Problem Of Cylinder Research Articles

Linear stability of radially-heated circular Couette flow with simulated radial gravity

The stability of circular Couette flow between vertical concentric cylinders in the presence of a radial temperature gradient is considered with an effective “radial gravity.” In addition to terrestrial buoyancy − ρgez we include the term − ρgmf(r)er where gmf(r) is the effective gravitational acceleration directed radially inward across the gap. Physically, this body force arises in experiments using ferrofluid in the annular gap of a Taylor–Couette cell whose inner cylinder surrounds a vertical stack of equally spaced disk magnets. The radial dependence f(r) of this force is proportional to the modified Bessel function K1(κr), where 2π/κ is the spatial period of the magnetic stack and r is the radial coordinate. Linear stability calculations made to compare with conditions reported by Ali and Weidman (J. Fluid Mech., 220, 1990) show strong destabilization effects, measured by the onset Rayleigh number R, when the inner wall is warmer, and strong stabilization effects when the outer wall is warmer, with increasing values of the dimensionless radial gravity γ = gm/g. Further calculations presented for the geometry and fluid properties of a terrestrial laboratory experiment reveal a hitherto unappreciated structure of the stability problem for differentially-heated cylinders: multiple wavenumber minima exist in the marginal stability curves. Transitions in global minima among these curves give rise to a competition between differing instabilities of the same spiral mode number, but widely separated axial wavenumbers.

E-Pulse Diagnostics of Curved Coated Conductors With Varying Thickness and Curvature

The use of the E-pulse technique to diagnose changes in the material parameters of a coating on a conducting surface is examined. To include the effects of varying curvature and coating thickness, the canonical problem of an elliptical cylinder coated with a circular dielectric layer is considered. It is shown that E pulses created using the natural resonance frequencies of a planar coated conductor may be used in the diagnosis, as long as the thickness of the planar coating is taken to be equal to the thickness of the coating on the elliptical cylinder at the specular point. The performance of the E-pulse technique improves as the size of the cylinder is increased, since the curvature of the surface approaches that of a plane

Squeeze films between a rigid cylinder and an elastic layer bonded to a rigid foundation

A numerical solution to the elastohydrodynamic lubrication problem of a rigid cylinder and an elastic layer firmly bonded to a rigid substrate in normal approach and separated by a fluid of constant viscosity is presented. The rate of change of the deformation with time was neglected in the present investigation. The governing equations were solved via an iterative method in order to compute the pressure distribution and the corresponding film profile. Influences of the layer thickness, the layer compressibility and the central squeeze-film velocity on the results were investigated. In the case of the Hertzian contact, the present method was validated against the results reported in Herrebrugh [Elastohydrodynamic squeeze films between two cylinders in normal approach, Trans ASME, J Lubric Technol Ser F 1970; 92:292–302] where the results showed a very good agreement.

Solving the stress problem for solid cylinders with different end conditions

The paper proposes an approach to solving a spatial stress problem for solid circular cylinders under axisymmetric surface loading. Two types of boundary conditions at the ends are examined: simply supported or clamped. The circumferential variable is separated using Fourier series for the former type of boundary conditions, and spline-approximation in longitudinal coordinate is used for the latter type of boundary conditions. The resulting one-dimensional problems are solved by the stable discrete-orthogonalization method, evaluating indeterminate forms on the cylinder axis in the governing equations. Radial displacements and circumferential and longitudinal stresses are plotted

Confinement effectiveness in circular concrete columns

This paper presents an analytical study of the confinement effectiveness in circular concrete columns confined by transverse reinforcement. The analytical derivation includes several stages. The first stage includes the solution to the passive confinement problem of a linear elastic cylinder, confined by a sequence of equally spaced lateral rings under axial stress. The derivation is based on and preceded by a solution to the problem of active confinement. Next, based on the solution to the passive problem, an equivalent lateral pressure is derived by replacing the steel ties with a uniform equivalent tube of constant thickness. The equivalent tube thickness is employed in this paper to analytically determine the confinement effectiveness of the problem’s variables, such as the ties spacing and cross-sectional area or the concrete–steel moduli ratio. The results are also examined and compared with the widely used empirical arch method. The comparison shows that within the practical range of the RC variables the current analytical model is in very good agreement with the empirically developed model.

Collision Probabilities in r-θ-z Geometry

An improved version of a numerical method for computing collision probabilities is developed for r-θ-z geometry. It is concluded from the results of numerous test cases that the method can be used to compute collision probabilities in this geometry with an accuracy better than 0.1% in typically <1 s (occasionally, in a few seconds when dealing with difficult cases) on the Athlon 64 3200+ processor. The developed algorithm is implemented into the framework of the collision probability method and tested for one-group criticality problems for finite circular and semicircular cylinders.

