Fractional model of thermoelasticity for a half-space overlaid by a thick layer

被引:22
作者
Abd El-Latief, A. M. [1 ]
Khader, S. E. [2 ]
机构
[1] Univ Alexandria, Fac Sci, Dept Math, Alexandria, Egypt
[2] Dept Math & Theoret Phys Atom Energy Author, Alexandria, Egypt
来源
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik | 2015年 / 95卷 / 05期
关键词
Different materials; fractional calculus; half space; thermoelasticity; Laplace transform; GENERALIZED THERMOELASTICITY; HEAT-CONDUCTION; ORDER THEORY; MEMORY; UNIQUENESS; EQUATIONS; CRACK; TIME;
D O I
10.1002/zamm.201300174
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, we apply the fractional order theory of thermoelasticity to a 1D problem for a half-space overlaid by a thick layer of a different material. The upper surface of the layer is taken to be traction free and is subjected to a constant thermal shock. There are no body forces or heat sources affecting the medium. Laplace transform techniques are used to eliminate the time variable t. The solution in the transformed domain is obtained by using a direct approach. The inverse Laplace transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the fractional order theory are discussed and compared with those for the generalized theory of thermoelasticity. We also study the effect of the fractional derivative parameters of the two media on the behavior of the solution. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
收藏
页码:511 / 518
页数:8
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