Author
A. M. Abd El-Latief
Bio: A. M. Abd El-Latief is an academic researcher from Alexandria University. The author has contributed to research in topics: Laplace transform & Fractional calculus. The author has an hindex of 10, co-authored 18 publications receiving 661 citations.
Papers
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TL;DR: In this paper, a new theory of thermoelasticity is derived using the methodology of fractional calculus, and a uniqueness theorem for this model is proved and a variational principle and a reciprocity theorem are derived.
445 citations
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TL;DR: In this article, the authors considered the problem of a half-space formed of a material with variable thermal conductivity and applied the theory of fractional order theory of thermoelasticity to the problem.
119 citations
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TL;DR: In this paper, the fractional order theory of thermoelasticity was applied to a 1D thermal shock problem for a half-space, and the predictions of the theory were discussed and compared with those for the coupled and generalized theories of thermodynamic properties.
Abstract: In this work, we apply the fractional order theory of thermoelasticity to a 1D thermal shock problem for a half-space. Laplace transform techniques are used. The predictions of the theory are discussed and compared with those for the coupled and generalized theories of thermoelasticity. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.
44 citations
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TL;DR: In this paper, a new theory of thermoelasticity associated with two relaxation times is derived using the methodology of fractional calculus, and a uniqueness theorem and a reciprocity theorem for this model are derived.
Abstract: In this work, a new theory of thermoelasticity associated with two relaxation times is derived using the methodology of fractional calculus. The theories of coupled thermoelasticity and of generalized thermoelasticity (Green–Lindsay Model) with two relaxation times follow as limiting cases. A uniqueness theorem and a reciprocity theorem for this model are derived. A variational principle theorem is obtained.
32 citations
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TL;DR: In this paper, the fractional order theory of thermoelasticity was applied to a one-dimensional problem for a spherical cavity subjected to a thermal shock, and the predictions of the theory were discussed and compared with those for the generalized theory of thermodynamics.
Abstract: We apply the fractional order theory of thermoelasticity to a one-dimensional problem for a spherical cavity subjected to a thermal shock. The predictions of the theory are discussed and compared with those for the generalized theory of thermoelasticity.
29 citations
Cited by
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01 Jan 20153,828 citations
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01 Jan 1997TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
1,820 citations
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TL;DR: In this article, two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained.
Abstract: Two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained, uniqueness an...
300 citations
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TL;DR: In this article, a memory-dependent derivative (MDD) was introduced into the Lord and Shulman (LS) generalized thermoelasticity, which might be superior to fractional ones.
189 citations
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TL;DR: In this article, a generalized thermo-viscoelasticity theory with memory-dependent derivatives is constructed, and the governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to one-dimensional problem of a half-space.
144 citations