TRANSIENT THERMOELASTIC CONTACT STRESS IN A SHORT-LENGTH CIRCULAR CYLINDER

This paper is a treatment of a transient thermoelastic contact problem in a short-length circular cylinder, to which a heated rigid band is bonded. The problem may be reduced to that of solving dual-series equations. The solution meets the boundary conditions on both the lateral surface and the plane ends of the cylinder. The radial, hoop, and axial stresses have singularities at the end of a rigid band on the cylindrical surface.     

The thermoelastic problem of a stretchable rigid line inhomogeneity at soft bimaterial interface

Abstract

The thermoelastic problem of a stretchable rigid line inhomogeneity at a bimaterial interface is considered. The closed-form solution is presented and the explicit expressions of the stress at the tip of the rigid line inhomogeneity are derived. The effects of thermal expansion of rigid line on the stress intensity factors are investigated. It is found that the singularity of stress maintains the same structure, and the stresses possess an apparent oscillatory character, as in the case of a rigid line without the effects of thermal expansion. However, there is a significant difference in the coefficient of the singular behavior of the stresses at the tip of rigid line, which is due to the temperature changes.     

Heterogeneous Problems in Plane Thermoelasticity

Within the framework of the linear theory of thermoelasticity, the heterogeneous problem associated with multiple inclusions, circularly cylindrical layered media and plane layered media is considered and solved in this paper. The number of inclusions and layers is arbitrary and the system is subjected to arbitrary loading (singularities). The solutions to heat conduction (or antiplane deformation) and thermoelasticity problems are derived by the heterogenization technique that allows us to write down the solution explicitly in terms of the solution of a corresponding homogeneous problem subjected to the same loading. A rapid convergent series solution for both the temperature (or antiplane displacement) and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations and geometrical configurations on the interfacial stresses.     

ANALYTICAL SOLUTIONS AND NUMERICAL EXAMPLES FOR THERMOELASTIC INTERFACE CRACK PROBLEMS IN DISSIMILAR ANISOTROPIC MEDIA

The problem associated with an interface crack between anisotropic dissimilar media subjected to a remote heat flux as welt as traction on the crack surface is studied in this article. Based on the complex variable representations of the plane elastic problem developed by Lekhnitskii and a special technique of analytical continuation, the full field solutions of the displacements and thermal stresses are obtained in closed form. It is indicated that the nature of singularities in the stress field at the crack tips is unaltered by the presence of an applied heat flux if the heat conductivity coefficients obey the Onsager reciprocal relations. The explicit expressions for the strain energy release rate and crack opening displacements are also provided. The former is treated as the fracture parameter to characterize the occurrence of interface cracking. Numerical examples for graphite / epoxy composite bonded to metal and ceramic materials bonded to metal substrates are examined and detailed results are given.     

ON THE EVALUATION OF THE FREE-EDGE STRESS INTENSITY FACTORS FOR A JOINT SUBJECTED TO A UNIFORM CHANGE IN TEMPERATURE

A contour integral is applied to the evaluation of the stress intensity factors at interface corners of bimaterial joints subjected to a uniform change in temperature. In order for the contour integral to work for the free-edge stress intensity factors, closed-form solutions for the stress and displacement fields near interface corners of bimaterial joints subjected to a uniform temperature change are derived. The derivation is based on the hypothesis that the two dissimilar materials, which are bonded along their common interface, experience identical rigid body displacements. Accordingly, the asymptotic displacements are continuous along the interface irrespective of the rigid body displace ments near the interface corner. A case study is carried out for a problem where the combination between the material properties and the geometry at the interface corner is such that the stresses at the interface corner are comprised of several stress fields of the form Hr     

ON AXISYMMETRIC THERMAL STRESSES IM AN ANISOTROPIC HOLLOW CYLINDER

Abstract

This paper deals with the problem of thermal stresses in a hollow anisotropic cylinder of finite extent arising from axisymmetric temperature variations at the plane ends, the inner and outer curved surfaces being in contact with rigid and smooth insulators. An exact solution is developed using potential functions of displacement. Numerical results are given for cylinders made of magnesium (anisotropic) and copper (isotropic).     

FRACTURE OF THICK-WALLED CYLINDERS SUBJECTED TO TRANSIENT THERMAL STRESSES

In this paper, the fracture problem of a thick cylinder subjected to transient thermal stresses is considered. The problem has practical significance in the conventional and nuclear power industries where the structural integrity of components may be damaged due to sudden temperature changes. Neglecting the inertia effects, the thermal fracture problem is uncoupled. First the thermal stresses in a thick cylinder due to a sudden change in temperature are computed separately as a function of time. Then, these stresses are used as external loads in analyzing the fracture of a thick cylinder. The assumed crack, may be an inner edge crack, outer edge crack or an embedded crack. Extensive results are obtained by varying the parameters of the problems. The main parameters affecting fracture are identified and the results are discussed in some detail.     