Using the method of fundamental solutions in conjunction with the degenerate kernel in cylindrical acoustic problems

This paper proposes applications of the method of fundamental solutions (MFS) to exterior acoustic radiation and scattering problems. By using the two‐point function of fundamental solutions, the coefficients of influence matrices are easily determined. It is found that this method also pordoces irregular frequencies as well as the boundary element method does. The position of the irregular frequency depends on the source point location. To avoid this numerical instability, the mixed‐layer potential method is employed to deal with the problem. Based on the circulant properties and degenerate kernels, an analytical scheme in the discrete system of a cylinder is achieved to demonstrate the existence of irregular frequencies. Three numerical examples of uniform radiation, nonuniform radiation and scattering problems of a circular cylinder are examined and are compared with the results by using direct BEM.

Finite Element Analyses of Cylinder Problems Using Pseudo General Plane Strain Elements (Planar Constraint)

A long cylinder composed of periodic structures along the axis can not be treated as a general plane strain(GPS) state, because within a repeated module, the geometry and loading condition may not be uniform along the axial direction. For this kind of situation, a ‘ more general kind of GPS ’ finite element is needed that uses a set of ‘ planar constraints ’, hereinafter called a ‘ pseudo general plane strain(PGPS) finite element ’. Otherwise, a high number of constraints need to be used, which is a tedious job and often gives rise to an input error. Plus, this can also cause a numerically ill conditioned stiffness matrix that results in a trivial or diverged solution. Accordingly, this study proposes several PGPS finite elements that use a set of planar constraints to solve long periodic cylinder problems, as well as conventional long cylinder and plane strain problems.

Generalized coupled transient thermoelastic problem of multilayered hollow cylinder with hybrid boundary conditions

The problems of the one-dimensional axisymmetric quasi-static coupled thermoelastic for multilayered hollow cylinder with clamped surface subjected to time-dependent boundary conditions. The formulation begins with the basic equations of thermoelasticity in polar coordinates. The results are obtained employing a method based on a hybrid Laplace transformation matrix similarity transformation and finite difference method. It was shown that the solutions are rapidly convergent. Solutions for the temperature, displacement and thermal stress distributions in both transient and steady state are obtained. The present method can obtain stable solutions at a specific time; thus it is a further concluded that the method and the computing process of the coupled transient thermoelastic problems of multilayered hollow cylinder are powerful and efficient.

Determination of Shakedown Limit Load for a 90-Degree Pipe Bend Using a Simplified Technique

In this paper a simplified technique is presented to determine the shakedown limit load of a 90-degree pipe bend subjected to constant internal pressure and cyclic in-plane closing bending moment using the finite element method. The simplified technique determines the shakedown limit load without performing time consuming full elastic-plastic cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit load is determined by performing two finite element analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit load is determined through the calculation of the residual stresses developed in the pipe bend. In order to gain confidence in the simplified technique, the output shakedown limit moments are used to perform full elastic-plastic cyclic loading simulations to check for shakedown behavior of the pipe bend. The shakedown limit moments output by the simplified technique are used to generate the shakedown diagram of the pipe bend for a range of constant internal pressure magnitudes. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. In order to get acquainted with the simplified technique, it is applied beforehand to a bench mark shakedown problem namely, the Bree cylinder (Bree, J., 1967, J. Strain Anal., 3, pp. 226–238) problem. The Bree cylinder is subjected to constant internal pressure and cyclic high heat fluxes across its wall. The results of the simplified technique showed very good correlation with the analytically determined Bree diagram of the cylinder.

Equilibrium of Elastic Hollow Inhomogeneous Cylinders of Corrugated Elliptic Cross-Section

The approach to the solution of a three-dimensional boundary-value stress problem for elastic hollow inhomogeneous cylinders of corrugated elliptic cross-section is proposed. The boundary conditions make it possible to separate variables along the length at the cylinder ends. It is proposed to include additional functions into the resolving system of differential equations. These functions enable the variables to be separated along a directrix using discrete Fourier series. The boundary-value problem derived for the system of ordinary differential equations is solved by the stable numerical method of discrete orthogonalization over the cylinder thickness. Results in the form of plots and tables are presented.

3646 調和振動圧力を受ける弾性円筒(S24-2 非定常応答(1),S24 数理・数値解析による先端材料評価)

This paper investigates on the elastodynamic problem of a circular thick walled cylinder subjected to harmonic vaibrational pressures on the inner surface, under a plane strain condition. A body force distribution method of solution is presented for the problem by applying fundamental solutions for harmonic vibrational loads in elasticity. The results are compared with exact solutions.

