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 inverse problem technique for detecting irregular cavities in circular cylinders by infrared scanning

An inverse problem technique has been developed for detecting irregular cavities in circular cylinders. In this method, the cavity is considered a part of the unknown geometry of the investigated system, and the evaluated temperature is used to locate this geometry. An auxiliary problem is introduced in the solution of this problem; and in the solution, the cavity wall is located by forcing the temperature to satisfy the condition imposed at the cavity. The new methodology is validated by an experiment presented in this paper, and the test results indicate that this method is highly successful in locating cavities. The accuracy of the method is closely related to the accuracy of the temperature that can be measured at the surface. A small error in the surface temperature results in a slight cavity error for deep cavities, while a shallow cavity is not severely affected by a surface temperature error. This method is particularly attractive in detecting shallow cavities in nondestructive evaluation.     

Plane contact thermoelasticity problem for a two-layer circular hollow cylinder with heat generation

We consider a contact thermoelasticity problem for a two-layer hollow cylinder. One of the layers rotates with respect to the other with a constant angular velocity. Constant stresses on the interface of cylindrical layers are caused by (a) compressive radial stresses or displacements on the side surfaces of the body and (b) a positive difference between ambient temperatures inside and outside the two-layer cylinder. Heat is generated as a result of friction on the contacting surfaces of the layers. We study the effects of the intensity of heat generation and physicomechanical properties of the cylinders on the distributions of stresses, displacements, and temperatures in the body.Franko L'viv State University, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 6, pp. 24–30, November – December, 1994.     

A unified formulation of RMVT-based finite cylindrical layer methods for sandwich circular hollow cylinders with an embedded FGM layer

A unified formulation of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) is developed for the quasi-three-dimensional (3D) analysis of simply-supported, multilayered composite cylinders and sandwich circular hollow cylinders with an embedded functionally graded material (FGM) cylindrical layer, subject to mechanical loads. The material properties of the FGM layer are assumed to obey an exponent-law varying exponentially with the thickness coordinate. In this formulation, the circular hollow cylinder is divided into a number of finite cylindrical layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the field variables of each individual layer, respectively. Because an h-refinement instead of a p-refinement process is adopted to yield the convergent solutions in this work, the layerwise linear, quadratic or cubic function distribution through the thickness coordinate is assumed for the related field variables. The accuracy of the FCLMs developed in this article is assessed by comparing their solutions with the exact 3D ones available in the literature, and the convergence rate and possibility of numerical instability of these FCLMs are also investigated.     

The transverse elastic impact response of thick hollow cylinders

The two objectives of the studies in this paper were to determine the transient elastic impact response of thick-walled hollow cylindrical structures and to determine how this response was affected by the presence of flaws in the cylinder. These studies were aimed at determining the feasibility of using the impact-echo method for detecting flaws in the cylindrical concrete structures, such as pipes. Three-dimensional finite element models and laboratory specimens containing various types of flaws at known locations were used in the studies. It is shown that, for a hollow cylinder having a length greater than about eight times its outer diameter, the impact response as measured at points close to the impact point is composed of a number of resonant frequencies caused by cross-sectional (flexural) modes and a thickness frequency caused by dilatational waves reflected between the inner and outer wall surfaces. Equations are presented which relate the response of a hollow cylinder to the frequency of the fundamental cross-sectional (flexural) mode of a solid circular bar. It is shown that the location of cracks, areas of reduced wall thickness, and honeycombing as well as the depth of surface-opening cracks can be determined.     

Homotopy approach for random eigenvalue problem

A novel approach, referred to as the homotopy stochastic finite element method, is proposed to solve the eigenvalue problem of a structure associated with some amount of uncertainty based on the homotopy analysis method. For this approach, an infinite multivariate series of the involved random variables is proposed to express the random eigenvalue or even a random eigenvector. The coefficients of the multivariate series are determined using the homotopy analysis method. The convergence domain of the derived series is greatly expanded compared with the Taylor series due to the use of an approach function of the parameter h. Therefore, the proposed method is not limited to random parameters with small fluctuation. However, in practice, only single‐variable and double‐variable approximations are employed to simplify the calculation. The numerical examples show that with a suitable choice of the auxiliary parameter h, the suggested approximations can produce very accurate results and require reduced or similar computational efforts compared with the existing methods.     

