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Structural Engineering and Mechanics Volume 63, Number 1, July10 2017 , pages 89-102 DOI: https://doi.org/10.12989/sem.2017.63.1.089 |
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A magneto-thermo-viscoelastic problem with fractional order strain under GN-II model |
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Sunita Deswal, Kapil Kumar Kalkal and Sandeep Singh Sheoran
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| Abstract | ||
| In this work, we present a theoretical framework to study the thermovisco-elastic responses of homogeneous, isotropic and perfectly conducting medium subjected to inclined load. Based on recently developed generalized thermoelasticity theory with fractional order strain, the two-dimensional governing equations are obtained in the context of generalized magneto-thermo-viscoelasticity theory without energy dissipation. The Kelvin-Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of the material. The resulting formulation of the field equations is solved analytically in the Laplace and Fourier transform domain. On the application of inclined load at the surface of half-space, the analytical expressions for the normal displacement, strain, temperature, normal stress and tangential stress are derived in the joint-transformed domain. To restore the fields in physical domain, an appropriate numerical algorithm is used for the inversion of the Laplace and Fourier transforms. Finally, we have demonstrated the effect of magnetic field, viscosity, mechanical relaxation time, fractional order parameter and time on the physical fields in graphical form for copper material. Some special cases have also been deduced from the present investigation. | ||
| Key Words | ||
| fractional order strain; GN-II model; magnetic field; viscosity; Laplace and Fourier transforms; inclined load | ||
| Address | ||
| Department of Mathematics, Guru Jambheshwar University of Science & Technology, Hisar-125001, Haryana, India | ||