Transient thermoelastic contact problem of a transversely isotropic cylinder

Summary This paper concerns a transient thermoelastic contact problem in a transversely isotropic infinite cylinder inserted into a heated rigid ring. It is assumed that the heat transfer coefficient at the bonded surface is different from the coefficient at the traction-free boundary surface. A finite difference formulation with respect only to time is used to solve the three-dimensional transient heat conduction equation for the temperature field. The thermal stress field is analyzed by means of the transversely isotropic potential function method. The radial, hoop and axial stresses have singularities at the end of the contact surface. The concentration factors that may be used to evaluate the strength of the stress singularities are introduced.

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Ein transientes thermoelastisches Kontaktproblem eines transversal-isotropen Zylinders

Übersicht Behandelt wird ein transientes thermoelastisches Kontaktproblem eines transversal-isotropen unendlichen Zylinders, der in einen geheizten starren Ring eingesetzt wird. Der Wärmeübergang in der Kontaktfläche und der freien Oberfläche seien verschieden. Bei der Lösung der instationären dreidimensionalen Wärmeleitungsgleichung wird bezüglich der Zeit eine Finite-Differenzen-Formulierung benutzt. Die Wärmespannungen werden nach der Potentialfunktionen-Methode im transversalisotropen Fall ermittelt. Radial-, Umfangs- und Axialspannung weisen am Ende der Kontaktzone Singularitäten auf, die durch eingeführte Spannungskonzentrationsfaktoren beschrieben werden.

     

Transient thermal stresses and thermal deformations in a solid cylinder with a moving boundary

Summary This paper is concerned with transient thermal stresses and thermal deformations of the axisymmetric problem of a solid cylinder on consideration of a moving boundary. Assuming that a heated edge of the cylinder which is kept at a constant temperature moves with a constant velocity, the temperature distribution of the cylinder is analyzed using a moving coordinate system. Thereafter, the associated thermal stress distributions and thermal displacements are determined with aid of the method of the thermoelastic potential function and Love's displacement function. As an illustration, numerical calculations are carried out for several values of the velocity of the moving boundary, and the influence of the velocity on the temperature distribution and the stress distribution are examined precisely.

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Wärmespannungen und Verformungen in einem Zylinder mit bewegter Wärmequelle

Übersicht Es werden die Wärmespannungen und Verformungen in einem Zylinder untersucht, bei dem sich eine Wärmequelle mit konstanter Geschwindigkeit in axialer Richtung bewegt. Zunächst wird dabei die Temperaturverteilung im Zylinder mit Hilfe eines bewegten Koordinatensystems ermittelt. Dann werden die Wärmespannungen und die Verformungen mit der thermoelastischen Potentialfunktion und mit der Loveschen Verschiebungsfunktion bestimmt. Numerische Beispiele zeigen den Einfluß der Geschwindigkeit der Wärmequelle auf die Temperatur- und die Spannungsverteilung.

     

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.     

Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.     

Nonaxisymmetric thermal and stressed state of layered bodies of revolution with rectilinearly orthotropic layers

A procedure is described for investigating the temperature fields and stressed states of multilayer bodies of revolution consisting of inelastically deformed, isotropic materials and rectilinearly orthotropic materials, in which one of the principal directions of anisotropy of the thermophysical and mechanical characteristics of the material coincides with the axis of revolution of the body. The procedure combines a semianalytical finite element technique with the method of successive approximations.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 9–15, September, 1994.     

Transient thermal stresses in an orthotropic hollow cylinder for axisymmetric problems

For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation method. The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made to show the effect of the axial strain on the displacements and stresses. The project supported by the National Natural Science Foundation of China (10172075) and China Postdoctoral Science Foundation (20040350712)     

Transient response of a thin cylinder with local material inhomogeneity

Analyzed is transient response of a thin cylinder with a local material inhomogeneity to a pulse of short duration. The Galerkin method is utilized to solve the inhomogeneous dynamic equations with the eigenfunctions of the homogeneous cylinder serving as trial functions. Also treated is response of the limiting cases of a disk and of a ring with the same local inhomogeneity. All limiting cases yield to analysis when modulus E is approximated by segments of constant E along the radius for the disk and circumference for the ring. Transfer matrices relating variables at the two ends of a segment combine to satisfy continuity of variables at interfaces of segments. Curvature and axial dependence make the cylinder unique in response properties that neither disk nor ring possess.     

Torsional contact of an elastic flat-ended cylinder

Torsion of a flat-ended elastic bar pressed onto an elastically similar half-space and subject to torsion, in the presence of friction, is used as a vehicle to study complete contact subject to in-plane and anti-plane shearing forces. It is shown that, below a critical coefficient of friction, slip starts at the edge and progress inwards as the torsion is increased, whereas above this critical value slip starts a little way in from the edge and progress both inwards and outwards. Care is taken to preserve frictional orthogonality, with slip modelled as a piecewise-linear distribution of edge and screw dislocations. The solutions may be applied to any complete contact edge, as the problem is solved within the context of a Williams eigenexpansion.     

Deformation of an elastic helix in contact with a rigid cylinder

Summary The deformation of a short helix in contact with a rigid cylinder is investigated. Deformations occur due to bending, torsion and longitudinal elasticity of the helix. Shear deformation is neglected. Some of the equations describing the problem have been given already in Love's Treatise on the Mathematical Theory of Elasticity, in terms of curvature changes. Nevertheless, the equations for small deformations have to be reformulated in terms of displacements and rotations, because contact constraints cannot be expressed in terms of curvature. Friction is neglected, thus the problem is symmetric, and it is sufficient to determine its solution for one half of the helix.Without friction between the cylinder and the helix, the contact problem arises only for a helix longer than one length of twist. For a shorter helix, the global equilibrium conditions cannot be satisfied for nonvanishing contact forces. For the minimum length, there are two noncontact zones, and the helix is in contact with the cylinder only at three points: at the ends and in the middle. For a slightly longer helix, four contact points and three noncontact regions are found. The dependence of the noncontact zones and the contact forces, which are of practical interest, can be calculated as a function of the length of the helix and its geometrical parameters. The case of a very long helix with more than four contact points remains unsolved.     

Transient natural convection along vertical cylinder with Heat and Mass transfer

A numerical solution for the transient natural convection flow over a vertical cylinder under the combined buoyancy effect of heat and mass transfer is presented. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt number and Sherwood number are shown graphically. It is observed that time taken to reach steady state increases with Schmidt number and decreases as combined buoyancy ratio parameter N increases. Stability and convergence of the finite difference scheme are established. Received on 8 July 1997     

Transient thermal stresses in a composite circular cylinder perfectly bonded on the end surfaces of two circular cylinders

Summary In this paper, we deal with the formulation of the transient thermoelastio problem in the case that two circular cylinders made of distinct materials are perfectly bonded in the axial direction and there exists heat generation on the bonded surface. Furthermore, the influences of differences of the physical properties on temperature and stress distributions are clarified by numerical calculation.

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Transiente Wärmespannungen in zwei an den Stirnflächen perfekt verbundenen Kreiszylindern

Übersicht Es wird das Wärmespannungsproblem für zwei Kreiszylinder aus verschiedenen Werkstoffen untersucht, die an den Stirnflächen perfekt verbunden sind. Dabei existiert eine Wärmequelle in dieser gemeinsamen Fläche. Der Einfluß der verschiedenen Werkstoffeigenschaften auf die Temperatur- und die Spannungsverteilung wird anhand von numerischen Beispielen geklärt.