Hollow Cylinder Of Finite Length Research Articles

Elastic Equilibrium of a Hollow Cylinder of Finite Length Under Axisymmetric Force Loading

Elastic Equilibrium of a Hollow Cylinder of Finite Length Under Axisymmetric Force Loading

FEM-BEM modeling dynamic responses of saturated soil around a fluid-filled lined tunnel subjected to water hammer

Dynamic stress responses of saturated soil around a fluid-filled lined tunnel caused by a water hammer are investigated by a frequency-domain FEM-BEM coupled model. The fluid is modeled as an inviscid and compressible fluid, the lining is modeled by elastic medium and conceptualized as a hollow cylinder of finite length, and the saturated poroelastic medium is adopted to model the soil. Initially, governing equations of fluid and those of lining are solved by FEM in the frequency domain, while those of soil are solved by BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility and force balance on their interfaces. Water pressure (inside the tunnel), the distribution of lining displacement and dynamic stress responses of saturated soil generated by the water hammer are presented. It is concluded that the dynamic stresses and the pore pressure change periodically in saturated soil under a water hammer. Modeling soil as an elastic medium inaccurately evaluates the distribution of lining displacement. The soil permeability has a significant influence on the normal stresses of soil and pore pressure but has a slight effect on the shear stresses of soil.

SOLUTION OF THE LAPLACE EQUATION BY THE METHOD OF SEPARATION OF VARIABLES FOR A LENGTH HOLLOW CYLINDER

The physical model of many electrical objects is a hollow cylinder of finite length. As a basis for constructing analytical models of electrical machines, linear equations of mathematical physics are used. They are the solution of the Laplace three-dimensional partial differential equation, which is widely used in analytical calculations.
 
 The purpose of the study is to solve the Laplace three-dimensional differential equation for a hollow cylinder of finite length, which can be adapted for the electromagnetic calculation of electromechanical devices with cylindrical active parts.
 
 Materials and methods. To solve the Laplace equation in a cylindrical coordinate system, the Fourier variable separation method was used. To obtain a non-trivial solution of the equation, eigenfunctions of the Sturm–Liouville problem were used. Dirichlet, Neumann boundary value problems of the mixed type for hollow cylinders are adapted to the electromagnetic calculation of electromechanical devices having cylindrical active parts.
 
 The results of the study. The Laplace equation given in a cylindrical coordinate system is considered, on the basis of which the Sturm–Liouville equation with zero initial values is compiled to find eigenfunctions. The complete solution of the Lapalace equation with given boundary conditions is obtained as the sum of the solutions of two separate Dirichlet problems with different boundary conditions.
 
 Findings. The obtained analytical expression can be used as a mathematical basis for constructing three-dimensional analytical models of electrical machines with cylindrical active parts and carrying out electromagnetic calculations of the corresponding electromechanical devices.

Memory impact of hygrothermal effect in a hollow cylinder by theory of uncoupled-coupled heat and moisture

PurposeThe purpose of the paper is to prepare the hygrothermal model with fraction order theory in a mathematical aspect.Design/methodology/approachIn this study, linear hygrothermoelastic theory is adopted to analyze and discuss the memory effect in a finite length hollow cylinder subjected to hygrothermal loading.FindingsAnalytical solutions of temperature, moisture and stresses are obtained in this study by using the decoupling technique and the method of Integral transform.Originality/valueThe paper deals with the original work based on hygrothermal response in hollow cylinder by theory of uncoupled-coupled heat and moisture.

Transient Response of a Hollow Functionally Graded Piezoelectric Cylinder Subjected to Coupled Hygrothermal Loading

In this paper, transient response of a simply supported finite length hollow cylinder made of functionally graded piezoelectric material (FGPM) subjected to coupled hygrothermal loading was investigated. The coupled equations of heat conduction and moisture diffusion as well as motion equations and the electrostatic equation of FGPM were solved employing the Fourier series expansion method through the longitudinal direction, the differential quadrature method (DQM) along the radius and Newmark method for time domain. Finally, the distribution of temperature, humidity, electric potential, stresses and displacements was achieved. The effect of coupled and uncoupled hygrothermal loading, grading index and hygrothermal loading was illustrated in the numerical examples. The results show that using the coupled model is vital for analysis of transient response of the cylinder subjected to hygrothermal loading.

