Thermal disturbances in twinned orthotropic thermoelastic material

• Autorzy: Rani L. , Singh V.

Identyfikatory

DOI

10.2478/ijame-2018-0050

• Języki publikacji: EN

Abstrakty

EN

This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.

Słowa kluczowe

EN

generalized thermoelasticity; orthotropic material; relaxation time; Fourier transforms; instantaneous loading

PL

termoelastyczność; transformaty Fouriera; czas relaksacji

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2018
• Tom: Vol. 23, no. 4
• Strony: 897--910
• Opis fizyczny: Bibliogr. 34 poz., rys., wykr.

Twórcy

autor

Rani L.

• School of Basic and Applied Sciences, Galgotias University Greater Noida, U.P, INDIA

autor

Singh V.

• School of Basic and Applied Sciences, Galgotias University Greater Noida, U.P, INDIA

Bibliografia

• [1] Duhamel J.M.C. (1837): Second memoire sur les phenomenes thermo-mecaniques. – J. de I’Ecole Polytechnique, vol.15, pp.1-15.
• [2] Neumann F. (1855): Vorlesungen uber die Theorie der Elastizität der Festen Körpern. – Leipzig.
• [3] Voigt W. (1910): Lehrbuch Kristall Physik. – Teubner.
• [4] Jeffreys H. (1930): The thermodynamics of an elastic solid. – Proc. Cambr. Philos. Soc., vol.26, pp.101-106.
• [5] Biot M.A. (1956): Thermoelasticity and irreversible thermodynamics. – J. Appl. Phys., vol.27, pp.240-253.
• [6] Hetnarski R.B. (1961): Coupled one-dimensional thermal shock problem for small time. – Arch. Mech. Stos., vol.13, pp.259-306.
• [7] Boley B.A. (1964): High Temperature Structures and Materials. – Oxford: Pergamon Press.
• [8] Lord H.W. and Shulman Y. (1967): A generalized dynamical theory of thermoelasticity.– J. Mech. Phys. Solids, vol.15, pp.299-309.
• [9] Müller I. (1971): The coldness, a universal function in thermoelastic bodies. – Arch. Rat. Mech. Anal., vol.41, pp.319-332.
• [10] Green A.E and Laws N. (1972): On the entropy production inequality. – Arch. Rat. Mech. Anal, vol.54, pp.17-53.
• [11] Green A.E. and Lindsay K.A. (1972): Thermoelasticity. – J. Elasticity, vol.2, pp.1-7.
• [12] Dhaliwal R.S. and Sherief H.H. (1980): Generalized thermoelasticity for anisotropic media. – Quart. of Applied Mathematics, vol.38, pp.1-8.
• [13] Wilms E.V. and Cohen H. (1985): Some one-dimensional problems in coupled thermoelasticity. – Mechanics Research Communications, vol.12, No.1, pp.41-47.
• [14] Green A.E. and Naghdi P.M. (1993): Thermoelasticity without energy dissipation. – J. Elasticity, vol.31, pp.189-208.
• [15] Dolotov M.V. ans Kill I.D. (1996): The coupled dynamic problem of thermoelasticity for a half-space. – Journal of Applied Mathematics and Mechanics, vol.60, No.4, pp.683-686.
• [16] Tzou D.Y. (1995): A unified field approach for heat conduction from macro to micro-scales. – ASME J. Heat Transf., vol.117, pp.8–16.
• [17] Chandrasekharaiah D.S. (1998): Hyperbolic thermoelasticity: A review of recent literature. – Appl. Mech. Rev., vol.51, pp.705–729.
• [18] Hetnarski R.B. and Ignaczak J. (1999): Generalized thermoelasticity. – J. Thermal Stresses, vol.22, pp.451-476.
• [19] Hetnarski R.B. and Ignaczak J.(1996): Solition-like waves in a flow temperature nonlinear thermoelastic solid. – Int. J. Engng. Sci., vol.34, pp.1767-1787.
• [20] Ishihara S., Goshima T., Iwawaki S., Shimizu M. and Kamiya S. (2002): Evaluation of thermal stresses induced in anisotropic material during thermal shock. – Journal of Thermal Stresses, vol.25, pp.647-661.
• [21] Kumar R. and Rani L. (2004): Deformation due to mechanical and thermal sources in generalized orthorhombic thermoelastic material. – Sadhana, vol.29, pp.429-447.
• [22] Kumar R. and Rani L. (2007): Disturbance due to mechanical and thermal sources in orthorhombic thermoelastic material. – IJAME, vol.12, pp.677-692.
• [23] Weinmann (2009): Equations of thermelasticity with time dependent coefficients. – J. Math. Anal. Appl. vol.350, pp.81–99.
• [24] Hany H., Sherief A.M. Abd El-Latief (2014): Application of fractional order theory of thermoelasticity to a 2D problem for a half-space. – Applied Mathematics and Computation, vol.248, pp.584–592.
• [25] Sciarra F.M.D. and Salerno M. (2014): On thermodynamic functions in thermoelasticity without energy dissipation. – European Journal of Mechanics - A/Solids, vol.46, pp.84-95.
• [26] Abbas I.A., Kumar R. and Rani L. (2015): Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating. – Applied Mathematics and Computation, vol.254, pp.360–369.
• [27] Abbas I.A. (2016): Eigenvalue approach to fractional order thermoelasticity for an infinite body with a spherical cavity. – Journal of the Association of Arab Universities for Basic and Applied Sciences, vol.20, pp.84-88.
• [28] El-Karamany A.S. and Ezzat M.A. (2016): On the phase- lag Green-Naghdi thermoelasticity theories. – Applied Mathematical Modelling, vol.40, pp.5643-5659.
• [29] Abbas I.A. and Marin M. (2017): Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating. – Vol.87, pp.254–260.
• [30] Leseduarte M.C., Quintanilla R. and Racke R. (2017): On (non-)exponential decay in generalized thermoelasticity with two temperatures. – Applied Mathematics Letters, in press, Accepted Manuscript, Available online 1 March 2017.
• [31] Choudhuri S.S.R. (2007): On a thermoelastic three-phase-lag model. – J. Thermal Stresses, vol.30, pp.231-238.
• [32] Ting T.C.T. (2000): Recent developments in anisotropic elasticity. – International Journal of Solids and Structures, vol.37, pp.401–409.
• [33] Destrade M. (2003): Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds. – Mechanics of Materials, vol.35, pp.931-939.
• [34] Press W.H., Teukolsky S.A., Vellerling W.T. and Flannery B.P. (1986): Numerical recipes. – Cambridge: Cambridge Univ. Press.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)