Transient response of an elastic solid to a moving torsional load in a cylindrical bore an approximate solution

This paper is an attempt to apply Cagniard's technique to a transient problem of a dispersive medium. The transient response of an elastic solid to a moving torsional ring load in a cylindrical bore is considered. By making an approximation to the modified Bessel function, Cagniard's technique is applied. An approximate solution, which has explicit expressions for the wave front geometry and has a more suitable form for numerical computations, is obtained. The applicability of the solution is also discussed.     

Transient behaviour of branched polymer melts through planar abrupt and rounded contractions using pom–pom models

In this paper, we study the transient flow of branched polymer melts with contrasting shear and elongational properties in planar 4:1 abrupt and rounded-corner contractions. This includes Single and Double Extended forms of the Pom–Pom model (SXPP and DXPP), comparing the transient behaviour for these two different models. With the DXPP version, the evolution of the molecular-chain backbone stretch (λ) is described by a dynamic equation, whilst in the SXPP form, stretch is an instantaneous algebraic function of the stress tensor (τ). Simulations are performed with a hybrid finite volume/element algorithm. The momentum and continuity equations are solved by a Taylor–Galerkin/pressure-correction finite element method, whilst the constitutive equation is dealt with by a cell-vertex finite volume algorithm. We demonstrate some novel features due to the influence and imposition of realistic transient boundary conditions on evolutionary flow-structure. The different effects of various model parameter choices are also exposed through transient field response in principle stress difference fringe patterns, rates of deformation, first and second normal stress difference, stress and stretch.     

Stability of a layer of liquid flowing down an inclined plane

Summary The stability of the flow down an inclined plane is studied for small angles of inclination β. The same problem has been studied by S. P. Lin, however using an incorrect boundary condition. The correctly formulated eigenvalueproblem is solved by a numerical integration of the Orr-Sommerfeld equation employing the orthonormalization technique. It is shown that in the range 3′<β<1° a decrease in β means a decrease in the critical Reynolds number for the hard mode, which is a shear wave modified by the presence of the free surface. In that range the stability is still more or less governed by the stability of the soft waves, which are essentially surface waves modified by the presence of shear. For values of β<1′ the stability is governed by the hard mode, contradictory to Lin's statements. In that case instability occurs at high Reynolds numbers.     

Near Field Enhancements from Angled Surface Defects; A Comparison of Scanning Laser Source and Scanning Laser Detection Techniques

Enhancement of the Rayleigh wave signal amplitude at a surface defect, due to interference of incident, reflected and mode converted waves, has been reported by several authors, and it has been suggested that this could be used as a fingerprint of the presence of such cracking. The scanning laser line source technique in particular, where signal amplitude is enhanced as the laser generating the Rayleigh waves is in the region of a surface defect, has been reported as a suitable detection tool. However, the previous work has looked primarily at defects propagating normal to the surface, which may not always be a suitable approximation, and the enhancement measured when a detection laser rather than a generation laser is near a crack may, in some cases, be more significant. This work explores near field effects for both laser generation and laser detection points near a defect, and compares the enhancements for defects which are angled relative to the surface. We use a combination of finite element method models and experimental results, and probe enhancements of both the amplitude and frequency signals, and show that scanning the detection point may be a better method for locating surface defects if they are inclined at an angle to the surface.     

Investigation of Fatigue Growth Behavior of an Inclined Crack in Aluminum Alloy Plate

In the present paper, fatigue tensile tests are carried out on a servo-hydraulic fatigue testing machine to study the whole propagation process of the inclined crack. And the scanning electron microscope is employed to observe the micromorphology of the fracture surface to further probe the crack growth rate from a microscopic point of view. Meanwhile, the finite element method has also been applied to predict the crack propagation trajectory and the fatigue life of the sample with two finite element analysis codes. The fatigue tensile tests indicate the inclined crack propagates along the direction perpendicular to the external loading and the crack growth rate increases continuously based on the micromorphology of the fracture surface. The numerical analysis results reveal the variation of the stress distribution at the crack tip as well as the crack trajectory at different extension steps. Moreover, the stress intensity factor values are discussed in detail. And the computed results, the inclined crack propagation path and fatigue life of the sample, agree well with the experimental ones, which provide certain referential significance for the prediction of the inclined crack propagation in thin plate.     

