Fibre-Reinforced Generalized Thermoelastic Medium under Hydrostatic Initial Stress

Abstract

The present problem is concerned with the deformation of an infinite fibre-reinforced generalized thermoe-lastic medium with hydrostatic initial stress under the influence of mechanical force. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress and temperature distribution. The numerical results are given and presented graphically for Green -Lindsay [4] theory of thermoelasticity. Comparisons are made in the presence and absence of hydrostatic initial stress and anisotropy.

The present problem is concerned with the deformation of an infinite fibre-reinforced generalized thermoe-lastic medium with hydrostatic initial stress under the influence of mechanical force. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress and temperature distribution. The numerical results are given and presented graphically for Green -Lindsay [4] theory of thermoelasticity. Comparisons are made in the presence and absence of hydrostatic initial stress and anisotropy.

Keywords

Generalized Thermoelastic, Hydrostatic Initial Stress, Fibre-Reinforced, Temperature Distribution, Normal Mode, Anisotropy

Generalized Thermoelastic, Hydrostatic Initial Stress, Fibre-Reinforced, Temperature Distribution, Normal Mode, Anisotropy

Cite this paper

nullP. Ailawalia and S. Budhiraja, "Fibre-Reinforced Generalized Thermoelastic Medium under Hydrostatic Initial Stress,"*Engineering*, Vol. 3 No. 6, 2011, pp. 622-631. doi: 10.4236/eng.2011.36074.

nullP. Ailawalia and S. Budhiraja, "Fibre-Reinforced Generalized Thermoelastic Medium under Hydrostatic Initial Stress,"

References

[1] A. E. Green and K. A. Lindsay, “Thermoelasticity,” Journal of Elasticity, Vol. 2, No. 1, 1972, pp. 1-7.
doi:10.1007/BF00045689

[2] H. W. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of Mechanics and Physics of solids, Vol. 15, No. 5, September 1967, pp. 299-309. doi:10.1016/0022-5096(67)90024-5

[3] I. M. Muller, “The Coldness, Universal Function in Ther- moelastic Bodies,” Ra-tional Mechanics Analysis, Vol. 41, No. 5, 1971, pp. 319-332.

[4] A. E. Green and N. Laws, “On the Entropy Production Inequality,” Archives of Rational Mechanics and Analysis, Vol. 45, No. 1, 1972, pp. 45-47.
doi:10.1007/BF00253395

[5] J. R. Barber, “Thermoelastic Displacements and Stresses Due to a Heat Source Moving over the Surface of a Half Plane,” ASME, Transactions, Journal of Applied Mecha- nics, Vol. 51, No. 3, 1984, pp. 636-640.
doi:10.1115/1.3167685

[6] H. H. Sherief, “Fundamental So-lution of the Generalized Thermoelastic Problem for Short Times,” Journal of Thermal Stresses, Vol. 9, No. 2, 1986, pp. 151-164.
doi:10.1080/01495738608961894

[7] R. S. Dhaliwal, S. R. Majumdar and J. Wang, “Thermoelastic Waves in an Infinite Solid Caused by a Line Heat Source,” International Journal of Mathematics and Mathematical Sciences, Vol. 20, No. 2, 1997, pp. 323-334.
doi:10.1155/S0161171297000434

[8] D. S. Chandrasek-haraiah and K. S. Srinath, “Thermoelastic Interactions without Energy Dissipation Due to a Point Heat Source,” Journal of Elasticity, Vol. 50, No. 2, 1998, pp. 97-108. doi:10.1023/A:1007412106659

[9] J. N. Sharma, R. S. Chauhan and R. Kumar, “Time- Harmonic Sources in a Gener-alized Thermoelastic Continuum,” Journal of Thermal Stresses, Vol. 23, No. 7, 2000, pp. 657-674. doi:10.1080/01495730050130048

[10] J. N. Sharma and R. S. Chauhan, “Mechanical and Thermal Sources in a Generalized Thermoelastic Half-Space,” Journal of Thermal Stresses, Vol. 24, No. 7, 2001, pp. 651-675. doi:10.1080/014957301300194823

[11] J. N. Sharma, P. K. Sharma and S. K. Gupta, “Steady State Response to Moving Loads in Thermoelastic Solid Media,” Journal of Thermal Stresses, Vol. 27, No. 10, 2004, pp. 931-951. doi:10.1080/01495730490440181

[12] S. Deswal and S. Choudhary, “Two-Dimensional Interactions Due to Moving Load in Generalized Thermoelastic Solid with Diffusion,” Ap-plied Mathematics and Mechanics, Vol. 29, No. 2, 2008, pp. 207-221.
doi:10.1007/s10483-008-0208-5

[13] A. C. Pipkin, “Finite Deformations of Ideal Fiber-Rein- forced Composites,” In: G. P. Sendeckyi, Ed, Composites materials, Academic, New York, 1973, pp. 251-308.

