Equilibrium of a Prestressed Strip Reinforced with Elastic Plates

The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied     

5级人防口部粘钢封堵接头抗爆实验研究

通过粘钢实现一典型汽车库人防口部封堵的设计方案,并对原设计方案进行相似设计后,对粘钢接头结构实验模型在核爆炸压力模拟器中进行模爆实验,得到沿竖向支座钢板的位移和应变时程曲线,并和有限元数值解进行了对比,其结果均较吻合,通过沿竖向支座钢板的应变分布规律得到钢板-混凝土界面之间的粘结应力;检验了在5级人防爆炸冲击波作用下,混凝土墙与钢板间粘结面承载力的可靠性;分析了5级人防爆炸荷载作用下支座钢板沿竖向应力的分布规律,为确定混凝土墙与钢板之间粘结应力的计算方法提供了参考。     

The symmetrical adhesive contact problem for circular elastic cylinders

The rolling contact problem involving circular cylinders is at the heart of numerous industrial processes, and critical to any elastohydrodynamic lubrication analysis is an accurate knowledge of the associated contact pressure for the static dry problem. In a recent article [1] the authors have obtained new horizontal pressure distributions, both exact and approximate for various problems involving the symmetrical contact of circular elastic cylinders. In [1] it is assumed that only the circumferential horizontal displacement is prescribed in the contact region while the vertical circumferential displacement is left arbitrary and is assumed to take on whatever value is predicted by the deformation. The advantage of this assumption is that the problem reduces to a single singular integral equation which by transformations can be simplified to an integral equation involving the standard finite Hilbert transform. Here we consider the more general displacement boundary value problem within the contact region, and to be specific we examine the problem with zero vertical circumferential displacement and prescribed horizontal circumferential displacement. The solution of this problem involves two coupled singular integral equations for the horizontal and vertical pressure distributions. Basic equations and some approximate analytical solutions are obtained for symmetrical contact of circular elastic cylinders by both parallel plates and circular cylinders which are either rigid or elastic. Numerical results for the approximate analytical solutions are given for contact by rigid parallel plates and rigid circular cylinders.     

Experimental study on condensation heat transfer of steam on vertical titanium plates with different surface energies

Visual experiments were employed to investigate heat transfer characteristics of steam on vertical titanium plates with/without surface modifications for different surface energies. Stable dropwise condensation and filmwise condensation were achieved on two surface modification titanium plates, respectively. Dropwise and rivulet filmwise co-existing condensation form of steam was observed on unmodified titanium surfaces. With increase in the surface subcooling, the ratio of area (η) covered by drops decreased and departure diameter of droplets increased, resulting in a decrease in condensation heat transfer coefficient. Condensation heat transfer coefficient decreased sharply with the values of η decreasing when the fraction of the surface area covered by drops was greater than that covered by rivulets. Otherwise, the value of η had little effect on the heat transfer performance. Based on the experimental phenomena observed, the heat flux through the surface was proposed to express as the sum of the heat flux through the dropwise region and rivulet filmwise region. The heat flux through the whole surface was the weighted mean value of the two regions mentioned above. The model presented explains the gradual change of heat transfer coefficient for transition condensation with the ratio of area covered by drops. The simulation results agreed well with the present experimental data when the subcooling temperature is lower than 10 °C.     

Further considerations of two-dimensional condensation drop profiles and departure sizes

The problem of the equilibrium shape and departure size of two-dimensional dropwise condensation drops on a vertical surface, presented in an earlier work, is extended to include advancing contact angles to 180°. The equation of the surface of the drop is obtained by minimizing (for a given volume) the total energy of the drop, consisting of surface and gravitational energy, using the techniques of variational calculus. The solution is tractable once the advancing contact angle is known, and is taken as an approximation to the axial meridian profile of a threedimensional drop. The receding contact angle is obtained as part of the solution. The drop size is specified by imposing its vertical length in contact with the wall. A maximum value of this length exists which provides a real solution, and this is taken as the departure size of the drop. It is shown that the general departure shape for an advancing contact angle of 180° includes the cases for all advancing contact angles.     

