Minimum and central film thickness formulae for an elastic layer firmly bonded to a rigid cylindrical substrate under entraining motion

Analytical minimum and central film thickness formulae have been derived for elastic layers firmly bonded to rigid cylindrical substrates under entraining motion when the contact width is significantly larger than the layer thickness. The elastic layer has been assumed to be either a compressible or an incompressible material; the corresponding Poisson's ratios are assumed to be 0.4 and 0.5 respectively. Good agreement has been found between the film thicknesses predicted by these film thickness formulae and some numerical solutions for similar conditions. Good agreement has also been found with the general full numerical solution for incompressible elastic layered surfaces.     

Contact problems for the thin elastic layer

Simple approximate solutions due to Jaffar and Johnson for the indentation by a rigid frictionless punch of a thin elastic layer on a rigid foundation are extended to the corresponding general three-dimensional problem. Results are given for the case where an incompressible layer is indented by an ellipsoidal punch and an analogy is demonstrated between the flat punch problem with arbitrary plan-form and the St Venant torsion problem.     

Finite deformations of an initially stressed cylindrical shell under internal pressure

This paper investigates the large deformations of an extended thick cylindrical tube under internal pressure, with emphasis on the static nonlinear behavior and instabilities of the shell. Thick elastic tubes that undergo large elastic deformations under internal pressure can exhibit novel instabilities. After some deformation, part of the tube becomes highly deformed taking the form of a bulge, while the remainder appears almost unchanged. This local instability phenomenon corresponds to a limit point along the nonlinear equilibrium path. After the onset of these highly nonuniform deformations, the local bulge initially grows with a marked decrease in internal pressure while the rest of the tube unloads. First, a detailed experimental analysis is carried out involving different geometries and initial axial forces and the influence of the axial force and of the internal pressure on the critical pressure is investigated. The shell used in the experiments is composed of an isotropic, homogeneous and hyperelastic rubber, which is modeled as a Mooney–Rivlin incompressible material, described by two elastic constants. These constants are obtained by comparing the experimental and numerical solutions for the shell under axial tension. The governing shell equations are solved numerically using the finite-element method, using the program ABAQUS. The experimental results are, as shown in the paper, in satisfactory agreement with the numerical analysis.     

Vibrations of the walls of a slot channel with a viscous fluid formed by three-layer and solid disks

An axisymmetric problem of hydroelastic vibrations of the walls of a channel with a pulsating layer of a viscous incompressible fluid is investigated. The channel walls are formed by the concentric circular three-layer elastic plate and absolutely solid disk with an elastic coupling. The laws of motion of the channel walls, their amplitude and phase frequency characteristics, as well as the hydrodynamic parameters of the fluid layer in the channel are found. An example of the computation of resonance vibrations of a hydromount with a three-layer elastic structural element is shown.     

A finite-element analysis of the indentation of an elastic-work hardening layered half-space by an elastic sphere

An elastic–plastic contact problem in elastic-work hardening layered half-space indented by an elastic sphere was solved numerically using the finite element method. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stresses and deformation fields are presented for a relatively thin elastic layer. Differences between the elastic and elastic–plastic solutions for the contact pressure distribution have been investigated for various layer thicknesses. Crack initiation and decohesion of the layer was also discussed with reference to the growth of the plastic zone.     

Viscoelastic flow between two infinite parallel porous plates,one plate oscillating and the other plate in uniform motion

The problem of viscoelastic incompressible flow between two infinite parallel porous plates, one oscillating and the other in uniform motion, was studied and an iteration method was used to solve the fluid dynamical equations. The solution obtained is valid for small values of the elastic parameter S. The effects of the flow parameters S and σ (the Reynolds number) on the velocity distribution and on the shearing stress at the plates are presented graphically.     

Studies of the amplitude frequency characteristics of oscillations of the tube elastic walls of a circular profile during pulsed motion of a viscous fluid under the conditions of rigid jamming on the butt-ends

The flow of a viscous incompressible fluid under harmonically changing pressure in a cylindrical slot formed by two coaxial cylindrical elastic shells with a finite length located concentrically is investigated. The flow parameters and elastic shifts of the shells have been found. Their amplitude and phase frequency characteristics and resonant frequencies have been determined.     

