Reference Temperature Dependent Thermoelastic Solid with Voids Subjected to Continuous Heat Sources

  • Sudip Mondal Basirhat College
Keywords: Lord Shulman Model, Thermoelastic Void Material, Eigenvalue Approach

Abstract

In the present article, the reference temperature dependency Lord--Shulman model of generalized thermoelasticity with voids subjected to a continuous heat source in a half-space is discussed. The Laplace transform together with eigenvalue approach technique is applied to find a closed-form solution for the physical variables viz. distribution of temperature, volume fraction field, deformation and stress field in the Laplace transform domain. The numerical inversions of those physical variables in the space-time domain are carried out by using the Zakian algorithm for the inversion of the Laplace transform. Numerical results are shown graphically and the results obtained are analyzed.

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Author Biography

Sudip Mondal, Basirhat College

Assistant Professor, Department of Mathematics, Basirhat College, 24PGS(N)–743412

References

Abbas, I. A. 2015a. A Dual Phase Lag Model on Thermoelastic Interaction in an InfiniteFiber–Reinforced Anisotropic Medium with a Circular Hole.Mechanics Based Design ofStructures and Machines43(4): 501–513. doi: 10.1080/15397734.2015.1029589.

Abbas, I. A. 2015b. Analytical Solution for a Free Vibration of a Thermoelastic Hol-low Sphere.Mechanics Based Design of Structures and Machines43(3): 265–276. doi:10.1080/15397734.2014.956244.

Abbas, I. A. 2017. Free vibration of a thermoelastic hollow cylinder under two–temperaturegeneralized thermoelastic theory.Mechanics Based Design of Structures and Machines45(3): 395–405. doi: 10.1080/15397734.2016.1231065.

Bachher, M., Sarkar, N., and Lahiri. A., Generalized Thermoelastic Infinite Medium withVoids Subjected to a Instantaneous Heat Sources with Fractional Derivative Heat Transfer.International Journal of Mechanical Sciences 89: 8491. doi:10.1016/j.ijmecsci.2014.08.029.

Biswas, S. 2019. Fundamental solution of steady oscillations for porous materials with dual–phase–lag model in micropolar thermoelasticity.Mechanics Based Design of Structures andMachines: 1–23. doi: 10.1080/15397734.2018.1557528.12

Caddock, B. D., and K. E. Evans. 1989. Microporous materials with negative Poissonsratios. I. Microstructure and mechanical properties.Journal of Physics D: Applied Physics22(12): 1877–1882. doi: 10.1088/0022–3727/22/12/012.

Stan Chirita, A. S. 2001. On the Spatial and Temporal Behavior in Linear Thermoe-lasticity of Materials with Voids.Journal of Thermal Stresses24(5): 433–455. doi:10.1080/01495730151126096.

Cowin, S. C., and J. W. Nunziato. 1983. Linear elastic materials with voids.Journal ofElasticity13(2): 125–147. doi: 10.1007/BF00041230.

Dhaliwal, R. S., and A. Singh. 1980. Dynamic coupled thermoelasticity. Hindustan Publish-ing Corporation.

Dhaliwal, R. S., and J. Wang. 1995. A heat–flux dependent theory of thermoelasticity withvoids.Acta Mechanica110(14): 33–39. doi: 10.1007/BF01215413.

Hilal, M. I. M., and M. I. A. Othman. 2016. Propagation of plane waves of magneto–thermoelastic medium with voids influenced by the gravity and laser pulse under G–N theory.Multidiscipline Modeling in Materials and Structures12(2): 326–344. doi:10.1108/MMMS–08–2015–0047.

Iesan, D. 1986. A theory of thermoelastic materials with voids.Acta Mechanica60(12):67–89. doi: 10.1007/BF01302942.

Kumar, R., and L. Rani. 2005. Deformation due to mechanical and thermal sources ingeneralized thermoelastic half–space with voids.Journal of Thermal Stresses28(2): 123145.doi: 10.1080/014957390523697.