1210 非軸対称加熱を受ける圧電中空円筒の非定常圧電熱弾性問題(GS-3 電磁熱弾性)

1210 非軸対称加熱を受ける圧電中空円筒の非定常圧電熱弾性問題(GS-3 電磁熱弾性)

10402 球状弾性介在物をもつ弾性円柱の引張り(材料(1))

This paper deals with a stress concentration problem of an elastic circular solid cylinder with an elastic spherical inclusion under tension. Effects of Poisson's ratio, especially effects of negative Poisson's ratio, on the stress concentrations are investigated. Lakes has shown that there are materials with negative Poisson's ratios. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of infinite circular solid cylinder and fundamental solutions for axisymmetric problems of elasticity.

Axisymmetric circumferential internal crack problem of a thick-walled cylinder with inner and outer claddings

The elastostatic axisymmetric problem for a long thick-walled cylinder containing an axisymmetric circumferential internal crack with two claddings is considered. The claddings having different elastic properties than the hollow cylinder are assumed to be bonded to inner and outer wall of the hollow cylinder. The problem is formulated in terms of a singular integral equation of a well known type, the derivative of the crack surface displacement being the density function, using the standard transform technique. By using appropriate quadrature formulas, the integral equation is reduced to a system of linear algebraic equations. This system is solved numerically and the related stress-intensity factors are calculated for the cases of hollow cylinder with two claddings bonded to inner and outer wall of the cylinder, a cladding bonded to inner wall of the cylinder, a cladding bonded to outer wall of the cylinder and no cladding under axial tensile load. The influence of the geometrical configuration, the claddings and internal crack length on the stress-intensity factors is shown graphically.

An Element-Free Galerkin-Finite Element Coupling Method for Elasto-Plastic Contact Problems

The element-free Galerkin-finite element (EFG-FE) coupling method, combined with the linear mathematical programming technique, is utilized to solve two-dimensional elasto-plastic contact problems. Two discretized models for an elastic cylinder contacting with a rigid plane are used to investigate the boundary effects in a contact problem when using the EFG-FE coupling method under symmetric conditions. The influences of the number of Gauss integration points and the size supporting the weight function in the meshless region on the contact pressure and stress distributions are studied and discussed by comparing the numerical results with the theoretical ones. Furthermore, the elasto-plastic contact problems of a smooth cylinder with a plane and a rough surface with a plane are analyzed by means of the EFG-FE method and different elasto-plasticity models.

New boundary element method for torsion problems of cylinder with curvilinear cracks

The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.

Non-slipping adhesive contact of an elastic cylinder on stretched substrates

The plane strain problem of an elastic cylinder in adhesive contact with a stretched substrate is studied via a generalized JKR model taking into account the transmission of both tangential and normal tractions across the contact interface. The width of the contact region is determined from the Griffith energy balance near the contact edge. In the absence of external loading, the tangential traction is found to have a negligible effect on the contact size. As an external stress is applied to stretch the substrate, the contact solution exhibits three distinct regimes characterized by two threshold strains: (i) the size of the contact region is hardly affected by the applied loading when the substrate strain is below the first threshold level; (ii) the contact size decreases quickly with stretch as the substrate strain increases to between the two threshold levels; (iii) the contact size approaches zero when the substrate strain exceeds the second threshold level. Interestingly, these results share a number of common features with the experimentally observed cell reorientation on a cyclically stretched substrate. An approximate solution is presented in an appendix to represent the numerical results in closed form.

Cracked infinite cylinder with two rigid inclusions under axisymmetric tension

This paper considers the problem of an axisymmetric infinite cylinder with a ring shaped crack at z = 0 and two ring-shaped rigid inclusions with negligible thickness at z = ± L. The cylinder is under the action of uniformly distributed axial tension applied at infinity and its lateral surface is free of traction. It is assumed that the material of the cylinder is linearly elastic and isotropic. Crack surfaces are free and the constant displacements are continuous along the rigid inclusions while the stresses have jumps. Formulation of the mixed boundary value problem under consideration is reduced to three singular integral equations in terms of the derivative of the crack surface displacement and the stress jumps on the rigid inclusions. These equations, together with the single-valuedness condition for the displacements around the crack and the equilibrium equations along the inclusions, are converted to a system of linear algebraic equations, which is solved numerically. Stress intensity factors are calculated and presented in graphical form.

Magneto–thermo–electro–elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings

The article presents an analytical solution for magneto–thermo–electro–elastic problems of a piezoelectric hollow cylinder placed in an axial magnetic field subjected to arbitrary thermal shock, mechanical load and transient electric excitation. Using an interpolation method solves the Volterra integral equation of the second kind caused by interaction among magnetic, thermal, electric and mechanical fields, the electric displacement is determined. Thus, the exact expressions for the transient responses of displacement, stresses, electric displacement, electric potential and perturbation of the magnetic field vector in the piezoelectric hollow cylinder are obtained by means of Hankel transforms, Laplace transforms, and inverse Laplace transforms. From sample numerical calculations, it is seen that the present method is suitable for a piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation, and the result carried out may be used as a reference to solve other transient coupled problems of magneto–thermo–electro–elasticity.