Elastic equilibrium of a hollow cylinder of finite length subjected to axisymmetric force loading

Elastic equilibrium of a hollow cylinder of finite length subjected to axisymmetric force loading

Axisymmetric thermal stresses in an elastic hollow cylinder of finite length

This article presents a technique for analytic-numerical evaluation of thermal stresses in a finite-length hollow cylinder subject to a steady-state temperature field. Based on the method of direct integration, the formulated thermoelasticity problem is reduced to solving a governing equation for an individual key function, while all the stress-tensor components are expressed through this key function uniquely. An efficient successive algorithm is developed in order to exactly satisfy the boundary conditions including the corner points of the cylinder. The solution allows for the exact analysis of thermal stresses in elastic cylinders with large and small length-to-radii ratios.

Variational estimates of the parameters of a thermal explosion of a stationary medium in an arbitrary domain

The variational formulation of the nonlinear problem of steady heat conduction in an arbitrary configuration domain is applied to investigate the conditions for the existence of a steady-state temperature distribution in a stationary medium with the intensity of volumetric energy release rising with increasing temperature. Based on the relations of the time-independent theory of thermal explosion, a variational model of this phenomenon is constructed, which makes it possible to obtain estimates of the critical values of the parameters that determine the temperature state of the medium preceding the thermal explosion. The examples of a comparative analysis of such values for a solid and a hollow cylinder of finite length are given.

Stress–Strain State of Coiled Steel

In a new mathematical model of the stress–strain state of steel strip in the course of cooling, the nonplanarity, surface roughness, and transverse thickness variation (convexity of the cross section) are taken into account. The stress–strain state of a coil of thin steel sheet has a significant influence on factors such as the temperature distribution in the coil; the scale formation on cooling in the course of hot rolling; the adhesion of adjacent turns in the annealing of cold-rolled strip; and the shape of the coil itself. The mathematical model is based on representation of the coil as individual nested hollow cylinders of finite length. The cylinders are divided into sections over the width. The sum of solutions of the Lame equation for individual sections is shown to converge to the solution for the cylinder as a whole. The model permits calculation of the coil’s stress–strain state, taking account of gap formation between adjacent turns as a result of the transverse variation in strip thickness. The modeling results show how the radial and tangential stress formed in strip winding is distributed within the coil. The model permits calculation of the stress–strain state of the coil in the winding of even strip; in the winding of convex even strip with no tension; in the loose winding of convex even strip with tension less than that in tight winding; in tight winding of even convex strip with the correct tension; and in the winding of convex uneven strip without tension. The decrease in distance between contacting rough surfaces is calculated on the basis of a probabilistic approach. An algorithm is presented for calculation of the coil’s stress–strain state. The result obtained for the stress distribution in the coil is typical for the winding of steel strip. The model is verified for the winding of hot-rolled strip, in terms of the size of the region with tight contact of adjacent turns. The tightness of contact is assessed on the basis of the temper color on the edges of the hot-rolled strip. The discrepancy between the calculated and measured size of the region with tight contact is 3%.

Axisymmetric Problem of the Theory of Elasticity for a Hollow Cylinder of Finite Length with Regard for Its Weight

We consider a hollow elastic cylinder of finite length subjected to the action of its own weight and an axisymmetric normal load applied to the upper base. The lower base of the cylinder is immovably fixed. The inner cylindrical surface is under the conditions of sliding restraint and its outer surface is immovably fixed. The problem is reduced to an integral equation of the first kind for normal stresses on the fixed lateral surface. We determine the character of singularity of the required function and propose an efficient algorithm for the solution of the obtained equation based on the expansion of the required function in a series in Jacobi polynomials. We present the results of calculations of normal stresses on the lateral surfaces of the cylinder, which show that, in the case of rigid fixing, the influence of the weight of the cylinder is much weaker than in the case of sliding restraint.