[14] T. G. Rogers, “Finite Deformations of Strongly Anisotropic Materials,” In: J. F. Hutton, J. R. A. Pearson, K. Walters, Eds., Theoretical Rheology, Applied Sci-ence Publication, London, 1975, pp. 141-168.

[15] T. G. Rogers, “Anisotropic Elastic and Plastic Materials,” In: P. Thoft-Christensen, Ed., Continuum Mechanics Aspects of Geodynamics and Rock Fracture, Mechanics, Reidel, 1975, pp. 177-200.

[16] M. S. Craig and V. G. Hart, “The Stress Bound-ary-Value Problem for Finite Plane Deformations of a Fi-bre-Rein- forced Material,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 32, No. 4, 1979, pp. 473-498.
doi:10.1093/qjmam/32.4.473

[17] P. R. Sengupta and S. Nath, “Surface Waves in Fobre-Reinforced Anisotropic Elastic Me-dia,” Sadhana, Vol. 26, No. 4, 2001, pp. 363-370. doi:10.1007/BF02703405

[18] B. Singh and S. J. Singh, “Re-flection of Plane Waves at the Free Surface of a Fi-bre-Reinforced Elastic Half- Space,” Sadhana, Vol. 29, No. 3, 2004, pp. 249-257.
doi:10.1007/BF02703774

[19] B. Singh, “Wave Propagation in an Incompressible Transversely Isotropic Fibre-Reinforced Elastic Media,” Archives of Applied Mechanics, Vol. 77, No. 4, 2007, pp. 253-258. doi:10.1007/s00419-006-0094-9

[20] B. Singh, “Effect of Anisotropy on Reflection Coefficients of Plane Waves in Fibre-Reinforced Thermoelastic Solid,” Inter-national Journal of Mechanics and Solids, Vol. 2, No. , 2007, pp. 39-49.

[21] R. Kumar and R. Gupta, “Dynamic Deforma-tion in Fibre-Reinforced Anisotropic Generalized Thermoelas-tic Solid under Acoustic Fluid Layer,” Multidispline Modeling in Materials and Structure, Vol. 5, No. 3, 2009, pp. 283-288. doi:10.1163/157361109789017014

[22] M. A. Biot, “Me-chanics of Incremental Deformations,” John Wiley, New York, 1965.

[23] A. Chattopadhyay, S. Bose and M. Chakraborty, “Reflection of Elastic Waves under Initial Stress at a Free Sur-face,” Journal of Acoustical Society of America, Vol. 72, No. 1, 1982, pp. 255-263. doi:10.1121/1.387987

[24] R. S. Sidhu and S. J. Singh, “Comments on ‘Reflection of Elastic Waves under Initial Stress at a Free Surface’,” Journal of Acoustical Society of America, Vol. 74, No. 5, 1983, pp. 1640-1642. doi:10.1121/1.390130

[25] S. Dey, N. Roy and A. Dutta, “Re-flection and Refraction of P-Waves under Initial Stresses at an Interface,” Indian Journal of Pure and Applied Mathematics, Vol. 16, No. , 1985, pp. 1051-1071.

[26] A. Montanaro, “On Singular Surface in Isotropic Linear Thermoelasticity with Initial Stress,” Journal of Acoustical Society of America, Vol. 106, No. 3, 1999, pp. 1586- 1588. doi:10.1121/1.427154

[27] B. Singh, A. Kumar and J. Singh, “Reflection of Generalized Thermoelastic Waves from a Solid Half-Space Under Hydrostatic Initial Stress,” Journal of Ap-plied Mathematics and Computation, Vol. 177, No. 1, June 2006, pp. 170-177. doi:10.1016/j.amc.2005.10.045

[28] B. Singh, “Effect of Hydrostatic Initial Stresses on Waves in a Thermoelastic Solid Half-Space,” Journal of Applied Mathe-matics and Computation, Vol. 198, No. 2, May 2008, pp. 494-505. doi:10.1016/j.amc.2007.08.072

[29] M. I. A. Othman and Y. Song, “Reflection of Plane Waves from an Elastic Solid Half-Space under Hydrostatic Initial Stress without Energy Dissipation,” International Journal of Solids and Structures, Vol. 44, No. 17, August 2007, pp. 5651-5664.
doi:10.1016/j.ijsolstr.2007.01.022

[30] P. Ailawalia, S. Kumar and G. Khurana, “Deformation in a Generalized Thermoelastic Medium with Hydrostatic Initial Stress Subjected to Different Sources,” Mechanics and Mechanical Engineering, Vol. 13, No. 1, 2009, pp. 5-24.

[31] P. Ailawalia, “Effect of Hydrostatic Initial Stress in Green-Naghdi (Type III) thermoelastic Half-Space Subjected to Ramp-Heating and Loading,” Journal of Technical Physics, Vol. 50, No. 4, 2009, 2010, pp. 403-415.