Elastodynamic stress intensity factors for a semi-infinite crack due to three-dimensional concentrated shear loadings on the crack faces

The dynamic stress intensity factors for a semi-infinite crack in an otherwise unbounded elastic body is investigated. The crack is subjected to a pair of suddenly-applied shear point loads on its faces at a distance l away from the crack tip. This problem is treated as the superposition of two problems. The first problem considers the disturbance by a concentrated shear force acting on the surface of an elastic half space, while the second problem discusses a half space with its surface subjected to the negative of the tangential surface displacements induced by the first problem in the front of the crack edge. A fundamental problem is proposed and solved by means of integral transforms together with the application of the Wiener–Hopf technique and Cagniard–de Hoop method. Exact expressions are then derived for the mode II and III dynamic stress intensity factors by taking integration over the fundamental solution. Some features of the solutions are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Response of a viscous liquid layer around a center-core to axial excitation in zero-gravity

The response of a viscous liquid layer around a center-core to axial excitation has been determined analytically. For a simplified analytical treatment the no-slip condition at the top and the bottom of the liquid column had to be abandoned while the normal condition could be satisfied. The free liquid surface elevation, the radial- and axial velocity distribution have been presented for various surface tension parameters σa/ρv³, aspect ratios h/a and at various locations inside and along the liquid bridge as functions of the forcing frequency parameter Ω a²/ν. It could be noticed that due to viscosity the resonance amplitudes are finite and that the lowest resonance is sharply tuned.     

Effect of electrode pore geometry modeled using Nernst–Planck–Poisson-modified Stern layer model

A planar electrode containing cylindrical pores with semi-circular ends is modeled using a finite element implementation of the transient nonlinear 2D Nernst– Planck–Poisson-modified Stern (NPPMS) model. The model uses a modified Stern layer to account for finite ion size. The study includes the effects of pore radius and depth on the predicted electric potential, ion concentration, surface charge density, surface energy density, and charging time. The ion concentration and electric potential are found to be sensitive to the change in radii of the pore and insensitive to the pore depth. The surface charge density is slightly higher within the pore than along the vertical flat regions of the electrode. The increase in surface area due to porosity increases the charging time.     

Dynamic fracture analysis of an inclined subsurface crack subjected to dynamic moving loadings

The transient response of a half-space containing a subsurface inclined semi-infinite crack excited by a dynamic moving antiplane loading on the surface of the half-space is investigated in this study. The solutions of dynamic stress intensity factors are derived for all load speeds (subsonic and supersonic) and are determined by superposition of a proposed fundamental solution in the Laplace transform domain. The fundamental problem is the problem of applying an exponentially distributed traction in the Laplace transform domain on crack faces. The method of analysis is based on integral transform techniques and the Wiener-Hopf technique. The exact closed form transient solutions of dynamic stress intensity factors are expressed in very compact formulations in this study. These solutions are valid for an infinite length of time and have accounted for all the contributions of infinitely many waves. Numerical results of the transient stress intensity factor are obtained and the results of the limit case of zero load speed is compared with the corresponding static values.     

Energy balance in the discharge circuit of an electric-discharge laser

The possibility of using transient processes in the discharge circuit of an electric-discharge laser to pump the active media is analyzed. It is shown that, due to the nonlinearity of the transient process, under certain conditions, the efficiency of the energy contribution to the alternate load can almost be doubled as compared with the circuit containing a permanent load. It has been established that the process is quasiperiodic when the discharge-plasma resistance changes by an exponential law. The conditions of realization of the maximum energy contribution as well as the regions of stabilization of the optimum parameters have been determined. The necessary calculations have been performed for active media that model solutions of organic dyes under excitation by flashlamps. Deceased. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 953–960, September–October, 2000.     

Response of a viscous liquid layer to pitching-and roll-excitation in zero-gravity environment

The response of a viscous liquid layer to pitching- and roll excitation has been determined. For a simplified analytical treatment the no-slip condition at the top and the bottom of the liquid column has been abandoned in the pitching case. The response of the free liquid surface displacement and the velocity distribution has been determined as a function of the reduced frequency ωa²/ν for various surface tension parameters σa/ρv². Due to viscosity the resonance amplitudes are finite and disappear for higher modes and shorter liquid layers. The velocity distribution, effective moment of inertia and effective damping was obtained for the liquid layer in roll excitation.     

倾斜转子-滑动轴承系统周期解稳定性研究

摘　要：针对倾斜转子-滑动轴承系统的周期解稳定性问题,考虑倾斜状态下滑动轴承径向载荷的变化,基于有限元法建立了系统的动力学方程。使用Newmark方法仿真得到了倾斜转子-轴承系统的动力学响应,并分析了倾斜角度变化对转子周期解失稳阈速和失稳区宽度的影响。仿真结果表明,转子倾斜角度增大会导致转子失稳阈速减小,失稳宽度增大,但对周期解失稳区域上边界影响不大。倾斜转子的升速实验验证了仿真结果。     

Optimization of thermal processes using an Eulerian formulation and application in laser surface hardening

