Rubber covered rolls—the thermoviscoelastic problem. A finite element solution

The coupled thermomechanical behaviour of a layer of thermorheologically simple material bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder is studied by the finite element method. The various approximations necessary to reduce the problem to one of tractable size and the computational methods used are discussed in some detail. The complete thermal, deformation and stress fields may be computed. Some results, computed for a grid using ‘rectangular’ elements, presented graphically include the temperature distribution, the stress distribution near the bond surface, the contact pressure distribution and the asymmetric surface deformation of the rubberlike layer.     

Quasistatic indentation of a rubber-covered roll by a rigid roll

The nonlinear elastic problem involving the indentation of a slightly compressible rubber-like layer bonded to a rigid cylinder and indented by another rigid cylinder is analysed by the finite element method. Both the geometric and material nonlinearities are accounted for. The finite element formulation of the problem is based upon a variational principle recently proposed by Cescotto and Fonder, and is valid for both slightly compressible and incompressible materials. The results computed and presented graphically include the shape of the indented surface, the pressure distribution over the contact surface, and the stress distribution at the bond surface. For the same contact width, the results for the compressible material are found to differ significantly from those for the case when the rubber-like layer is assumed to be incompressible.     

Axisymmetric contact of an elastic layer underlain by rigid base

Axisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.     

Torsional impact of a layer or a cylinder bonded to an elastic half-space

In this paper two torsional impact problems are considered. The first problem deals with the solution of a layer bonded to an elastic half-space when the layer is driven by the torsional impact over a bonded rigid circular disc. In the second problem sudden torsion by a rigid disc attached over the plane face of a circular cylinder is considered and the rest of the plane surface of the cylinder is stress free. The cylinder is bonded to the half-space, making use of Laplace and Hankel transforms the solution of each problem is reduced into Fredholm integral equations of the second kind. A numerical Laplace inversion technique is then used to recover the time depencence of the solution. The numerical values for the applied torque at the surface of rigid disc are calculated for each problem and then are displayed graphically.     

Axisymmetric contact problem for a frictionless elastic layer indented by an elastic cylinder

This paper is concerned with the elastostatic contact problem of a semi-infinite cylinder compressed against a layer lying on a rigid foundation. It is assumed that all the contacting surfaces are frictionless and that only compressive normal tractions can be transmitted through the interfaces. Upon loading the contact along the layer-foundation interface shrinks to a circular area whose radius is unknown. The analysis leads to a system of singular integral equations of the second kind. The integral equations are solved numerically and the contact pressures, extent of the contact area between the layer and the foundation, and the stress intensity factor round the edge of the cylinder are calculated for various material pairs.     

Interfacial Effects on Stress Transfer in Fiber-Reinforced Composites

A three-dimensional solution for a fiber-reinforced circular cylinder is presented for axisymmetric force and displacement boundary conditions. The solution, which can satisfy all the boundary conditions prescribed on the curved and end surfaces of the cylinder, can be used directly in the micromechanical analysis of fiber-reinforced composites to investigate the typical representative volume element (RVE). The element consists of a combined circular cylinder composed of a solid inner circular cylinder of transversely isotropic fiber, a concentric outer circular cylinder of isotropic matrix material, and an interface layer between the fiber and the matrix. The radial and tangential flexural compliances of the interfacial material are considered, and their effects on the stress transfer at the interface are studied parametrically. The numerical results presented show that the material properties of the interfacial layer have significant influences on the stress distribution within the RVE, particularly at the cross sections near the ends of the cylinder, where external loads are applied.     

Free-surface flow of a fluid body with an inner circular cylinder in impulsive motion

An analytical theory and numerical computations are developed for the two-dimensional free-surface flow of an initially circular layer of inviscid fluid surrounding a rigid circular cylinder. The two cylinders are initially concentric. The fluid packet is released from rest and the flow suddenly starts forced by gravity and by the simultaneous impulsive motion of the inner body. A small-time expansion of the fully nonlinear free-surface problem is developed and a closed-form solution is found up to third order for an arbitrary radius of the rigid cylinder. For the gravitational flow around the body at rest, the solution is extended up to fourth order. Free-surface profiles and hydrodynamic forces on the cylinder are calculated and discussed against numerical solutions of the exact unsteady nonlinear problem. Some basic features, such as the formation of an almost uniform layer surrounding the upstream side of the body, are captured by the theory quite well and only later on in time significant quantitative differences appear. Similarly, the behaviour of hydrodynamic loads is rather well predicted during initial stages preceding larger fluctuations observed on a longer time-scale.     

