Transient thermal stresses in a composite hollow cylinder subjected to γ-ray heating

Transient temperature and thermal-stress distributions arising in an infinite long composite hollow circular cylinder subjected to internal heat generation decaying exponentially along the wall thickness resulting from γ-ray radiation are analyzed, under the thermal conditions of cooling by convection on the inner surface and insulation on the outer surface. Numerical calculations of the transient temperature and thermal-stress distributions are carried out for the case of a composite cylinder of stainless steel and carbon steel. The influence of the absorption coefficient, the Biot number and the splicing radius on the results are considered.     

Transient thermal stresses and displacements in a transversely isotropic, heat-generating circular cylinder

The transient thermal stress field in a traction-free, transversely isotropic, heat-generating circular cylinder is studied by means of a set of stress functions developed by Singh. The purpose of this paper is to present the results of theoretical analysis which consider the effects of the thermo-elastic anisotropies of the material on the thermal stress field in the transversely isotropic, circular cylinder due to an abrupt axial change in the internal heat-generation rate. A detailed qualitative picture of the thermal stress state for two values of the Biot number and various values of the ratio of the thermal conductivity coefficients in the axial and radial directions is given and it is demonstrated that the magnitude of the maximum thermal stress is significantly sensitive to the anisotropies of the thermal conductivity coefficient and the Young's modulus.     

Asymmetrical transient thermoelastic problems in a composite hollow circular cylinder

The present paper is concerned with the transient thermal stresses in a bonded composite hollow circular cylinder under an arbitrary asymmetrical heat supply. Numerical work is carried out using Laplace transforms and is given for the composite cylinder made of the different materials under three, band heat sources on its outer surface.     

Transient thermal stresses in a finite solid circular cylinder due to a cylindrical surface heat source over the lateral surface

An exact solution is given for the determination of transient thermal stresses in a traction-free, finite solid, circular cylinder subjected to a cylindrical surface heat source over the lateral surface and having a heat loss to a surrounding medium over the entire boundary surface. The problem is formulated in terms of thermo-elastic displacement potential and Love's function, and the solution rigorously satisfies traction-free boundary conditions on both the lateral and end surfaces of the cylinder.

The problem is of considerable technological importance, particularly to certain nuclear reactor analyses related to the behavior of fuel elements and control rods during power transients.

Numerical calculations are carried out for various combinations of Biot's number and the ratio of length to diameter of the cylinder. The results obtained are compared with those of an infinite, solid, circular cylinder and of a solid circular disc.     

Transient thermal stresses and displacements in a transversely isotropic semi-infinite circular cylinder subjected to an arbitrary surface heat generation and a convective heat loss

The transient thermal stresses and displacements in a traction-free, transversely isotropic, semi-infinite circular cylinder subjected to a convective heat loss on the end surface is analyzed by means of a set of stress functions and a generalized Fourier-integral representation for exponential function.The purpose of this paper is to present the results of theoretical analysis which considers the effects of the thermal and elastic anisotropes of the material properties on the thermal stresses and displacements in the transversely isotropic, semi-infinite circular cylinder due to an arbitrary cylindrical surface heat generation.A detailed numerical result of the thermal stresses and displacements is given for various values of the ratios of the thermal conductivity coefficients, Young's moduli and linear thermal expansion coefficients in the axial and radial directions and it is demonstrated that the sensivity of the maximum stress and displacement to the anisotropy of the thermal conductivity coefficient is significant.     

Length effects of unsteady thermal stresses in a finite short circular cylinder with an arbitrary heat supply

An unsteady thermoelastic study, taking consideration of the length effects, was made of a finite short circular cylinder under an arbitrary heat supply along its cylindrical surface in the longitudinal direction. The analysis was treated by the thermoelastic potential method using a general form of the Love's displacement function which has not so far been used. The results obtained were compared with those of an approximate solution for the finite cylinder using Saint-Venant's principle. From the results the effects of the length-to-diameter ratio evidently appear in the transient thermal stress distributions for the finite short cylinder.     

Transient natural convection cooling of a vertical circular cylinder

A numerical solution is presented for transient natural convection cooling of a finite vertical circular cylinder standing on a semi-infinite horizontal base. The method used is the quasi-finite element approach introduced by Mansour et al. in the determination of the steady state temperature field in metal cutting. The method is able to solve heat transfer problems in a more economical way (memory and computing time requirements) than the classical finite element method and the finite difference techniques.     

