Stress intensity factors for axial cracks in hollow cylinders subjected to thermal shock

Stress intensity factors are determined for one and two, internal and external axial cracks in hollow cylinders subjected to stress gradients arising from a thermal shock. A closedform weight function formula was used in the calculation. Results covering a wide range of cylinder geometries are presented in graphical form.     

Boundary element analysis of thermoelastic contact problems

A boundary element method (BEM) is applied to thermoelastic contact problems where thermal resistance at the contact interface is not negligible. The displacement, traction, temperature and temperature gradient in the contact zone are unknown quantities to be determined numerically. Due to the existence of thermal resistance, temperature and stress fields are mutually coupled. To solve the problem, two kinds of methods are presented. In the first method, the solution is obtained by minimizing a suitably defined objective function. In the second method, discretized equations of each of the bodies in contact are computed alternately until all prescribed boundary conditions are satisfied. The applicability of these methods to practical problems is examined through several numerical examples.     

Three-dimensional thermoelastic problems of interface cracks in periodic two-layered composites

This paper outlines the potential function method for solving three-dimensional interface crack problems of a two-layered periodic space, treated within the framework of linear stationary thennoelasticity with microlocal parameters. By constructing the appropriate harmonic functions, the resulting boundary-value problems regarding an interface crack are reduced to corresponding ordinary problems dealing with mechanical loading in homogeneous isothermal elasticity. This result—known as an analogy between the thermal crack problems and their mechanical counterparts—may be exploited to yield closed-form solutions following directly from that obtained in the isotropic case.

In connection with the theory of fracture mechanics, the thermal stress singularities as well as the effects of the geometrical and mechanical parameters of the composite structure on them are discussed.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

An approximate estimation of the contact characteristics in axial cylinders with constraints

A method is presented for the approximate estimation of maximum pressures and the contact half-angle in the conjugacy of cylindrical configurations with constraints. Relationships have been established to permit simple and quite precise determination of these contact interaction characteristics with variation in radial clearances and contour disruption.Translated from Problemy Prochnosti, No. 8, pp. 65–69, August, 1991.     

Coupled tangential-axial resonant modes of piezoelectric hollow cylinders and their application in ultrasonic motors

This paper describes a tangential-axial eigen-mode of a piezoelectric hollow cylinder. A new type of piezoelectric ultrasonic motor using this oscillation mode has been developed. The motor is a traveling-wave-type motor. The stator of such a motor consists of a solid piezoelectric hollow cylinder, which, excited in the tangential-axial resonant mode by a three-phase electrical signal, will exhibit elliptical displacement and transfer rotation to the rotor. The behavior of the stator has been simulated with finite element method (FEM) software. The simulation results have been checked with single-point contact measurements on the surface of the ultrasonic motors. The paper closes with the introduction of new ultrasonic motors based on this oscillation mode.     

Determining the mixed mode stress intensity factors of surface cracks in functionally graded hollow cylinders

This work reports about an investigation on mixed mode stress intensity factors (SIFs) of three-dimensional (3D) surface cracks in hollow cylinders made-up of functionally graded material (FGM). A finite element implementation of the interaction energy integral in domain form is employed to extract the SIFs. In turn, surface cracks located at the inner and outer wall of the cylinders are considered, and the influence of exponentially varying Poisson’s ratio and Young’s modulus in radial direction on the SIFs is studied in detail. The computational results reported herein show that graded materials properties can significantly affect the magnitude and the distribution of SIFs along 3D crack fronts in FGM hollow cylinders.     

Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders

An analytical approach to solve plane static non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders is presented. This approach is based upon the direct integration method proposed by Vihak (Vigak). The essence of the method mentioned is in the integration of the original differential equilibrium equations, which are independent of the stress–strain relations. This gives the opportunity to deduce the relations, which are invariant with respect to various properties of the material, for the stress-tensor components. From these relations each of the stress-tensor components have been expressed in terms of the governing one. A solution of the equation for the governing stress in the form of Fourier series is presented. To determine the Fourier coefficients, an integral Volterra-type equation is derived and solved by a simple iteration method with rapid convergence. Other stress-tensor components are expressed through the obtained governing stress in the form of an explicit functional dependence on force and thermal loadings.     