Thermo-contact mechanics of a rigid cylindrical punch sliding on a finite graded layer

A steady-state thermo-contact model of a rigid insulated cylinder of radius R sliding on a finite graded elastic layer is studied, whose Young’s modulus, thermal conductivity coefficient and thermal expansion coefficient vary exponentially in the thickness direction. The transfer matrix method and Fourier integral transform technique are used to obtain a Cauchy-type singular integral equation for the contact stresses. Numerical calculation yields the interface traction and temperature distributions below the rigid punch. It shows that crack damage in the finite graded layer due to the frictional sliding can be prevented by several alternative ways, such as decreasing the shear modulus ratio of the surface to the bottom, decreasing the friction coefficient, increasing the thickness of the finite graded layer, increasing the thermal conductivity coefficient ratio of the surface to the bottom or increasing the sliding velocity. The finding should be very useful for the design of novel graded materials with potential applications in aerospace, tribology, coatings, etc.     

Flexural vibration of a pyrocomposite hollow cylinder

Flexural vibration of an infinite pyrocomposite circular hollow cylinder composed of an inner and outer pyroelectric layer of class 6 bonded together by a linear elastic material with voids (LEMV) is studied. The exact frequency equation is obtained for traction-free surfaces with continuity conditions at the interfaces. Numerical results in the form of data and dispersion curves for the first and second modes of the flexural vibration of the cylinder ceramic-1/Adhesive/ceramic-2 by taking the adherents as BaTio₃ and the adhesive as an existing carbon fibre-reinforced polymer (CFRP) or as a hypothetical LEMV layer with and without voids are compared with that of a single-layered pyroelectric hollow cylinder. The damping is analyzed through the imaginary parts of the complex frequencies.     

A note on the limit load of welded joints of a rectangular cross-section

A flat layer of a rigid perfectly plastic material subjected to tension between two rigid blocks is considered. The layer is assumed to have a rectangular cross-section. The influence of the ratio of the in-plane layer dimensions on the limit load and the maximum tensile stress is studied. Comparison with numerical calculations of the limit load based on the assumption of the plane strain conditions is made.     

基于表面涡方法的单列圆柱流体诱导振动及流弹性不稳定研究

基于表面涡方法和流固耦合模型研究了Re=2.67×104时的单列圆柱流体诱导振动问题,计算了流体力、振动响应、涡脱落频率等,并给出了涡云图。计算模拟结果很好地重现了刚性单列圆柱在T/D=1.5(小间隙比)下以宽窄尾涡交替和多频为特征的非均匀流态,以及T/D=2.0的涡脱落现象。此外,该文还研究了单列弹性圆柱在T/D=1.5时的流体诱导振动以及流体弹性不稳定问题,计算了SG=1.29时圆柱列的无量纲临界速度。     

Analysis of shear bands in a dynamically loaded viscoplastic cylinder containing two rigid inclusions

Summary We study plane strain thermomechanical deformations of a hollow circular cylinder containing two rigid non-heat-conducting ellipsoidal inclusions placed on a radial line symmetrically with respect to the center. These inclusions can be viewed as precipitates or second phase particles in an alloy. The material of the cylinder is presumed to exhibit thermal softening, but strain and strain-rate hardening. The impact load applied on the inner surface of the cylinder is modeled by prescribing a radial velocity and zero tangential tractions at material particles situated on the inner surface. Rigid body motion of the inclusion is considered and no slip condition between the inclusion and the cylinder material is imposed.It is found that shear bands initiate from points adjacent to inclusion tips near the inner surface of the cylinder and propagate toward this surface. At inclusion tips near the outer surface of the cylinder, the maximum principal logarithmic strain and the temperature are high and the effective stress is low, but severe deformations there do not propagate outward.     

Stresses in cross-ply laminated circular cylinders of axially variable thickness

Summary This paper presents the results from an analytical investigation of the behavior of composite circular cylinders subjected to internal and external surface loading. The present cylinder consists of a number of homogeneous ply groups of axially variable thickness. Each ply group forming a layer is treated as an individual thin elastic cylinder of generally orthotropic material with interfacial stresses on the inner and outer surfaces of the layer as boundary loading. The deformation and stresses in each layer can be expressed in terms of interfacial stresses along the exterior surfaces of each layer. All displacement and stresses throughout the composite cylinder can be determined subsequently after satisfying boundary conditions at the inside and outside surfaces of the cylinder in conjunction with the recurrence relationship among interfacial stresses. Numerical results are presented for different values of the inner-to-outer ratio, number of layers, stacking sequence, axially-variable-thickness parameter, and load factor. Based on the presented results, conclusions can be drawn concerning the cylinder behavior and its sensitivity to different parameter variations.     

