Abstract
The present work is aimed at studying the effect of fractional order and thermal relaxation time on an unbounded fiber-reinforced medium. In the context of generalized thermoelasticity theory, the fractional time derivative and the thermal relaxation times are employed to study the thermophysical quantities. The techniques of Fourier and Laplace transformations are used to present the problem exact solutions in the transformed domain by the eigenvalue approach. The inversions of the Fourier-Laplace transforms hold analytical and numerically. The numerical outcomes for the fiber-reinforced material are presented and graphically depicted. A comparison of the results for different theories under the fractional time derivative is presented. The properties of the fiber-reinforced material with the fractional derivative act to reduce the magnitudes of the variables considered, which can be significant in some practical applications and can be easily considered and accurately evaluated.
Highlights
Fiber-reinforced composites are used widely in structural engineering
A fiber-reinforced thermoelastic material is a composite material that exhibits strongly anisotropic elastic behaviors such that elastic parameters have extensions in the fiber directions that are on the order of 50 or more times greater than their parameter in the transverse directions
The aim of this paper is to study the effect of a fractional order derivative in a two-dimensional fiber-reinforced anisotropic material
Summary
Fiber-reinforced composites are used widely in structural engineering. Continuous models are used to illustrate the mechanical properties of these materials. Sengupta and Nath [5] studied the problem of surface waves in fiber-reinforced anisotropic elastic materials. Singh [7] discussed the problem of reflections of a plane wave on the free surfaces of a fiber-reinforced elastic plane. Lotfy and Othman [12] investigated the effects of magnetic fields for mode-I cracks on a fiber-reinforcing two-dimensional problem under a generalized thermoelastic model. Abbas et al [21,22,23] used the finite element method to study several problems of thermoelastic interaction in fiber-reinforced media. Many researchers have discussed many problems in fiber-reinforced media due to thermal/mechanical loadings using different methods as previously published [24,25,26,27,28,29,30]. For the considered physical quantities, numerical outcomes are obtained and presented graphically
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