Grillages of maximum strength and maximum stiffness

Assuming a preassigned beam depth, minimum weight solutions are derived for both perfectly plastic and elastic grillages of given strength as well as elastic grillages of given stiffness. The solutions presented also give a minimum reinforcement volume for perfectly plastic fibre-reinforced plates. Common kinematic optimality conditions are stated for the foregoing classes of problems and a method is outlined for finding the optimal solution for any clamped boundary. Morley's claim regarding the non-existence of certain kinematically admissible optimal solutions is shown to be erroneous. The proposed technique is illustrated with a number of examples.     

Elasticity solution for an axially compressed and encased cylindrical specimen

We present the solution of the linear elasticity equations governing the deformation of an elastic cylinder encased in a tube and subjected to uniform compression on the flat ends. The solutions for the stresses, strains, and displacements in the encased and compressed cylinder are all systematically determined from the basic solution of Lamé's classical elasticity problem of the long tube subjected to internal and external pressures. We first derive the general elastostatic analysis for an encased hollow cylinder, stress-free at the cavity, and later particularize the solution to a solid cylindrical specimen. The effective modulus E_eff of the encased sample is found to be a function of the bulk modulus k and Poisson's ratio ν of the material. E_eff differs from k except for nearly incompressible materials, where E_eff approaches the bulk modulus value. In the incompressible case, we also show how a load applied on the cylinder's flat ends is equivalent to, and can be replaced by, the same load acting on the curved surface. For compressible materials, a more general expression for E_eff is found that also accounts for the case deformation. These results explain the deformation of an axially compressed and encased cylindrical specimen tested in compressibility measuring devices such as those described by Matsuoka and Maxwell [Response of linear high polymers to hydrostatic pressure. Journal of Polymer Science 1958; 32:131–59]. The present analysis thus contributes to a better understanding of how this device works and to the interpretation of measurements taken with it.     

超高压力温度状态液压油体积弹性模量测量装置故障分析

液压油的体积弹性模量和热膨胀系数是分析研究液压系统动、静态特性的两个不可或缺的重要参数。在超高压力及温度状态下,液压油就不能再视为不可压缩流体,其压缩和膨胀将对液压系统的动、静态特性产生极其重要的影响。因此,测量超高压力及超高温度状态液压油的体积弹性模量和热膨胀系数对设计研究超高压力温度液压系统有着重要的理论和实际意义。针对所设计的超高压力温度液压油体积弹性模量测量装置,结合测量过程中出现的实际问题,进行故障原因分析研究,并提出改进措施,以利于后续对不同高温高压液压油进行体积弹性模量测量研究。     

Modified boundary layer analysis for a mode III crack problem

A modified boundary layer problem of a semi-infinite crack in an elastic-perfectly plastic material under a Mode III load is analyzed. The analytic solution of elastic fields is derived by using complex function theory. It is found that the size and the shape of the plastic zone near the crack tip depend on the elastic T-stress given on the remote boundary. A method for determining higher order singular solutions of elastic fields is also proposed. In order to determine the higher order singular solutions of the elastic fields, Williams expansion of the solution is used. Higher order terms in the Williams expansion are obtained through simple mathematical manipulation. The coefficients of each term in the Williams expansion are also calculated numerically with the J-based mutual integral     

Dynamics of interaction of elastic elements of a vibrating machine with the compressed liquid layer lying between them

The interaction of channel walls having an elastic yielding with a layer of viscous incompressible liquid between them is studied under channel vibration. The pressure distribution in the liquid, laws of motion of the walls, and their amplitude and phase-frequency characteristics which allow us to study dynamical processes in vibrating machines with an external source of vibration are determined.     