Dynamic response of a clamped/free hollow circular cylinder under travelling torsional impact loads

Impact-induced vibrations in the casing of a gas centrifuge due to a sudden failure of the spinning rotor (crash) can cause structural disintegrity of the casing. In order to study the influence of the rotor failure behaviour and the impact load histories on the dynamic response of the casing, a simple crash model is proposed in this paper to analyse the transient torsional response due to tangential components of the impact loads. The casing is modeled as a linear-elastic hollow circular cylinder, clamped at the lower end and free at the upper end. The rotor is thought to break up in identical sections in a sequence determined by its fracture behaviour. Each section is assumed to cause an axi-symmetric load distribution at the inner surface of the casing. Therefore the problem is essentially reduced to the analysis of a clamped/free cylinder under travelling torsional impact loads. The problem is solved by representing the impact loads as local pulses acting over the length of the sections. A perturbation method is used to show that the general two-dimensional theory of axi-symmetric torsional wave propagation in circular cylinders, for the problem under consideration, may be approximated by the elementary one-dimensional theory. Solutions are obtained according to the usual modal expansion approach. Measurements of transient torsional responses are shown to be in good agreement with the calculated responses by choosing a suitable shape of the pulses. The effects of travelling velocity and pulse shape are investigated. Finally the transfer of kinetic energy in the rotor to vibrational energy of torsion in the casing is studied.     

A structural analysis of the circular cylinder with multi holes under thermal loading

A structural analysis of the circular cylinder with multi holes is performed using the finite element analysis program . This structure is an analytical model of the capsule used for material irradiation tests. The temperature distributions of the cylinder due to gamma heating are obtained and various parameters, such as specimen size, quantity of specimens and gap sizes between the holder and the specimen are considered in the analysis to obtain the thermal and mechanical characteristics. To assess the structural integrity of the capsule, stress analysis under thermal loading is also performed. The analysis results show that, in all specimens, the peak temperature occurred, and is significantly dependent on gap sizes between the holder and the external tube or the specimen. The stress of the cylinder, under thermal loading, is lower than the allowable stress of the material used.     

Elasto-plastic behaviour of a thin cylinder under thermal stress cycling

A simple biaxial model is chosen to represent the stress state of a thin cylinder and the elasto-plastic behaviour under thermal stress cycling is studied to determine:

1. 1. shakedown limits,

2. 2. plastic cycling limits,

3. 3. magnitude of cyclic strains and ratchet strains,

4. 4. strain ratios in various regimes.

The studies have been carried out for two material models: elastic-perfectly plastic and Prager-hardening. Results are given in the form of graphs and compared with the results of uniaxial models.     

Unsteady thermal stresses in fuel elements under heat generation

In designing some types of fuel elements, it is necessary to find the thermal stresses in a continuous medium performated by cylindrical channels of circular cross-section. In order to set up the problem, assume that the strength and heat transfer calculation are based on the phenomena that occur in a typical unit lattice cell, and that the heat generation is uniform over the whole section: Therefore, the problems reduce to solve the temperature and thermal stresees in a polygonal prism with a central circular hole under uniform heat generation and for insulated outer boundary. In out previous papers we obtained the steady thermal stress distribution in such formed regions by use of the five elementary functions method.

In starting up or shutting down of the reactor, however, the problem becomes one of the unsteady state. It is felt that no analysis has been given to the transient thermoelastic problem of the multiply-connected region. The problems considered here are concerned with unsteady thermal stresses in a polygonal prism with a circular hole under a uniform heat generation. The solving process is divided into two basic steps. First, the heat conduction equation is solved by the technique of Laplace transform. Secondly, the plane thermoelastic problem is solved by use of the five elementary functions method. Throughout the treatment of both problems, in order to satisfy the boundary conditions, we use the point-matching technique in conjunction with the least square method.     

Eigenvalues basic to radial diffusion in a hollow cylinder

The eigenvalues of the eigenvalue problem basic to radial diffusion in a hollow cylinder with azimuthal symmetry are determined for nine different combinations of the boundary conditions of the first, second and third kind. The first ten eigen values are systematically tabulated for different values of the radius ratio and Biot number for the inner- and outer-boundary surfaces.     

Transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations

The transient thermal stresses in an orthotropic finite rectangular plate due to arbitrary surface heat-generations on two edges are studied by means of the Airy stress function.The purposes of this paper are to present a method of determining the transient thermal stresses in an orthotropic rectangular plate with four edges of distinct thermal boundary condition of the third kind which exactly satisfy the traction-free conditions of shear stress over all boundaries including four corners of the plate, and to consider the effects of the anisotropies of material properties and the convective heat transfer on the upper and lower surfaces on the thermal stress distribution.     

Eigenvalues basic to diffusion in a hollow cylinder without azimuthal symmetry

The eigenvalues needed for the computation of transient heat or mass diffusion in a hollow cylinder without azimuthal symmetry are calculated. The first 10 eigenvalues are tabulated for the convection boundary condition at the outer and inner surfaces for several different values of the radius ratio, the Biot number and the separation constant associated with the azimuthal variation.     

Thermal stresses in a cylindrical shell containing a circular hole or a rigid inclusion

The thermal stress problem of a circular discontinuity in a cylindrical shell has been solved by continuum approach. Two types of discontinuities are considered: (i) a circular hole and (ii) a circular regid inclusion. The effect of a uniform temperature or a linearly varying temperature across the thickness has been studied. The problem is converted into an equivalent boundary value problem and boundary conditions are specified around the discontinuity. The results are presented in a graphical form for ready use.