Eigenvalue approach to a magneto-thermoelastic problem in transversely isotropic hollow cylinder: comparison of three theories

2019 ◽  
pp. 1-17 ◽  
Author(s):  
Siddhartha Biswas
Keyword(s):  
Hollow Cylinder ◽  
Transversely Isotropic ◽  
Thermoelastic Problem ◽  
Eigenvalue Approach

Eigenvalue Approach in a Generalized Thermal Shock Problem for a Transversely Isotropic Half-Space

2017 ◽  
Vol 05 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Ibrahim A. Abbas ◽  
Aatef D. Hobiny
Keyword(s):  
Fourier Transforms ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Eigenvalue Approach ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Matrix Differential ◽  
Vector Matrix ◽  
Thermal Shock Problem ◽  
Thermoelastic Theory

In the present work, the investigating of the disturbances in a homogeneous, transversely isotropic elastic medium with generalized thermoelastic theory has been concerned. The formulation is applied to generalized thermoelasticity based on three different theories. Laplace and Fourier transforms are used to solve the problem analytically. The essential equations have been written as a vector-matrix differential equation in the Laplace transform domain, then solved by an eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The result is used to solve a specific two-dimensional problem. The technique is illustrated by means of several numerical experiments performed. The results were verified numerically and are plotted.

scholarly journals Analytical and Numerical Solution of 2D Problem for Transversely Isotropic Generalized Thermoelastic Medium with Green-Naghdi Model II

2018 ◽  
Vol 23 (No 3, September 2018) ◽  
pp. 294-301
Author(s):  
Inrahim A. Abbas ◽  
Mohamed I. A. Othman
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Element Formulation ◽  
Eigenvalue Approach ◽  
Thermoelastic Medium ◽  
Mode Method ◽  
Generalized Thermoelastic

In this paper, a comparison was made between the analytical and numerical solution of a two-dimensional problem for a transversely isotropic generalized thermoelastic medium. The study is carried out in the context of generalized thermoelasticity proposed by Green and Naghdi’s theory of type II. The problem has been solved analytically using the normal mode method with the eigenvalue approach and numerically using a finite element method. The accuracy of the finite element formulation was validated by comparing the analytical and numerical solutions for the field quantities.

Transient Thermoelastic Fields in a Transversely Isotropic Infinite Solid With a Penny-Shaped Crack

1987 ◽  
Vol 54 (4) ◽  
pp. 854-860 ◽  
Author(s):  
N. Noda ◽  
F. Ashida
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transient Heat Conduction ◽  
Thermoelastic Problem ◽  
Conduction Equation ◽  
Thermal Stress Field ◽  
Penny Shaped Crack ◽  
Shaped Crack

The present paper deals with a transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid with a penny-shaped crack. A finite difference formulation based on the time variable alone is proposed to solve a three-dimensional transient heat conduction equation in an orthotropic medium. Using this formulation, the heat conduction equation reduces to a differential equation with respect to the spatial variables. This formulation is applied to attack the transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid containing a penny-shaped crack subjected to heat absorption and heat exchange through the crack surface. Thus, the thermal stress field is analyzed by means of the transversely isotropic potential function method.

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