Energy, Adhesion, and the Elastic Foundation

A theory for elastic contact adhesion between a rigid sphere and an elastic foundation is developed. The theory derives relationships between the contact deformation and the externally applied force. The derivation is based on elastic contact between a sphere and a thin linear-elastic foundation in which the strain energies are balanced by the work of indentation and the change in surface energy. Contacting regimes where there is either compressive strain energy or only tensile strain energy (pull-off regime) are both treated. The model is non-dimensionalized and an order of magnitude analysis is performed in order to develop simplified closed form solutions; the simplified model is then evaluated and compared to the full solution. This theory finds that the adhesion force is significantly larger for an elastic foundation in which the surface elements act independently as compared to more traditional solutions for elastic solids. The theory gives an adhesion force of $ F_{\text{adh}} \cong 7\pi R\Updelta \gamma . $      

Review on open-problems of spin-up flow of an incompressible fluid

Open-problems on spin-up flow of an incompressible homogeneous fluid have been reviewed. Characteristics of spin-up are followed by a summary of well-established previous papers along the order: linear spin-up, weakly nonlinear spin-up and non-linear spin-up. Discussions are given to open problems from previous analytic theories as compared with full numerical solutions for Navier-Stokes equation.     

Contact problem for elastic layer and rigid cylinder with friction forces

The contact problem for the elastic layer of an arbitrary thickness and the rigid cylinder with friction forces acting in the contact area is solved and the solution is analyzed. Domains of applicability of the widely used solutions, i.e. the solution for a rigid cylinder and elastic half-space and the solution for a thin elastic layer, are determined for the contact under consideration. It is shown that for coatings from composite materials with a low elastic modulus both solutions can result in a significant error. Typical modes of the elastic displacement of the layer surface are given for different contact area width, Poisson’s ratio, and friction coefficient. The example of the calculation of the particular contact for the layer of the polymer composite with a low elastic modulus is presented.     

Techniques of analysis for nonlinear transient flow in a pipe

Analytical solutions to the time-dependent, nonlinear equation governing incompressible, one dimensional flow in a pipe are presented. The flow is pressure-driven, and a valve on the pipe controls the flow rate. Power-law losses and an exponential closing action of a valve are assumed. Four different approximation methods are used. Of these, perturbation and Adomian's decomposition are seen to be valid only for small time. The WKB approximation works only for a quadratic loss term. Homotopy analysis is broadly applicable but needs parameter tuning, optimal values of which have been determined.     

The effect of fluid inertia on the film pressure between two axially oscillating parallel circular plates with a viscoelastic lubricant

A viscoelastic incompressible fluid between two parallel circular plates separated by a small distance with sinusoidal axial vibration of the top plate including fluid inertia terms was considered. Flow phenomena were characterized by non-dimensional parameters such as the Reynolds number Re and the elastic number S. An iteration method was used to solve the non-linear equations. The effects of Re and S on the fluid pressure were studied.     

Integrated adaptive element free Galerkin model for elastoplastic contact of engineering surfaces

Abstract

This paper presents an h-adaptive element free Galerkin (EFG) model and its formulation based on stain energy gradient for solving elastoplastic contact problems. In this model, the element free Galerkin finite element (EFG–FE) coupling method uses the initial stiffness method, and an error estimation approach based on strain energy gradient and a local adaptive refinement strategy are combined. Two-dimensional elastic contact problem between a rigid cylinder and an elastic plane is analysed to validate the adaptive elastoplastic EFG model. The results indicate that the adaptively refined solutions are accurate as compared to the Hertz theoretical solution or the uniformly refined solutions, while the cost of CPU time used by the adaptive model is less than that by the uniformly refined model under the same condition. Furthermore, the elastoplastic contacts involving a rough surface of elastic perfectly plastic and elastoplastic properties are investigated.     

Indentation of an elastic layer(s) bonded to a rigid cylinder—I. Quasistatic case without friction

A quasistatic, frictionless indentation problem for an incompressible elastic layer(s) bonded to a rigid cylinder is solved by use of a stress function in the form of a series. The method of Yau is then applied to obtain the solution of the dual series equations resulting from the mixed-type boundary condition which categorizes the problem. Although the analysis is given in detail only for a single-layered cylinder, comments on the many-layered case are made and some numerical results are given for a two-layered covering. In addition, some observations are made concerning a specific numerical example typical of rubber-covered steel rolls of the sort used in paper mills.     

Numerical simulation of beam unloading from elastic linkages in a plane-parallel medium flow

The process of profile unloading from elastic linkages in a plane-parallel flow of an incompressible medium is examined. The beam model of profile deformation is used. The parameters of the transient mode under different pause durations between linkage breaks are determined. The procedure permitting the solution of the connected problem of aeroelasticity by means of the vortex elements method used to determine the nonstationary aerodynamic loads is verified and the results of the verification are given.