Axisymmetric finite cylinder with one end clamped and the other under uniform tension containing a penny-shaped crack

This study considers the axisymmetric analysis of a finite cylinder containing a penny-shaped transverse crack. Material of the cylinder is assumed to be linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subjected to uniform axial tension. Solution is obtained by superposing the solutions for an infinite cylinder loaded at infinity and an infinite cylinder containing four cracks and a rigid inclusion loaded along the cracks and the inclusion. When the radius of the inclusion approaches the radius of the cylinder, its mid-plane becomes fixed and when the radius of the distant cracks approach the radius of the cylinder, the ends become cut and subject to uniform tensile loads. General expressions for the perturbation problem are obtained by solving Navier equations with Fourier and Hankel transforms. Formulation of the problem is reduced to a system of five singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these five singular integral equations are converted to a system of linear algebraic equations which is solved numerically. Stress distributions along the rigid support, stress intensity factors at the edges of the rigid support and the crack are calculated.     

Nonisothermal cross-flow around a cylinder with a square cross section and an impermeable core covered with a porous layer

Nonisothermal cross flow of a viscous incompressible fluid around a porous cylinder with a square cross section is considered. Main attention is paid when an impermeable core of the cylinder is surrounded with a porous layer. The full system of Navier–Stokes and energy equations is integrated numerically by the finite-volume method. The hydrodynamic interaction between the flow and the matrix of the porous layer is described by Darcy’s law. At moderate Reynolds numbers, the influence of the permeability of the porous layer on the nature of the flow and the heat exchange between the cylinder and the flow is studied. It is shown that, with increasing permeability, heat transfer from the cylinder increases mainly on its front side. From the analysis of the data obtained, an approximate formula for the mean Nusselt number as a function of the Reynolds and Darcy numbers is derived. The results of the calculation of hydrodynamic and thermal characteristics of the cross-flow around an impermeable and a fully permeable cylinder are also presented.     

Stress intensity factor calculation of steel-lined hoop-wrapped cylinders with internal semi-elliptical circumferential crack

The purpose of this paper is to present mode I stress intensity factor for a circumferential semi-elliptical crack on the inner surface of a hoop-wrapped steel-lined CNG cylinder. The stress intensity factors along the crack front are directly computed by 3D finite element method for a wide range of variations of the crack geometry. Also influence of many parameters such as cylinder internal pressure, composite layer thickness, composite material properties and undertaking Auto-Frettage pressure are studied on the stress intensity factor of the crack and some conclusive results are drawn. For the sake of validation of the results and because of lack of the results for a circumferential semi-elliptical crack in the literature, a semi-elliptical axial crack in a composite hoop-wrapped cylinder has been modeled and the results have been compared with those in the literature showing a good agreement.     

基于ADAMS的柴油机曲轴扭振仿真

以某V型8缸柴油机为研究对象,通过多体动力学方法对该曲轴进行扭振研究。首先在ADAMS中建立曲柄连杆机构的刚体模型;然后把曲轴作为柔性体,建立曲轴的有限元模型并对其进行模态计算;最后用曲轴的柔性体模型代替曲柄连杆机构的曲轴刚体模型,得到曲柄连杆机构的刚-柔混合体动力学仿真模型。对曲轴在正常工况下和单缸熄火时的扭振进行研究,得到曲轴在正常工况下和单缸熄火时的扭振特性。     

Thermoelastic state of a two-component hollow cylinder with edge radial cracks

Stationary two-dimensional axisymmetric problems of thermal conductivity and thermoelasticity for a hollow two-component cylinder with cracks are studied by the method of singular integral equations. The cross section of the cylinder has the form of a circular concentric ring with a layer of another material that also has the form of a concentric ring and contains edge radial cracks. The surfaces of the cylinder are free of stresses. Thermal processes on these surfaces are characterized by temperature conditions of the third kind. Conditions of ideal thermal and mechanical contact are satisfied on the interface of the two media. A numerical solution is obtained for the case where the inner and outer cylindrical surfaces are kept at different constant temperatures. Stress intensity factors near the tip of one or two edge cracks were found for various values of thermal and mechanical characteristics of the cylinder.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 76–80, July – August, 1994.     

The axisymmetric double contact problem for a frictionless elastic layer indented by an elastic cylinder

This paper is concerned with the smooth receding contact between an elastic layer and a half space when the layer is compressed by a frictionless semi-infinite elastic cylinder. Upon loading, the contact along the layer-subspace interface shrinks to a circular area, radius of which is unknown. The analysis leads to a system of singular integral equations of the second kind. The integral equations are solved numerically and the contact pressures, extent of contact and the stress intensity factor round the edge of the cylinder are calculated for various material combinations.     

Directive gain from an axially slotted dielectric clad cylinder embedded in a metamaterial

The gain properties of an axially slotted cylinder coated with a lossless dielectric layer and embedded in a lossless metamaterial have been studied analytically. It is studied that the gain pattern of this cylinder when embedded in Epsilon near-zero or double-near-zero metamaterial loses its directional characteristics as compared with the same cylinder embedded in the free space. It is also found that the dielectric coated slotted cylinder embedded in a single-negative metamaterial has a directive gain pattern as compared with the gain pattern of dielectric coated slotted cylinder when embedded in the free space background.