A unified formulation of RMVT-based finite cylindrical layer methods for sandwich circular hollow cylinders with an embedded FGM layer

A unified formulation of finite cylindrical layer methods (FCLMs) based on the Reissner mixed variational theorem (RMVT) is developed for the quasi-three-dimensional (3D) analysis of simply-supported, multilayered composite cylinders and sandwich circular hollow cylinders with an embedded functionally graded material (FGM) cylindrical layer, subject to mechanical loads. The material properties of the FGM layer are assumed to obey an exponent-law varying exponentially with the thickness coordinate. In this formulation, the circular hollow cylinder is divided into a number of finite cylindrical layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the field variables of each individual layer, respectively. Because an h-refinement instead of a p-refinement process is adopted to yield the convergent solutions in this work, the layerwise linear, quadratic or cubic function distribution through the thickness coordinate is assumed for the related field variables. The accuracy of the FCLMs developed in this article is assessed by comparing their solutions with the exact 3D ones available in the literature, and the convergence rate and possibility of numerical instability of these FCLMs are also investigated.     

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.     

Material tailoring for functionally graded hollow cylinders and spheres

We present a technique to tailor materials for functionally graded (FG) linear elastic hollow cylinders and spheres to attain through-the-thickness either a constant hoop (or circumferential) stress or a constant in-plane shear stress. The volume fractions of two phases of a FG material (FGM) are assumed to vary only with the radius and the effective material properties are estimated by using either the rule of mixtures or the Mori-Tanaka scheme; the analysis is applicable to other homogenization methods. For a FG cylinder we find the required radial variation of the volume fractions of constituents to make a linear combination of the radial and the hoop stresses uniform throughout the thickness. The through-the-thickness uniformity of the hoop stress automatically eliminates the stress concentration near the inner surface of a very thick cylinder. The through-the-thickness variations of Young’s moduli obtained with and without considering the variation of Poisson’s ratio are very close to each other for a moderately thick hollow cylinder but are quite different in a very thick hollow cylinder. For an FG sphere the required radial variation of the volume fractions of the two phases to get a constant circumferential stress is similar to that in an FG cylinder. The material tailoring results presented here should help structural engineers and material scientists optimally design hollow cylinders and spheres comprised of inhomogeneous materials.     

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.     

Dynamical magnetothermoelastic problem in circular cylinders—II: Thermal,magnetic and elastic fields

On using the approximate small-parameter method, the linearized magnetothermoelastic equations[1] are solved. The analysis of the magnetic, thermal and elastic fields, and magnetothermoelastic waves, based on the solutions of above equations, is presented.     

Reissner mixed variational theorem-based finite cylindrical layer methods for the static analysis of functionally graded piezoelectric circular hollow cylinders under electro-mechanical loads

A unified formulation of Reissner's mixed variational theorem-based finite cylindrical layer methods is developed for the static analysis of simply-supported, multilayered functionally graded piezoelectric material (FGPM) circular hollow cylinders. The material properties of the cylinder are assumed to obey an exponent-law exponentially varying through the thickness coordinate of this. The trigonometric functions and Lagrange polynomials are used to interpolate the in-surface and thickness variations of the primary variables of each individual layer, respectively. The coupled electro-elastic effects on the static behaviors of multilayered FGPM cylinders are closely examined.     

Single scattering of light by circular cylinders

We consider two topics pertaining to light scattering by circular cylinders. (A) Scattering properties of cylinders with increasing aspect ratio are studied. It is shown that the solution for finite cylinders does not converge to the solution for infinitely long cylinders if the aspect ratio increases. This is due to differences in the treatment of diffraction for finite and infinite cylinders. (B) Finite cylinders have sharp edges, so their scattering properties differ from those of spheroids having the same aspect ratio. To illustrate these differences we present scattering matrix elements of cylinders and spheroids for a large set of aspect ratios. To handle the large amount of data, the scattering matrix elements as functions of aspect ratio and scattering angle are presented in so-called three-dimensional figures.     

Cross flow past successively positioned circular cylinders

The numerical scheme of A. Arakawa is used to carry out a numerical analysis of the cross flow past two successively positioned cylinders.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 2, pp. 310–317, August, 1981.     

Polaritons in uniaxial materials propagating in hollow cylinders

The properties of polaritons propagating in hollow dielectric and magnetic cylinders embedded in an optically inert medium are studied. We pay special attention to those solutions of Maxwell's equations that give the behavior of the nonradiative modes (confined and localized) propagating in an optically active cylindrical medium. The dispersion relation of surface (localized) modes is obtained. Numerical results are presented for cylinders constituted by magnetic and dielectric materials, such as the uniaxial Heisenberg antiferromagnet MnF2 and the dielectric TiO2.     

Boundary layer growth on two circular cylinders

This paper deals with the problem of boundary layer growth on two circular cylinders in a flow with large Reynolds and Strouhal numbers. Analytic solutions for the stream function of the inner and outer flow field are obtained to the second order by using the method of matched asymptotic expansions. The dependence of the movement of the detachment points and the drag coefficients of the two cylinders on (i) the distance between them, (ii) the ratio of their radii, (iii) the Reynolds number and (iv) the acceleration parameter of the flow is investigated. The results obtained indicate that the mutual hydrodynamic interaction between two cylinders leads to some new relations and findings.