., Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material, Lat. Am. J. Solids Struct., vol. 12, pp. 1415-1431,2015.
-
Abd El-Latief, A.M., New State-Space Approach and Its Application in Thermoelasticity, J. Therm. Stresses, vol. 40, pp. 135-144, 2017.
-
Abousleiman, Y. and Ekbote, S., Solutions for the Inclined Borehole in a Porothermoelastic Transversely Isotropic Medium, J. Appl. Mech.-TASME, vol. 72, pp. 102-114, 2005.
-
Bai, B., Fluctuation Responses of Saturated Porous Media Subjected to Cyclic Thermal Loading, Comput. Geotech., vol. 33, pp. 396-403, 2006a.
-
Bai, B., Thermal Consolidation of Layered Porous Half-Space to Variable Thermal Loading, Appl. Math. Mech., vol. 27, pp. 1531-1539, 2006b.
-
Bai, B. and Li, T., Irreversible Consolidation Problem of a Saturated Porothermoelastic Spherical Body with a Spherical Cavity, Appl. Math. Model, vol. 37, pp. 1973-1982, 2013.
-
Biot, M.A., General Theory of Three-Dimensional Consolidation, J. Appl. Phys., vol. 12, pp. 155-164, 1941.
-
Biot, M.A., Thermoelasticity and Irreversible Thermodynamics, J. Appl. Phys., vol. 27, pp: 240-253, 1956.
-
Biot, M.A., Variational Lagrangian-Thermodynamics of Non-Isothermal Finite Strain Mechanics of Porous Solids and Thermo-molecular Diffusion, Int. J. Solids Struct., vol. 13, pp. 579-597, 1977.
-
Booker, J.R. and Savvidou, C., Consolidation Around a Spherical Heat Source, Int. J. Solids Struct., vol. 20, pp. 1079-1090,1984.
-
Caputo, M., Vibrations on an Infinite Viscoelastic Layer with a Dissipative Memory, J. Acoust. Soc. Am., vol. 56, pp. 897-904, 1974.
-
Caputo, M. and Mainardi, F., A New Dissipation Model based on Memory Mechanism, Pure Appl. Geophys., vol. 91, pp. 134-147, 1971a.
-
Caputo, M. and Mainardi, F., Linear Models of Dissipation in Anelastic Solids, LaRivista delNuovo Cimento, vol. 1,pp. 161-168, 1971b.
-
Ezzat, M.A., Thermoelectric MHD Non-Newtonian Fluid with Fractional Derivative Heat Transfer, Physica. B, vol. 405, pp. 4188-4194, 2010.
-
Ezzat, M.A., Magneto-Thermoelasticity with Thermoelectric Properties and Fractional Derivative Heat Transfer, Physica. B, vol. 406, pp. 30-35,2011.
-
Ezzat, M.A., El-Karamany, A.S., and El-Bary, A.A., Application of Fractional Order Theory of Thermoelasticity to 3D Time-Dependent Thermal Shock Problem for a Half-Space, Mech. Adv. Mater. Struct., vol. 24, pp. 27-35, 2017.
-
Green, A.E. and Lindsay, K.A., Thermoelasticity, J. Elasticity, vol. 2, pp. 1-7, 1972.
-
Green, A.E. and Naghdi, P.M., A Reexamination of the Basic Results of Themomechanics, Proc. R. Soc. Lond. A, vol. 432, pp. 171-194, 1991.
-
Green, A.E. and Naghdi, P.M., On Undamped Heat Waves in an Elastic Solid, J. Therm. Stresses, vol. 15, pp. 252-264, 1992.
-
Green, A.E. and Naghdi, P.M., Thermoelasticity without Energy Dissipation, J. Elasticity, vol. 31, pp. 189-208,1993.
-
Joseph, D.D. and Preziosi, L., Heat Waves, Rev. Mod. Phys, vol. 61, pp. 41-73, 1989.
-
Joseph, D.D. and Preziosi, L., Heat Waves, Rev. Mod. Phys, vol. 62, pp. 375-391, 1990.
-
Jumarie, G., Derivation and Solutions of Some Fractional Black-Scholes Equations in Coarse-Grained Space and Time. Application to Merton's Optimal Portfolio, Comput. Math. Appl., vol. 59, pp. 1142-1164, 2010.
-
Liu, G.B., Xie, K.H., and Zheng, R.Y., Model of Nonlinear Coupled Thermo-Hydro-Elastodynamics Response for a Saturated Poroelastic Medium, Sci. China Ser. E: Tech. Sci., vol. 52, pp. 2373-2383, 2009.
