Transient Thermoelastic Analysis of Pressurized Thick Spheres Subjected to Arbitrary Boundary and Initial Conditions (original) (raw)

Generalized thermoelasticity problem of a hollow sphere under thermal shock

European Journal of Pure and Applied Mathematics, 2009

This problem deals with the thermo-elastic interaction due to step input of temperature on the boundaries of a homogeneous isotropic spherical shell in the context of generalized theories of thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector-matrix differential equation which is then solved by eigen value approach. The inverse of the transform solution is carried out by applying a method of Bellman et al. Stresses, displacements and temperature distribution have been computed numerically and presented graphically in a number of figures for copper material. A comparison of the results for different theories (CTE, CCTE, TRDTE(GL), TEWOED(GN-II), TEWED(GN-III)) is presented. When the outer radius of the shell tends to infinity, the corresponding results agree with that of existing literature.

Thermoelastic Behaviour in a Multilayer Composite Hollow Sphere with Heat Source

Journal of Solid Mechanics, 2020

This paper deals with the mathematical approach to discuss the radially varying transient temperature distribution in a multilayer composite hollow sphere subjected to the time independent volumetric generation of heat in each layer. Initially the layers are at arbitrary temperature and the analysis assumes all the layers of the body are thermally isotropic and having a perfect thermal contact. It is novel to obtain the exact solution for temperature field by the separation of variables by splitting the problem into two parts homogeneous transient and non-homogeneous steady state. The set of equations obtained are solved by using the rigorous applications of analytic techniques with the help of eigen value expansion method. The thermoelastic response is studied in the context of uncoupled Thermoelasticity. The results obtained pointed out that the magnitude and distribution of the temperature and thermal stresses are greatly influenced by the layered heat generation parameter. The a...

Transient response of multilayered hollow cylinder using various theories of generalized thermoelasticity

Natural Science, 2010

The present paper deals with thermoelastic problems of finitely long hollow cylinder composed of two different materials with axial symmetry. The medium is traction-free, with negligible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoelasticity are written in terms of displacement and temperature increment. The exact solution of the problem, using different theories of generalized thermoelasticity, has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphically to find the responses of different theories.

Solution for One-Dimensional Transient Heat Conduction And Thermoelasticity in a Multilayer Hollow Sphere

2018

An analytical solution is obtained for the problem of one dimensional transient heat conduction and thermo elasticity in the multilayered hollow sphere. The sphere has multiple layers in the radial direction and each layer is time dependent and spatially without heat sources are considered. To obtain the temperature distribution The eigen value problem is solved by use of separation of variables method. At t > 0 homogenous boundary conditions of the first kind are set on the inner radial surface (i = 1, r = r0) and third kind are set on the outer (i = n, r = rn) radial surfaces (Convection).

Analytical solution of dynamic thermo elasticity problem for the FGM thick-walled sphere

Abstract: Thermo-mechanical analysis of functionally graded hollow sphere subjected to time dependant mechanical and thermal boundary conditions is carried out analytically in this study. The material properties are assumed to vary non-linearly in the radial direction, and the Poisson’s ratio is assumed constant. For thermal boundary conditions, temperature is prescribed on both surfaces whereas for mechanical boundary conditions tractions are prescribed on the boundaries. Obtaining the distribution of the temperature, the dynamical structural problem is solved and closed form solution is obtained for stress components. Keywords: Thermoelasticity; FGM; hollow sphere; Hankel transform; thermal shock; wave propagation

Transient Thermoelastic Analysis of a Cylinder Having a Varied Coefficient of Thermal Expansion

Periodica Polytechnica Mechanical Engineering

This paper is concerned with the mathematical modeling of transient thermal elastic problem involving a layered cylinder with a varied coefficient of thermal expansion and powered by a heat flux from an external surfaces. All material's properties are the same for each cylinder's layers, besides the coefficient of linear thermal expansion which is varied and corresponds to hardened and unhardened layers. An obtained solution is a transient state of a heat transfer for the one-dimensional temperature change under the action of heat flux in continuous time. Cumbersome analytical solutions are converted into simple approximation. They are used to solve the inverse problems of the thermal stressed state–determining the time of action of the heat flux to achieve the specified maximum temperature or stress. Some numerical results for the stress distributions are shown in figures.

THERMOELASTIC BEHAVIOR OF THIN HOLLOW CYLINDER WITH INTERNAL MOVING HEAT SOURCE

The present paper intended to reveal the stresses and temperature distribution in a thin hollow cylinder. The author has investigated the transient thermoelastic problem for evaluation of temperature distribution, displacement and thermal stresses of a thin hollow cylinder. The known boundary conditions are utilized for this purpose. The integral transform technique delivers the solution to the problem. The outcome of this analysis contains an infinite series. The variation of said parameters observed by using necessary graphs.

Thermoelastic Behavior In Thin Hollow Cylinder using Internal Moving Heat Source

Blue Eyes Intelligence Engineering & Sciences Publication , 2019

A hollow cylinder having cylindrical hole at the center has been examined under the temperature variation condition. This composition deals with study of temperature distribution in thin hollow cylinder and corresponding stresses. The author has worked to carry out the transient thermo elastic problem for evaluation of temperature distribution, displacement and thermal stresses of a thin hollow cylinder. The known non homogeneous boundary conditions are applied to obtain the solution of this problem. The integral transform technique yields the solution to the problem. The analysis contains an infinite series. The variation of said parameters observed and analyzed by using necessary graphs.

Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green–Lindsay theory

Acta Mechanica, 2009

This paper is concerned with the investigation of thermoelastic displacements and stresses in a functionally graded spherically isotropic hollow sphere due to prescribed temperature in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Both the surfaces of the body are free from radial stresses, and the inner surface is subjected to a time-dependent thermal shock whereas the outer one is maintained at constant temperature. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by an eigenvalue approach. The numerical inversion of the transforms is carried out using a method of Bellman et al. The displacements and stresses are computed and presented graphically. It is found that the variation of the thermophysical properties of a material as well as the thickness of the body strongly influence the response to loading. A comparative study with the corresponding homogeneous material has also been made. The solution of the problem of a spherically isotropic infinite medium containing a spherical cavity has been derived theoretically by tending the outer radius to infinity, as a particular case.

Two-Temperature Generalized Thermoelasticity in a Fiber-Reinforced Hollow Cylinder Under Thermal Shock

International Journal for Computational Methods in Engineering Science and Mechanics, 2013

This work is dealing with two-temperature generalized thermoelasticity without energy dissipation infinite medium with spherical cavity when the surface of this cavity is subjected to laser heating pulse. The closed form solutions for the two types of temperature, strain, and the stress distribution due to time exponentially decaying laser pulse are constructed. The Laplace transformation method is employed when deriving the governing equations. The inversion of Laplace transform will be obtained numerically by using the Riemann-sum approximation method. The results have been presented in figures to show the effect of the time exponentially decaying laser pulse and the two temperature parameter on all the studied fields.