Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating

In this paper, the thermoelastic interactions in a homogeneous, thermally conducting cubic crystal, elastic half-plane has been studied. A linear temperature ramping function is used to more realistically model. The general solution obtained is applied to a specific problem of a half space subjected to ramp-type heating. The components of displacement, stresses, and temperature distribution are obtained by applying a numerical finite element method. Some particular cases are also discussed in the context of the problem. The comparison in Lord and Shulman (LS), Green and Lindsay (GL) and Green and Naghdi (GN) theories have been shown graphically to estimate the effect of ramping parameter of heating for isothermal boundary.

[1]  Ashraf M. Zenkour,et al.  Dual-Phase-Lag Model on Thermoelastic Interactions in a Semi-Infinite Medium Subjected to a Ramp-Type Heating , 2014 .

[2]  Ibrahim A. Abbas,et al.  Plane Deformation Due to Thermal Source in Fractional Order Thermoelastic Media , 2013 .

[3]  Hany H. Sherief,et al.  Generalized thermoelasticity for anisotropic media , 1980 .

[4]  P. M. Naghdi,et al.  ON UNDAMPED HEAT WAVES IN AN ELASTIC SOLID , 1992 .

[5]  Ibrahim A. Abbas,et al.  Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method , 2011 .

[6]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[7]  Mohammad Matin,et al.  Eigenvalue Solution of Thermoelastic Damping in Beam Resonators Using a Finite Element Analysis , 2007 .

[8]  Ibrahim A. Abbas,et al.  Generalized Thermoelasticity of Thermal-Shock Problem in a Non-homogeneous Isotropic Hollow Cylinder with Energy Dissipation , 2012 .

[9]  Magdy A. Ezzat,et al.  State Space Approach for Conducting Magneto-Thermoelastic Medium with Variable Electrical and Thermal Conductivity Subjected to Ramp-Type Heating , 2009 .

[10]  Ibrahim A. Abbas,et al.  Response of thermal source in a transversely isotropic thermoelastic half-space with mass diffusion by using a finite element method , 2012 .

[11]  D. Tzou A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales , 1995 .

[12]  Ibrahim A. Abbas,et al.  Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli , 2012 .

[13]  P. Wriggers Nonlinear Finite Element Methods , 2008 .

[14]  P. M. Naghdi,et al.  Thermoelasticity without energy dissipation , 1993 .

[15]  D. Chandrasekharaiah,et al.  Hyperbolic Thermoelasticity: A Review of Recent Literature , 1998 .

[16]  Tong Earn Tay Finite element analysis of thermoelastic coupling in composites , 1992 .

[17]  Rajneesh Kumar,et al.  DEFORMATION DUE TO THERMAL SOURCE IN MICROPOLAR THERMOELASTIC MEDIA WITH THERMAL AND CONDUCTIVE TEMPERATURES , 2013 .

[18]  I. Abbas,et al.  Three-Phase Lag Model on Thermoelastic Interaction in an Unbounded Fiber-Reinforced Anisotropic Medium with a Cylindrical Cavity , 2014 .

[19]  Ibrahim A. Abbas,et al.  Deformation Due to Thermal Source in Micropolar Generalized Thermoelastic Half-Space by Finite Element Method , 2014 .

[20]  J. N. Sharma,et al.  Propagation of generalized thermoelastic waves in cubic crystals , 1990 .

[21]  Ibrahim A. Abbas,et al.  A Nonlinear Generalized Thermoelasticity Model of Temperature-Dependent Materials Using Finite Element Method , 2012 .

[22]  Ibrahim A. Abbas,et al.  Generalized Magneto-thermoelastic Interaction in a Fiber-Reinforced Anisotropic Hollow Cylinder , 2012, International Journal of Thermophysics.

[23]  Ashraf M. Zenkour,et al.  LS model on electro–magneto–thermoelastic response of an infinite functionally graded cylinder , 2013 .

[24]  Ibrahim A. Abbas,et al.  Plane Waves in Generalized Thermo-microstretch Elastic Solid with Thermal Relaxation Using Finite Element Method , 2012 .

[25]  Ibrahim A. Abbas,et al.  Finite element analysis of two-temperature generalized magneto-thermoelasticity , 2009 .

[26]  Tasawar Hayat,et al.  Effects of Heat Transfer in Flow of Nanofluids Over a Permeable Stretching Wall in a Porous Medium , 2014 .

[27]  Ibrahim A. Abbas,et al.  Two-temperature generalized thermoelasticity under ramp-type heating by finite element method , 2013 .

[28]  Hamdy M. Youssef,et al.  Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading , 2006 .

[29]  P. M. Naghdi,et al.  A re-examination of the basic postulates of thermomechanics , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[30]  Yih-Hsing Pao,et al.  THERMOELASTIC WAVES IN ANISOTROPIC SOLIDS , 1974 .

[31]  Li Xu,et al.  A generalized theory of thermoelasticity for an anisotropic medium , 1992 .

[32]  Hamdy M. Youssef,et al.  Generalized Thermoelastic Infinite Layer Subjected to Ramp-Type Thermal and Mechanical Loading under Three Theories—State Space Approach , 2009 .

[33]  M. Biot Thermoelasticity and Irreversible Thermodynamics , 1956 .

[34]  Ibrahim A. Abbas,et al.  A GN model for thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a circular hole , 2013, Appl. Math. Lett..

[35]  M. Eslami,et al.  Classical and generalized coupled thermoelasticity analysis in one-dimensional layered media , 2012 .

[36]  H. Lord,et al.  A GENERALIZED DYNAMICAL THEORY OF THERMOELASTICITY , 1967 .