Forced convection of non-Newtonian fluids on a heated flat plate

Forced convective heat transfer due to a non-Newtonian fluid flowing past a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved by (numerically) marching downstream from the leading edge as is common for boundary layers involving Newtonian fluids. For shear-thinning and shear-thickening fluids, non-Newtonian effects are illustrated via velocity and temperature distributions, shear stresses, and heat transfer rates. The most significant effects occur near the leading edge, gradually tailing off far downstream where the variation of shear stresses becomes smaller.     

On the central connection problem for equations with an irregular singular point of a single level

We study the central connection problem for linear systems of equations with two singularities: one at the origin which is assumed to be regular-singular, and another one at infinity having a formal fundamental solution of only one level (in the Newton polygon).     

AN EIGENFUNCTION APPROACH TO SINGULAR THERMAL STRESSES IN BONDED STRIPS

Solutions for thermal stress singularities infinite bonded strips are sought by using an eigenfunction expansion in the neighborhood of the singularity. The coefficients in the resulting series are determined by satisfying the boundary conditions on surfaces far removed from the singularity either pointwise or in an integrated sense. The latter of these techniques is found to be more reliable. The accuracy of the solution is checked by comparing it to a semianalytical solution for thermal stresses in bonded quarter planes, which is derived by using the Mellin transformation. It is shown that the eigenfunction approach provides accurate solutions for the leading term in the series, thus capturing the essence of the thermal stress fields near the edge of the interface. The far-field solutions, however, are found to feature excessive inaccuracies, which are attributed to numerical errors     

Generic Singularities of the Optimal Averaged Profit among Stationary Strategies

We consider the problem of maximizing the (time) averaged profit of a smooth profit density on a smooth compact one-dimensional manifold along a trajectory provided by a stationary strategy of a polydynamical system. When the problem depends on a k-dimensional parameter, this optimal averaged profit can have singularities (points of nonsmoothness) as a function of the parameter. We present the generic classification of these singularities for k ≤ 3.      

Discontinuity phenomena around the supports of stepwise-thickened spherical steel tanks. Part 1: Theoretical considerations and parametric results

The present study examines the ‘edge-effect’ phenomena that occur at the upper and lower thickness-discontinuity locations of spherical steel tanks in which shell thickness is stepwise-increased in a band centred about the support circle of latitude. Such phenomena are considered in relation to the ‘edge effect’ occurring at the support itself as a result of the reactions and constraints there. The uniform local thickening of the shell in the vicinity of the supports is usually adopted to counter the excessive bending-disturbance stresses that would otherwise occur in this region were a constant shell thickness (chosen on the basis of peak membrane stresses) adopted throughout, especially where the vertical supports happen to be positioned well below the equatorial plane.

Presently, the necessary expressions for a full static analysis of the structural problem are derived, and some parametric data given. In a follow-up paper (Zingoni and Pavlovi , Int. J. Pres. Ves. & Piping, 53 (1993) 437-56, numerical examples are considered, and design implications pointed out.     

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation,Part I: Methodology

This work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.     

Radial loading of a cylindrical vessel through a rectangular rigid attachment

This paper examines the behaviour of a cylindrical vessel which is radially loaded through a rigid attachment of rectangular plan form. The resulting radial and tangential interface forces between the vessel and the attachment are derived assuming that the attachment is fixed to the vessel at all points over the mating surface and subjected to a radial displacement. From these interfacial forces the stresses in an illustrative vessel are found to be some 37% higher than those which are obtained when a uniformly distributed radial interface pressure is assumed.     

The determination temperature-dependent thermal conductivity as inverse steady heat conduction problem

The paper deals with the non-iterative inverse determination of the temperature-dependent thermal conductivity in 2-D steady-state heat conduction problem. The thermal conductivity is modeled as a polynomial function of temperature with the unknown coefficients. The identification of the thermal conductivity is obtained by using the boundary data and additionally from the knowledge of temperature inside the domain. The method of fundamental solutions is used to solve the 2-D heat conduction problem. The golden section search is used to find the optimal place for pseudo-boundary on which are placed the singularities in the frame of method of fundamental solutions.     

Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading

The transient thermal stress crack problem for a half-space with a multilayer coating under thermal surface loading containing an undercoat crack, perpendicular to the interface, is considered. The problem is solved using the principle of superposition and uncoupled quasi-static thermoelasticity. Transient temperature distribution and corresponding thermal stresses for the uncracked multilayer assembly are obtained in a closed analytical form using the model with generalized thermal boundary conditions of heat exchange of a half-space with ambient media via the coating. The crack problem is formulated as a perturbation mixed boundary value problem, in which the crack surface loading should be equal and opposite to the thermal stresses obtained for the uncracked medium, and is reduced to a singular integral equation and solved numerically. Numerical computations are performed for the analysis of influence of the coating upon thermal stresses and thermal stress intensity factor.     

Generic profit singularities in time averaged optimization. The case of a control space with a regular boundary

For one-parameter smooth families of pairs of control systems and profit densities on the circle, we consider the problem of maximizing the averaged profit in the infinite horizon from the singularity theory point of view. Namely, we study the generic classification of the optimal averaged profit as function of the parameter. This approach to the problem was introduced in 2002 by V. I. Arnold and all generic classifications in related problems obtained since then, assume a compact control space without boundary. The existence of a boundary in the control space is usual in real problems and so it is worthwhile to be considered. In this work, we consider the existence of a regular boundary in the control space and study the case of one-dimensional parameter. We present all generic singularities of the optimal averaged profit as function of the parameter and conclude that three new singularities appear.     

Design of supporting devices for large diameter thin pipes

When an analysis is made in accordance with ASME Code Class 1 for piping by the stress indices method (NB 3650), the stresses induced locally in the piping by the supports are not taken into account. For piping whose thickness is small in relation to its diameter, which is subject to sudden temperature changes and to seismic shocks and which also operates at high temperature, it is undesirable to ignore these effects. This is particularly the case with piping carrying liquid sodium since the classic solutions do not provide a satisfactory answer to the thermomechanical problems and cannot resolve many uncertainties in the analysis. The design finally selected must meet the double requirement of permitting free radial expansion of the piping whilst enabling it to withstand considerable loads with minimal deformation. The design must also be justifiable by easily verified hypotheses.The design adopted consists of a rigid collar connected to the piping by blades which are flexible radially in relation to the pipe and rigid tangentially. These blades are attached to very short ring lugs welded on to the piping. In this way, the outside forces acting on the piping are reduced almost exclusively to circumferential forces which, combined with the circumferential shearing flux due to the adjacent sections, constitute a distribution of forces which is particularly favourable for limiting the circumferential bending moments in the pipe. The resulting deformation of the circular section is thus sufficiently small not to affect the longitudinal bending strength, and particularly the buckling strength.The most significant stresses prove to be those due to the moment on the lug; these are well known and are limited due to the small height of the lug. The thermal stresses due to the presence of the lug were calculated by the finite element method. The thermal and mechanical disturbance created by the lug has the effect of multiplying by about a factor of 2 the maximum total stresses occurring during thermal transients in the straight part; they thus remain limited and less than those developed in other straight discontinuities affecting the piping; for instance, the changes in thickness between straight parts and bends. To back up these calculations, a series of tests was performed to check that the technological requirements of manufacture did not question the load distribution hypotheses taken into account in the calculations.     

Two-Dimensional Green's Function for Thermal Stresses in a Semi-Layer Under a Point Heat Source

We present specific new expressions for thermal stresses as Green's functions for a plane boundary value problem of steady-state thermoelasticity for a semi-layer. We also obtain new integration formulas of Green's type, which determine the thermal stresses in the form of integrals of the products of the given distributed internal heat source, boundary temperature, and heat flux and derived kernels. Elementary functions results obtained are formulated in a theorem, which is proved using the harmonic integral representations method to derive thermal stresses Green's functions, which are written in terms of Green's functions for Poisson's equation. A new solution to particular two-dimensional boundary value problem for a semi-layer under a boundary constant temperature gradient is obtained in explicit form. Graphical presentations for thermal stresses Green's functions created by a unit heat source (line load in out-of-plane direction) and by a temperature gradient are also included.     

Body Force Analogy for Transient Thermal Stresses

A body-force analogy for transient thermal stresses in linear elastic solids is presented. The analogy is derived in the framework of the stress equations of motion and the corresponding stress-based characterization of initial boundary-value problems of elasticity. The latter framework was introduced by Professor Jozef Ignaczak, to whom the present contribution is dedicated. Starting from Ignaczak's stress-based formulation, we subsequently derive a body-force analogy by studying conditions, under which a certain time-dependent volume integral, being positive in case of non-vanishing stresses, and vanishing otherwise, becomes zero. These conditions lead us to the formulation of a boundary-value problem, which must be satisfied by the auxiliary body-forces, surface tractions and kinematic boundary conditions, in order that the stresses in the auxiliary isothermal problem and in the thermal stress problem do coincide. As a numerical example, Finite Element Computations for a beam-type structure are presented.