Ibrahim A. Abbas

Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays

In this paper, the exponential stability problem is investigated for a class of Cohen-Grossberg neural networks with Markovian jumping parameter and mixed time-delays. The mixed time-delays under consideration consist of both the mode-dependent discrete time-delays and the mode-dependent distributed time-delays. By constructing a new Lyapunov-Krasovskii functional and employing the stochastic analysis techniques, sufficient conditions are proposed to guarantee that the addressed neural networks are exponentially stable in the mean square sense. It is shown that the developed stability criteria can be easily verified by using the standard numerical software. Finally, an illustrative example is provided to show the feasibility and usefulness of the developed results.

Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties

A three-dimensional model of the generalized thermoelasticity without energy dissipation under temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of the reference temperature. The resulting formulation in the context of Green and Naghdi model II is applied to a half-space subjected to a time-dependent heat source and traction free surface. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the field quantities are given in the physical domain and illustrated graphically. The results are also compared to results obtained in the case of temperature-independent modulus of elasticity.

A Dual Phase Lag Model on Thermoelastic Interaction in an Infinite Fiber-Reinforced Anisotropic Medium with a Circular Hole

The model of generalized thermoelasticity proposed by dual phase lag (DPL), is applied to study the thermoelastic interactions in an infinite fiber-reinforced anisotropic medium with a circular hole. A decaying with time thermal field on the boundary of the hole, which is stress free, causes the thermoelastic interactions. The solutions for displacement, temperature, and stresses are obtained with the help of the finite element procedure. The effects of the reinforcement on temperature, stress, and displacement are studied. The exact solution in the case of isotropic medium is discussed explicitly. The accuracy of the finite element method validated by comparing between the finite element and exact solutions for absence the reinforcement.

Generalized thermoelastic interaction in a fiber-reinforced anisotropic half-space under hydrostatic initial stress

The propagation of plane waves in fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord-Shulman under hydrostatic initial stress is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of pressure. It is found that the hydrostatic initial stress has a great effect on the distribution of field quantities.

A GN MODEL FOR THERMOELASTIC INTERACTION IN AN UNBOUNDED FIBER-REINFORCED ANISOTROPIC MEDIUM WITH A CIRCULAR HOLE

Abstract In this work, we have constructed the equations for generalized thermoelasticity of an unbounded fiber-reinforced anisotropic medium with a circular hole. The formulation is applied in the context of Green and Naghdi (GN) theory. The thermoelastic interactions are caused by (I) a uniform step in stress applied to the boundary of the hole with zero temperature change and (II) a uniform step in temperature applied to the boundary of the hole which is stress-free. The solutions for displacement, temperature and stresses are obtained with the help of the finite element procedure. The effects of the reinforcement on temperature, stress and displacement are studied. Results obtained in this work can be used for designing various fiber-reinforced anisotropic elements under mechanical or thermal load to meet special engineering requirements.

Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

In this paper, we construct the equations of generalized thermoelasticity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

A GN model based upon two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity

Two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity are presented.The eigenvalue approach techniques are used to solve the non-dimensional coupled equations in the domain of Laplace.The graphical results indicate that the two-temperature parameter has significant effects on all the physical quantities. In this paper, a general solution to the field equations of two-temperature generalized thermoelastic theory in an unbounded medium with a spherical cavity has been obtained in the context of Green and Naghdi model. The eigenvalue approach is adopted for the solution of application for unbounded medium with a spherical cavity. The medium is assumed to be initially quiescent. The inner surface of the cavity is taken traction free and subjected to a ramp-type heating. The Laplace transform technique is used. Some comparison have been shown in figures to estimate the effect of the ramp type and two-temperature parameters.

Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method:

In this article, the magneto-thermo analysis problem of an infinite functionally graded (FG) hollow cylinder is studied. The radial displacement, mechanical stresses and temperature, as well as the electromagnetic stress, are all investigated along the radial direction of the infinite cylinder. Material properties are assumed to be graded in the radial direction according to a novel power-law distribution in terms of the volume fractions of the metal and ceramic constituents. The inner surface of the FG cylinder is pure metal, whereas the outer surface is pure ceramic. The equations of motion and the heat-conduction equation are used to derive the governing second-order differential equations. A finite element scheme is presented for the numerical purpose. The system of differential equations is solved numerically and some plots for displacement, radial and electromagnetic stresses, and temperature are presented.

A PROBLEM OF GENERALIZED MAGNETOTHERMOELASTICITY FOR AN INFINITELY LONG, PERFECTLY CONDUCTING CYLINDER

This article concerns the investigation of the stress, temperature, and magnetic field in a transversely isotropic, elastic cylinder of infinite length and perfectly conducting material placed in a primary constant magnetic field when the curved surface of the cylinder is subjected to periodic loading. The analysis encompasses Lord and Shulman and Green and Lindsay theories of generalized thermoelasticity to account for the finite velocity of heat equation. The analysis of the numerical results for stress, temperature, and numerical values of the perturbed magnetic field in the free space is carried out at various points of the cylindrical medium. It is found that the effect of the applied magnetic field is an increase in the elastic wave velocity or, in other words, the increase of the solidity of the body. Furthermore, it has been shown graphically that the stress and perturbed magnetic field are modified due to the thermal relaxation time effect. In the absence of the magnetic field or relaxation times, our results reduce to those of generalized thermoelasticity and classical dynamical thermoelasticity, respectively.

Nonlinear Transient Thermal Stress Analysis of Temperature-Dependent Hollow Cylinders Using a Finite Element Model

In this paper, the nonlinear transient thermal stress analysis is conducted for temperature-dependent hollow cylinders subjected to a decaying-with-time thermal field. By the finite element method, the highly nonlinear governing equations are solved. The time histories of temperature, displacement, and stress due to the decaying-with-time thermal load are computed. A sensitivity analysis includes the effects of exponent of the decayed heat flux and temperature-dependency of density and material properties is carried out. Numerical results show some interesting characteristics of the thermoelastic behaviors of the hollow cylinders studied. In particular, the effect of temperature-dependency of the material properties on the thermoelastic parameters was demonstrated to be significant.