Lakes, R. 1987. Foam Structures with a Negative Poissons Ratio. Science 235(4792): 1038–1040. doi: 10.1126/science.235.4792.1038.

Lee, T., and R. S. Lakes. 1997. Anisotropic polyurethane foam with Poissonsratio greaterthan 1.Journal of materials science32(9): 2397–2401. doi: 10.1023/A:1018557107786.

Lord, H. W., and Y. Shulman. 1967. A generalized dynamical theory of thermoelastic-ity.Journal of the Mechanics and Physics of Solids15(5): 299–309. doi: 10.1016/0022–5096(67)90024–5.

Othman, M. I. A., and E. M. Abd–Elaziz. 2015. The Effect of Thermal Loading Due toLaser Pulse in Generalized Thermoelastic Medium with Voids in Dual Phase Lag Model.Journal of Thermal Stresses38(9): 1068–1082. doi: 10.1080/01495739.2015.1073492.

Othman, M. I. A., and S. Y. Atwa. 2012. Response of Micropolar Thermoelastic Solid withVoids Due to Various Sources Under Green Naghdi Theory.Acta Mechanica Solida Sinica25(2): 197–209. doi: 10.1016/S0894–9166(12)60020–2.

Othman, M. I. A., and M. I. M. Hilal. 2015. Rotation and gravitational field effect on two–temperature thermoelastic material with voids and temperature dependent properties typeIII.Journal of Mechanical Science and Technology29(9): 3739–3746. doi: 10.1007/s12206–015–0820–8.

Othman, M. I., and K. Lotfy. 2010. The effect of thermal relaxation times on wave propaga-tion of micropolar thermoelastic medium with voids due to various sources.MultidisciplineModeling in Materials and Structures6(2): 214–228. doi: 10.1108/15736101011068000.13

Othman, M. I., M. E. Zidan, and M. I. Hilal. 2013. Effect of rotation on thermoelasticmaterial with voids and temperature dependent properties of type III.Journal of Thermoe-lasticity1(4): 1–11.

Puri, P., and S. C. Cowin. 1985. Plane waves in linear elastic materials with voids.Journalof Elasticity15(2): 167–183. doi: 10.1007/BF00041991.

Sarkar, N. 2013. On the discontinuity solution of the Lord–Shulman model in general-ized thermoelasticity.Applied Mathematics and Computation219(20): 10245–10252. doi:10.1016/j.amc.2013.03.127.[24] Sarkar, N., and A. Lahiri. 2012. A three–dimensional thermoelastic problem for a half–spacewithout energy dissipation.International Journal of Engineering Science51: 310–325. doi:10.1016/j.ijengsci.2011.08.005.

Sarkar, N., and A. Lahiri. 2013. The Effect of Gravity Field on the Plane Waves in a Fiber–Reinforced Two–Temperature Magneto–Thermoelastic Medium Under Lord–Shulman The-ory.Journal of Thermal Stresses36(9): 895–914. doi: 10.1080/01495739.2013.770709.

Scalia, A., A. Pompei, and S. Chirita. 2004. On the behavior of steady time–harmonicoscillations in thermoelastic materials with voids.Journal of Thermal Stresses27(3): 209–226. doi: 10.1080/01495730490264330.[27] Zakian, V. 1969. Numerical inversion of Laplace transform.Electronics Letters5(6): 120–121. doi: 10.1049/el:19690090.[28] Zakian, V. 1970. Optimisation of numerical inversion of Laplace transforms.ElectronicsLetters6(21): 677–679. doi: 10.1049/el:19690090

Published
2019-08-30
How to Cite
Mondal, S. (2019). Reference Temperature Dependent Thermoelastic Solid with Voids Subjected to Continuous Heat Sources. MathLAB Journal, 3, 78-90. Retrieved from http://purkh.com/index.php/mathlab/article/view/436
Section
Research Articles