Generalized Thermo-Viscoelasticity under Three Theories

• Autorzy: Othman M. I. A.
• Języki publikacji: EN

Abstrakty

EN

The model of the equations of the two-imensional generalized thermo-viscoelasticity based on Lord-Shultnan (L-S), Green and Lindsay (G-L) and Classical dynamical-coupled (CD) theories are studied. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, displacement components, and the thermal stresses. The resulting formulation is applied to two different concrete problems. The first concerns to the case of a heat, punch across the surface of a semi-infinite thermo-viscoelastic half-space subject to appropriate boundary conditions. The second deals with a plate with thermo-isolated surfaces subjected to a time-dependent compression. A comparison is carried out between temperature, displacement and stress as calculated for each problem from view of the different theories of generalized thermo-viscoelasticity. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by three theories. The analysis presented in this paper is more general than any previous investigation.

Słowa kluczowe

EN

generalized thermoelasticity; temperature; displacement; stress

PL

teoria sprężystości; temperatura; przemieszczenie; naprężenie

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2009
• Tom: Vol. 13, nr 1
• Strony: 25--44
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Othman M. I. A.

• Faculty of Education, Department of Mathematics, Salalah-211, P.O. Box 2801, Sultanate of Oman

Bibliografia

• [1] Gross, B: Mathematical structure of the theories of viscoelasticity, Hermann, Paris, 1953).
• [2] Staverman, A.J. and Schwarzl, F.: Die physik der hochpolymeren, Ed. H. A. Stuart, vol. 4, Springer Verlag, Ch. 1, (1956).
• [3] Alfrey T. and Gurnee, E.F.: Rheology theory and applications, Ed. F. R. Eirich, vol. 1, Academic Press, New York, (1956).
• [4] Ferry, J.D.: Viscoelastic properties of polymers, J. Wiley and Sons, New York, (1970).
• [5] Biot, M.A.: Theory of stress-strain relations in an isotropic viscoelasticity, and relaxation phenomena, J. Applied Physics, 25, (1954).
• [6] Biot, M.A.: Variational principal in irreversible thermodynamics with application to viscoelasticity, Physical Review, 97, (1955).
• [7] Morland, L.W. and Lee, E.H.: Trans Soc. RheoL, 4, (1960).
• [8] Tanner, R.I.: Engineering rheology, Oxford Un. Press., (1988).
• [9] Huilgol, R. and Phan-Thien, N.: Fluid mechanics of viscoelasticity, Elsevier, (1997).
• [10] Bland, D.R.: The theory of linear viscoelasticity, Pergamon Press, Oxford, (1960).
• [11] Gurtin, M.E. and Sternberg, E.: On the linear theory of viscoelasticity, Arch. Ration. Mech. Anal, 11, 182-191, (1962).
• [12] Sternberg, E.: On the analysis of thermal stresses in viscoelastic solids, Brown Univ. Dir, Appl. Math. TR., 19, 213-219, (1963).
• [13] Ilioushin, A.A.: The approximation method of calculating the constructures by linear thermal viscoelastic theory, Mekhanika Polimerov, Riga, 2, 168-178, (1968).
• [14] Ilioushin, A.A. and Pobedria, B.E.: Mathematical theory of thermal visco-elasticity, Nauka, Moscow, (1970).
• [15] Pobedria, B.E.: Coupled problems in continuum mechanics, J. Durabilility and plasticity, No. l, Moscow State University, Moscow, (1984).
• [16] Koltunov, M.A.: Creeping and relaxation, Moscow, (1976).
• [17] Lord, H. and Shulman, Y.: A Generalized dynamical theory of thermo-elasticity, J. Mech. Phys. Solid, 15, 299-309, (1967).
• [18] Dhaliwal, R. and Sherief, H.H.: Generalized thermoelasticity for an isotropic media, Quart. Appl. Math., 33, 1-8, (1980).
• [19] Ezzat, M.A., Othman, M.I.A. and El Karamany, A.S.: State space approach to two-dimensional generalized thermo-viscoelasticity with one relaxation time, J. Thermal Stresses, 25, 259-316, (2002).
• [20] Othman, M.I.A.: Generalized electromagneto-thermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time, Ada Mechanica, 169, no. 1-4, 37-51, (2004).
• [21] Miiller, I.: The Coldness, A Universal function in thermo-elastic Solids, Arch. Rat. Mech. Anal., 41, 319, (1971).
• [22] Green, A.E. and Laws, N.: On the entropy production inequality, Arch. Rat. Mech. Anal., 45, 47, (1972).
• [23] Green, A.E. and Lindsay, K.A.: Thermoelasticity, J. Elasticity, 2, 1, (1972).
• [24] Suhubi, E.S.: Thermoelastic solids. In Continuum Physics II, Ch. 2 ed. A. C. Erin-gen., Academic Press, New York, (1975).
• [25] Ezzat, M.A. and Othman, M.I.: Electromagneto-thermoelastic plane waves with two relaxation times in a medium of perfect conductivity, Int. J. Engng. Sci., 38, 107-120, (2000).
• [26] Fung, Y.C.: Foundation of solid mechanics, Prentice-Hall, Englewood Cliffs, NJ, (1968).