Vol. 14, No. 2, 2019

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The effect of variable thermal conductivity on an infinite fiber-reinforced thick plate under initial stress

Mohamed I. A. Othman, Ahmed E. Abouelregal and Samia M. Said

Vol. 14 (2019), No. 2, 277–293
Abstract

The present paper includes an analytical study of the effect of variable thermal conductivity and initial stress on a fiber-reinforced transversely isotropic thick plate. The model of the equations of generalized thermoelasticity with phase lags in an isotropic elastic medium with temperature-dependent mechanical properties are established. The upper surface of the plate is thermally insulated with prescribed surface loading while the lower surface of the plate rests on a rigid foundation and temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress and temperature distribution. Numerical results for the physical quantities are given and illustrated graphically with temperature-dependent and temperature-independent thermal conductivity. A comparison is made with results obtained with initial stress and without initial stress. Also, a comparison is made with results obtained with reinforcement and without reinforcement proprieties. It is found from the graphs that the initial stress, the reinforcement and phase lags have great effects on the distribution of the field quantities.

Keywords
dual-phase-lag model, fiber-reinforced, initial stress, normal mode analysis, variable thermal conductivity, thick plate
Milestones
Received: 18 April 2018
Revised: 23 March 2019
Accepted: 2 May 2019
Published: 26 July 2019
Authors
Mohamed I. A. Othman
Department of Mathematics, Faculty of Science
Zagazig University
Egypt
Ahmed E. Abouelregal
Department of Mathematics, Faculty of Science
Mansoura University
Mansoura
Egypt
Department of Mathematics, College of Science and Arts
Aljouf University
El-Qurayat
Saudi Arabia
Samia M. Said
Department of Mathematics, Faculty of Science
Zagazig University
Zagazig
Egypt
Department of Mathematics, Faculty of Science and Arts
Qassim University
Al-mithnab
Saudi Arabia