-
Liu, G.B., Xie, K.H., and Zheng, R.Y., Thermo-Elastodynamic Response of a Spherical Cavity in Saturated Poroelastic Medium, Appl. Math. Model, vol. 34, pp. 2203-2222, 2010a.
-
Liu, G.B., Xie, K.H., and Zheng, R.Y., Mode of a Spherical Cavity's Thermo-Elastodynamic Response in a Saturated Porous Medium for Non-Torsional Loads, Comput. Geotechnol., vol. 37, pp. 381-390,2010b.
-
Lord, H.W. and Shulman, Y., A Generalized Dynamical Theory of Thermoelasticity, J. Mech. Phys. Solids, vol. 15, pp. 299-309, 1967.
-
Lotfy, K.H., Two Temperature Generalized Magneto-Thermoelastic Interactions in an Elastic Medium under Three Theories, Appl. Math. Comput., vol. 227, pp. 871-888, 2014.
-
Lotfy, K.H. and Hassan, W., Normal Mode Method for Two-Temperature Generalized Thermoelasticity under Thermal Shock Problem, J. Therm. Stresses, vol. 37, pp. 545-560,2014.
-
Lu, Z., Yao, H.L., and Liu, G.B., Thermomechanical Response of a Poroelastic Half-Space Soil Medium Subjected to Time Harmonic Loads, Comput. Geotechnol., vol. 37, pp. 343-350, 2010.
-
Santra, S., Das, N.C., Kumar, R., and Lahiri, A., Three-Dimensional Fractional Order Generalized Thermoelastic Problem under the Effect ofRotation in a Half Space, J. Therm. Stresses, vol. 38, pp. 309-324,2015.
-
Sarkar, N., Atwa, S.Y., and Othman, M.I.A., The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer, Int. Appl. Mech, vol. 52, pp. 203-216, 2016.
-
Sherief, H.H. and Abd El-Latief, A.M., Application of Fractional Order Theory of Thermoelasticity to a 1D Problem for a Half-Space, ZAMM-Z. Angew. Math. Me., vol. 94, pp. 509-515, 2014a.
-
Sherief, H.H. and Abd El-Latief, A.M., Application of Fractional Order Theory of Thermoelasticity to a 2D Problem for a Half-Space, Appl. Math. Comput., vol. 248, pp. 584-592, 2014b.
-
Sherief, H.H., El-Sayed, A.M.A., and Abd El-Latief, A.M., Fractional Order Theory of Thermoelasticity, Int. J. Solids Struct, vol. 47, pp. 269-275,2010.
-
Smith, D.W. and Booker, J.R., Green's Functions for a Fully Coupled Thermoporoelastic Material, Int. J. Numer. Anal. Met., vol. 17, pp. 139-163, 1993.
-
Tao, H.B., Liu, G.B., Xie, K.H., Zheng, R.Y., and Deng, Y.B., Characteristics of Wave Propagation in the Saturated Thermoelastic Porous Medium, Transp. Porous Media, vol. 103, pp. 47-68, 2014.
-
Xiong, C.H. and Guo, Y., Electromagneto-Thermoelastic Diffusive Plane Waves in a Half-Space with Variable Material Properties under Fractional Order Thermoelastic Diffusion, Int. J. Appl. Electrom., vol. 53, pp. 251-269, 2017.
-
Youssef, H.M., Theory of Fractional Order Generalized Thermoelasticity, J. Heat Transf., vol. 132, pp. 1-7, 2010.
-
Youssef, H.M. and Al-Lehaibi, E.A., Variational Principle of Fractional Order Generalized Thermoelasticity, Appl. Math. Lett, vol. 23, pp. 1183-1187, 2010a.
-
Youssef, H.M. and Al-Lehaibi, E.A., Fractional Order Generalized Thermoelastic Half-Space Subjected to Ramp-Type Heating, Mech. Res. Commun, vol. 37, pp. 448-452, 2010b.
-
Rao Ping-ping, Ouyang Pei-hao, Nimbalkar Sanjay, Chen Qing-sheng, Wu Zhi-lin, Cui Ji-fei, Analytical modelling of the mechanical damage of soil induced by lightning strikes capturing electro-thermal, thermo-osmotic, and electro-osmotic effects, Journal of Mountain Science, 19, 7, 2022. Crossref