The eigenvalue problem for hollow circular cylinders

In three-dimensional elasticity the solution of the biharmonic equation for a hollow circular cylinder can be presented in terms of Bessel functions. If there are no surface tractions on either of the radial faces and no thermal effects, an eigenvalue problem arises. A method of establishing these eigenvalues and tables of them for various types of hollow cylinders are presented. Two special cases are investigated, namely, as the ratio of radii tends to unity, that is, a ‘thin shell’, and as the ratio tends to infinity, which can either be regarded as the inner radius tending to zero for a fixed outer radius or as the outer radius tending to infinity for a fixed inner.The eigenvalues are subsequently used for the calculation of the effect of end loading on a semi-infinite length cylinder. From this a quantitative comparison can be made with thin shell theory in the transition region between thin and thick shells of this type.     

Stress intensity factors for cylindrical cracks in long cylinders

Stress intensity factors for a long cylindrical crack in a long cylinder have been calculated using the energy release rate approach. The investigated loading cases include centrifugal forces (Mode I), radial surface forces (Mode I), forces parallel to the axis (Mode II), and twisting moments (Mode III).     

Thermoelectric effect in hollow superconducting cylinders

The thermoelectric effect in hollow cylindrical specimens (of circular and slit-like shapes) is considered. The detailed analysis of the behavior of the superconducting thin-walled cylinder in presence of normal current, is presented. The ratio of magnetic fluxes through the cylinder in superconducting and normal states is calculated as a function of temperature, wall thickness and other parameters of the superconductors. The gigantic thermoelectric effect is discussed using the concept of quantum transitions between the magnetic levels of cylindrical system. Some experimentally observable predictions are made.     

An axisymmetric thermoelastic contact problem for rotating bodies

Summary A contact thermoelastic treatment is considered for two bodies of rotation in contact on a circular area and rotating with a relative angular velocity. Heat is produced in the contact area by friction, which is redistributed in the bodies. The thermal contact between the bodies is nonideal. Heat transfer in accordance with Newton's law occurs with the external medium between the surfaces of the bodies outside the contact area.An integral Hankel transformation is used to reduce the treatment to two singular integral equations, which are examined by mechanical quadrature. A study is made of how the heat production affects the contact-pressure and temperature distributions.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 93–97, May–June, 1991.     

压电空心圆柱体中的周向SH波

基于三维线性压电弹性理论,采用一种正交多项式级数方法研究了轴向极化、电开路时正交各向异性压电空心圆柱中的周向SH波。把位移和电势展开成勒让德多项式级数,引入点确定的材料常数以解决边界条件,最后把问题的解简化为一个特征值问题。计算了不同径厚比下FZT-4管道周向SH的波频散曲线和电势分布。讨论了压电的影响。     

正交各向异性空心圆柱体的周向SH波

基于线性三维弹性理论,得到了正交各向异性管道中位移表示的周向波控制方程.波动方程中的轴向位移独立于其它两个方向.即波的传播可以分解为SH波和类Lamb波.通过贝塞尔函数求得了这个周向SH波频散方程.方程中决定周向SH波特性的弹性常数有两个,一个决定了波的频率,另一个决定了波速.最后分别讨论了两个弹性常数和波数变化对周向SH波位移模式的影响.     

Analysis of free vibrations in axisymmetric functionally graded thermoelastic cylinders

The free vibrations of an axisymmetric functionally graded, transversely isotropic, thermoelastic hollow cylinder have been modeled and analyzed. The material has been assumed to be graded according to a simple power law in the radial coordinate. The Laplace transform method has been used to solve the problem. The complex Laplace transform parameter has directly been used to find the natural frequencies of free vibrations without performing inversion of the transforms. The frequency equations of free vibrations in a hollow cylinder have been solved by using the software Maple. The natural frequencies of the first ten modes for different values of the grading index have been computed numerically for zinc material. The numerical results for radial stress, circumferential stress, temperature change, frequency shift, and thermoelastic damping (inverse quality factor) have been presented graphically. The closed form solutions obtained here are interesting and allow further parametric studies of functionally graded structures. The inhomogeneity parameter is useful in design and it can be tailored for specific applications as a controller.     

Implementation of thermoelastic forces in boundary element analysis of elastic contact and fracture mechanics problems

This paper presents a pseudo-body-force approach multi-domain boundary integral equation method for the analysis of thermoelastic and body-force type elastic contact and fracture mechanics problems. Using this approach only the boundaries of the bodies involved have to be discretized. The transformation of the domain integrals due to body-force and pseudo-force to their equivalent boundary integrals are shown. Also, it is shown that by employing the initial strain approach the same set of equivalent boundary integrals would be obtained. Isoparametric quadratic elements are employed to represent the geometries and the functions. This two-dimensional BEM thermoelastic implementation can be found very simple and can be applied to both harmonic and nonharmonic temperature distributions. The accuracy is asserted by applying it to several thermoelastic fracture mechanics and contact problems.