Free Axisymmetric Vibrations of a Hollow Cylinder of Finite Length Made of a Functionally Graded Material

On the basis of the three-dimensional elasticity theory, we study a problem of free axisymmetric vibrations of inhomogeneous hollow cylinders of finite length made of functionally graded materials under different boundary conditions imposed on their end faces. The elastic properties of the material continuously vary in the radial direction. We propose a numerical-analytic approach for the solution of this problem. The original problem of the elasticity theory containing partial differential equations is reduced to a boundary-value problem for the systems of ordinary differential equations of high order in the radial coordinate by using spline approximations and collocation methods. The obtained one-dimensional problem is solved by using a stable numerical method of discrete orthogonalization together with the method of step-by-step search. We also present the results of determination of the frequencies and modes of vibrations of the cylinder made of a functionally graded material obtained as a composition of stainless steel and nickel for different types of boundary conditions imposed at the end faces and different values of temperature.

Elastic Mechanical Stress Analysis in a 2D-FGM Thick Finite Length Hollow Cylinder with Newly Developed Material Model

In this paper a new 2D-FGM material model based on Mori-Tanaka scheme and third-order transition function has been developed for a thick hollow cylinder of finite length. Elastic mechanical stress analysis is performed by utilizing the finite element method. The corresponding material, displacement and stress distributions are evaluated for different values of nr and nz. Moreover, the effects of different material property distributions on the effective stress with respect to the metallic phase volume fraction are investigated. It is demonstrated that the increase in nr and Vm leads to a significant reduction in the effective stress. Finally, it is shown that the ceramic phase rich cylinder wall has lower maximum effective stresses of which the lowest value of effective stress has been evaluated for nr = 20 and nz = 5. This minimum value is about half the maximum effective stress which has been evaluated for the non-FGM cylinder case (nr = nz =0.1).

Exact Solution of Some Axisymmetric Problems for Elastic Cylinders of Finite Length Taking Into Account Specific Weight

The finite Hankel transform is used to find the exact solution of two axisymmetric problems of elasticity for solid and hollow cylinders of finite length taking their specific weight into account. The boundary conditions at the lower end and on the lateral faces of the cylinders are sliding restraint. Axisymmetric normal and tangential forces act on the upper end. The transforms of the displacements and stresses are obtained. The calculated normalized stresses on the outside and inside cylindrical surfaces are plotted for different height ratios

Stress Analysis and Parameter Optimization of an FGM Pressure Vessel Subjected to Thermo-Mechanical Loadings

The thermo-mechanical behavior and material design of functionally graded materials (FGMs) has been gaining increasing attention in the past two decades. However, little work can obtain the exact solution of FGM vessel consisting of a finite length hollow cylinder and two closed ends due to the difficult in calculating the axial strain. By constructing an exponentially function determining the material properties and based on the steady state thermo-elastic theory and Euler-Cauchy formula, the closed-form analytical solutions of the thermo-mechanical stresses for the FGM vessel subjected to an internal pressure and a thermal load were firstly established taking the effect of closed ends into consideration. And then, a numerical model of the FGM pressure vessel was developed using the finite element (FE) method for validating the analytical solution. Lastly, a double-variable optimization model was proposed for determining the optimal material distribution of the FGM pressure vessel. The results demonstrated the accuracy and efficiency of the proposed stress formulations and optimization model in this paper, which would be helpful for better understanding and scientific design of FGM vessel or related structures.