A systematic design approach has been developed for thermal processes combining the finite element method, design sensitivity analysis and optimization. Conductive heat transfer is solved in an Eulerian formulation, where the heat flux is fixed in space and the material flows through a control volume. For constant velocity and heat flux distribution, the Eulerian formulation reduces to a steady-state problem, whereas the Lagrangian formulation remains transient. The reduction to a steady-state problem drastically improves the computational efficiency. Streamline Upwinding Petrov–Galerkin stabilization is employed to suppress the spurious oscillations. Design sensitivities of the temperature field are computed using both the direct differentiation and the adjoint methods. The systematic approach is applied in optimizing the laser surfacing process, where a moving laser beam heats the surface of a plate, and hardening is achieved by rapid cooling due to the heat transfer below the surface. The optimization objective is to maximize the rate of surface hardening. Constraints are introduced on the computed temperature and temperature rate fields to ensure that phase transformations are activated and that melting does not occur. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite element analysis of the thermoelastic interactions in an unbounded body with a cavity

Thermoelastic interactions in an infinite homogeneous elastic medium with a spherical or cylindrical cavity are studied. The cavity surface is subjected to a ramp-type heating of its internal boundary which is assumed to be traction free. A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Lord–Shulman and Green–Lindsay for the generalized thermoelasticity model are selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. The problem has been solved numerically using a finite element method (FEM). Numerical results for the temperature distribution, displacement, radial stress and hoop stress are represented graphically. A comparison is made with the results predicted by the three theories.     

双向梯度复合材料板瞬态热应力分析

该文通过编写一种8节点高阶双向梯度单元建立了结构的连续梯度有限元模型,采用细观力学方法结合混合律准则描述了双向梯度单元变化的热物理属性。分别采用有限单元-有限差分法和有限单元法分析了在循环热载荷作用下双向梯度板Al 1100/Ti-6Al-4V/ZrO2的瞬态热传导和热弹性问题,给出了温度场和瞬态热应力场的时间响应历程和空间分布形式。最后讨论了相关参数的影响规律,得到了一些重要的结论:冷却阶段更加容易萌生表面裂纹;沿x方向组分的分布形式影响了瞬态热应力的大小,但对其时间响应和分布形式影响很小;沿y方向组分的分布形式影响了瞬态热应力的时间响应和分布形式,但对其大小影响很小。     

STUDIES OF STRESS CONCENTRATION BY USING SPECIAL HYBRID STRESS ELEMENTS

The stresses around rectangular holes of rounded corners and rounded notches are analysed by using the combination of three kinds of three-dimensional special hybrid stress finite elements. One kind of three-dimensional hybrid stress finite element with a traction-free inclined surface has been developed here based on an extended Hellinger–Reissner principle by a rational approach. Other two kinds of 12-node three-dimensional hybrid stress elements with a traction-free cylindrical surface and a traction-free perpendicular surface, respectively, were derived based on the Hellinger–Reissner principle. Examples have indicated that the combination of these special solid elements is far superior in predicting the stress concentration factors, the distributions of circumferential stresses and normal stresses for solids with holes and notches. © 1997 by John Wiley & Sons, Ltd.     

Induced free surface oscillations in a freely floating visco-elastic liquid sphere imposed to an oscillatory temperature gradient

The response of a visco-elastic liquid sphere in zero-gravity due to a time-wise oscillating temperature gradient applied at the free liquid surface has been determined analytically for a fluctuating axisymmetric temperature field. The amplitudes of the radial and angular velocity distribution as well as the free surface elevation of the liquid drop have been determined as a function of the “reduced” forcing frequency of the temperature and have numerically been evaluated for a quadratic temperature field. It was found, that visco-elasticity as described by the Maxwell model has quite some influence and appears besides the resonance amplitude with increasing relaxation time as additional peaks below and above resonance. It particularly shows inside the drop, indicating a more pronounced elastic behavior of the liquid.     

Carrying bodies with an adverse longitudinal pressure gradient

Features of formation of an adverse longitudinal pressure gradient in a supersonic flow around a carrying body with a surface inclined at a constant angle to its symmetry plane have been numerically investigated within the framework of the Euler equations. A mathematical model of such bodies constructed on the basis of pieces cut from the surface of a backward-facing hyperelliptic cone is proposed. This model allows one to obtain a wide variety of carrying bodies. The data obtained were compared with the corresponding data for equivalent bodies with a plane downstream face. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 5, pp. 100–108, September–October, 2006.     

等温黑体空腔积分发射率响应面法研究

高性能黑体辐射源是高精度复现辐射温度的关键装置。采用有限体积法模拟计算了黑体空腔积分发射率,其结果与Monte-Carlo法计算结果吻合良好,且在高发射率时较Monte-Carlo法能更准确地模拟空腔积分发射率的变化趋势。基于响应面试验设计,模拟了圆锥-圆柱黑体空腔长径比L/D、光阑开孔直径比Da/D、圆锥顶角θ和腔壁材料发射率ε及其交互作用对空腔积分发射率εe的影响。结果表明:Da/D和ε对εe影响显著;L/D和θ对εe的影响不显著。研究结果可为高性能黑体辐射源的研制和研究提供借鉴。