Contact problems for a circular plate with sliding fixation at the end face

Two mixed elasticity problems of punch indentation into a circular plate placed without clearance in a rigid cylindrical holder with smooth walls are considered. In the first problem, the plate lies without friction on a rigid base, and in the second problem, the plate is rigidly fixed to the base. The problems are solved by a method that was developed for bodies of finite dimensions and is based on the properties of closed systems of orthogonal functions. Each of the problems is reduced to two integral equations, namely, a Volterra integral equation of the first kind for the contact pressure function and a Fredholm integral equation of the first kind for the derivatives of the displacement of the plate upper surface outside the punch. The displacement function is sought as the sum of a trigonometric series and a power function with a root singularity. After truncation, the obtained illposed system of linear algebraic equation has a stable solution. A method for solving Volterra integral equations is given. The contact pressure distribution function and the dimensionless indentation force are determined. Examples of calculation of the plate interaction with the plane punch are given. Contact problems were earlier studied for a rectangle and a circular plate with a stress-free end both without taking account of their fixation [1, 2] and with regard for their fixation [3, 4]. The solution method described here was used to study the interaction of elastic hollow cylinder of finite length with a rigid bandage and a rigid insert [5, 6]. Other papers dealing with contact problems for bodies of finite dimensions, in particular, for a circular plate, should also be mentioned. In these papers, the problems under study were solved by the method of homogeneous solutions [7, 8] and by the method of coupled series-equations [9].

Torsional Vibrations of Finite Hollow Poroelastic Circular Cylinders

In this paper, the problem of torsional vibrations of a homogeneous, isotropic poroelastic hollow cylinder of finite length is solved. Results of solid cylinder of finite length and classical theory of elasticity are obtained as a particular case. Frequency is calculated numerically for different materials and presented in tables.

Vibroacoustic response and active control of a fluid-filled functionally graded piezoelectric material composite cylinder

The linear three-dimensional piezoelasticity theory in conjunction with the versatile transfer matrix approach is employed to investigate the steady-state nonaxisymmetric fluid–structure-coupled vibrations of an arbitrarily thick bilaminate simply supported hollow cylinder of finite length, composed of an inner layer of orthotropic functionally graded material perfectly bonded to an outer layer of radially/axially/circumferentially polarized functionally graded piezoceramic material. The cylinder is filled with a compressible nonviscous fluid and may be subjected to arbitrary time-harmonic on-surface mechanical drives. The analytical results are illustrated with numerical examples in which water-filled homogeneous PZT4–steel composite cylinders are driven by harmonic external concentrated or distributed radial surface loads. When the outer piezoelectric layer is operating in the receiving (sensing) mode, the frequency spectrums of the induced voltage, stress components, and on-axis acoustic pressure are calculated and discussed for the selected loading configurations. Also, when the piezolayer operates in the active vibration mode, the effects of polarization direction and number of control modes on the voltage required for partial or complete cancellation of the on-axis internal pressure are investigated. Limiting cases are considered, and the validity of results is established by comparison with the data in the existing literature as well as with the aid of a commercial finite element package.

Analytical modelling of the three-dimensional steady-state temperature in a bearing ring

An analytical solution to compute the 3D steady state temperature distribution in a bearing ring is presented in this paper. The ring is formed by a hollow cylinder of finite length. Its radial external surface is subjected to localized, identical heat sources, equally spaced in the azimuth direction. This surface is also subjected to convective cooling while as the internal surface is maintained at a uniform temperature. The developed solution is explicit and does not impose any restriction on the geometrical or physical parameters.

Modelling of electrospinning process at various electric fields

In electrospinning process nanostructured solid fibres are produced from charged polymer jet oriented at external electrostatic field. Materials such as polymer, composites and tissue scaffold fibres have been fabricated with electrospinning techniques. The typical obstacle of electrospun fibre production is the whipping instability, resulting from the chaotic oscillation of polymer jet. In this Letter, feasibility of suppressing the whipping instability is analysed and explained using a mathematical model based on the usage of secondary electrostatic field created by finite length hollow cylinder. It is shown that the three-dimensional path of polymer jet calculated by computer simulations focus the characteristic spot size of the deposited electrospun fibre to a smaller diameter, which is coherent to the experimental observations.

Free vibrations of axially polarized piezoceramic hollow cylinders of finite length

The problem of the free axisymmetric vibrations of longitudinally polarized piezoceramic hollow cylinders is solved by a numerical analytic method. The spline-collocation method with respect to the longitudinal coordinate is used to reduce the original problem of electroelasticity to an eigenvalue boundary-value problem for ordinary differential equations with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed for a wide range of their geometric characteristics