含膦酸酯官能团离子液体对钢/铝摩擦副的润滑作用研究

合成了3种新型1-(O,O-二乙基膦酰丙基)-3-烷基咪唑六氟磷酸盐离子液体,采用SRV型摩擦磨损试验机评价了所制备的离子液体作为润滑剂对钢／铝摩擦副摩擦学性能的影响,并探讨了其润滑机理．结果表明,所合成的离子液体作为润滑剂对钢／铝摩擦副具有优良的润滑作用,摩擦系数低,抗磨性能优良．表面分析结果表明含膦酸酯官能团的离子液体在摩擦副接触表面形成化学吸附边界润滑膜,从而有效地起到抗磨和提高承载能力的作用．     

Action of a Local Time-Periodic Load on an Ice Sheet with a Crack

The problem of vibrations of an ice sheet with a rectilinear crack on the surface of an ideal incompressible fluid of finite depth under the action of a time-periodic local load is solved analytically using the Wiener–Hopf technique. Ice cover is simulated by two thin elastic semi-infinite plates of constant thickness. The thickness of the plates may be different on the opposite sides of the crack. Various boundary conditions on the edges of the plates are considered. For the case of contact of plates of the same thickness, a solution in explicit form is obtained. The asymptotics of the deflection of the plates in the far field is studied. It is shown that in the case of contact of two plates of different thickness, predominant directions of wave propagation at an angle to the crack can be identified in the far field. In the case of contact of plates of the same thickness with free edges and with free overlap, an edge waveguide mode propagating along the crack is excited. It is shown that the edge mode propagates with maximum amplitude if the vertical wall is in contact with the plate. Examples of calculations are given.     

Dynamics of explosive boiling of drops at the superheat limit

A physical model for explosive boiling of drops is presented. Loss of stability of the liquid-vapor interface results in occurrence of evaporation fronts. Their propagation in a metastable liquid is determined by the vapor recoil momentum. Detachment of drops from the interface is due to thermocapillary forces. The validity of the model is supported by comparison of calculations with experimental data. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Science, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 83–91, November–December, 1999.     

高速列车车轮踏面剥离引起的轮轨冲击力学响应有限元模拟

车轮踏面剥离是轨道车辆车轮非圆化损伤的常见形式之一。轮轨滚动接触过程中,车轮踏面剥离会循环冲击钢轨,诱发异常大的轮轨动态相互作用,严重影响高速列车运行平稳性和安全性。基于三维轮轨滚动接触有限元模型,模拟了高速列车车轮踏面剥离引起的轮轨冲击力学响应,分析了轮轨冲击过程中的轮轨接触力/压力、接触斑及黏/滑特性、钢轨表面节点速度分布和应力/应变状态等响应特征,讨论了列车速度、剥离长度和剥离深度等关键参数对轮轨冲击响应的影响。结果发现,车轮踏面剥离引起的轮轨动态垂向接触力随列车速度的提高呈现出先增大后减小的变化趋势,并在列车速度为300 km/h出现最大值,约为轮轨准静态垂向接触力的1.35倍;随着剥离长度的增大,轮轨动态接触力、轮/轨von Mises应力和等效塑性应变均显著增大;随着剥离深度的增大,仅车轮von Mises应力和等效塑性应变显著增大。     

Profile and departure size of condensation drops on vertical surfaces

The problem of the equilibrium shape and departure size of two-dimensional dropwise condensation drops on a vertical surface is considered. The equation of the surface of the drop is obtained by minimizing (for a given volume) the total energy of the drop, consisting of surface and gravitational energy, using the techniques of variational calculus. The solution is tractable once the advancing contact angle is known, and is taken as an approximation to the axial meridian profile of a three-dimensional drop. The receding contact angle is obtained as part of the solution. The drop size is specified by imposing its vertical length. Upon increasing this vertical length, a point is reached at which no real solution exists, and this is taken as the departure size of the drop. Comparison with measured departure sizes under various body forces from standard to 100 times earth gravity are good.     

Dynamic Stability of Equilibrium Capillary Drops

We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence to equilibrium) in a class of star-shaped initial data for which we show that topological changes of drops can be ruled out for all times. Our result applies to any drop which is initially star-shaped with respect to a small ball inside the drop, given that the volume of the drop is sufficiently large. For the analysis, we combine geometric arguments based on the moving-plane type method with energy dissipation methods based on the formal gradient flow structure of the problem.     

On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.     

Closed-form solution for the contact problem of reinforced pin-loaded joints used in glass structures

In a typical pin-loaded joint used to assemble glass plates, the hole in a glass plate is reinforced by a steel ring glued to the glass plate via a soft resin layer. Thus, the ring is in direct contact with the steel bolt and prevents the glass plate from high stress concentration. This paper proposes an analytical approach to solving the resulting conforming contact problem. The strain and stress fields inside the resin layer are first determined by exploiting the fact that the stiffness of the material constituting it is much smaller than the stiffness of steel and glass. After finding the relevant Green functions for the ring and pin, the frictionless contact between them is then formulated in terms of an integral equation with a Fourier series as the kernel. This integral equation is solved by neglecting the terms of high orders and transforming it into the Cauchy singular integral equation. The derived analytical results for the contact pressure and angle are finally compared to and validated by those obtained by the finite element method.     

Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes

The wicking height of a heated, evaporating meniscus formed by surface-wetting liquid in a vertical capillary tube with dynamic flow has been investigated. Previous experimental results and analytical models for measuring/predicting wicking heights in capillaries are also reviewed. An analytical model is presented that accounts for both major and minor vapor pressure losses along the vertical capillary tube. It is shown that during thermo-mechanical instability, vapor/meniscus interaction can become more prevalent due to increased vapor generation/pressure near the meniscus free surface. A relatively simple procedure for estimating onset of meniscus instability is presented and, when used with the vapor Reynolds number, can estimate whether vapor pressure loss is significant. By comparing the current model with the available experimental data, it is shown that the wicking height of an unstable, evaporating meniscus of n-pentane in a vertical, glass capillary tube is better estimated by considering vapor flow pressure losses – providing a 40% improvement over previous models that neglect vapor flow. In addition to vapor flow pressure loss, the dynamic contact angle and thin film profile must also be calculated to ensure accurate prediction of wicking height. Although the proposed model shows improvement, it is prone to under-predicting the actual meniscus wicking height for stable, evaporating menisci at lower relative heat loads. The proposed model can be used for predicting wicking behavior of heated, vertically-aligned liquid columns in capillary structures – which is relevant to the design of miniature heat transfer equipment/media such as wicked heat pipes, micro-channels and sintered/porous surfaces.     

Hydroelastic impact of a horizontal floating plate with forward speed

The hydroelastic responses of a horizontal plate impacting with the water at both forward and downward speeds are investigated theoretically. The longitudinal bending behavior of a horizontal elastic plate is approximated by the behavior of longitudinal strips represented as an Euler-beam model. A simplified method of hydroelastic responses of the plate is extended to the cases with forward speed and compressive force, for which the hydrodynamic pressure is found by solving a two-dimensional boundary value problem based on the linearized wave theory. In order to validate the theoretical model, a fully-coupled algorithm in LS-DYNA and the available experimental measurements are used for the predictions of the hydrodynamic pressure and deformations of the horizontal plates impacting with water at vertical velocities. The effects of the forward speed and compressive force which can occur at the bottom of ship ships, are investigated theoretically for the plates with different edge boundary conditions. The critical values of the forward speed and longitudinal compression are discussed regarding the plates with various longitudinal lengths.     

Modeling fragmentation of plasma-sprayed particles impacting on a solid surface at room temperature

Molybdenum particles were melted and accelerated by a plasma jet to impact on glass surfaces held at room temperature. A fast charge-coupled device (CCD) camera was triggered to capture images of the particles during spreading. Splats on the glass held at ambient temperature fragmented, leaving only a solidified central core. A 3D model of droplet impact and solidification was used to simulate the impact and spreading of these plasma-sprayed particles. The thermal contact resistance, which was estimated from an existing heat conduction model, was used as an input parameter in the 3D model. It was found that the thermal contact resistance between the splat central core and the glass was two orders of magnitude lower than that between the rest of the splat fluid and the surface. This suggests that the physical contact between the fluid in the splat central core and the glass surface can be improved by the large pressure generated during impact. To cite this article: A. McDonald et al., C. R. Mecanique 335 (2007).     

Force and shapes of liquid bridges between circular pads

An analytical model is presented relating the shape of an axisymmetric liquid bridge in terms of volume,v, height,h, bounding radius,r, and contact angle, , to the residual force,f, resulting from the surface tension at the liquid-vapor interface. The model is based on the assumption that gravity is negligible and the surface of the liquid bridge possesses constant mean curvature. Measurements are made of the height, bounding radius, contact angle and force for known volumes of individual, axisymmetric liquid bridges between parallel plates. Force and height comparisons are made for mercury on aluminum plates, mercury on polysiloxane-coated plates and water on polysiloxane-coated plates in air for dimensionless volumes (v/r ³) of 10 and 18. Comparisons with model predictions are also made for mercury bridges spanning a contact angle range between 138 deg and 150 deg. Finally, the shapes of liquid bridges are compared to analytical predictions. The results suggest that the constant mean curvature model, even when gravity is neglected, is an appropriate design tool that can be useful for specifying solder volumes and standoff heights for solder grid array packages.     

Surface topography formation in a region of plate collision: Mathematical modeling

The collision of earth’s crustal plates is modeled mathematically based on a numerical solution of the equations of deformable solid mechanics using a finite element method with the MSC software. The interaction of the plates with each other and with the mantle is described by the solution of the contact problem with an unknown contact boundary between the solids considered. The mantle material is assumed to be ideal elastic-plastic with the Huber-Mises yield surface, and the properties of the plate material are described using an elastic-plastic model with the Drucker-Prager parabolic yield function which takes into account fracture in the tensile stress region. The results of the mathematical modeling show that the surface profiles of the plates in the region of their collision are consistent, both qualitatively and quantitatively, to the surface topography observed in nature under similar conditions.     

A friction contact stiffness model of fractal geometry in forced response analysis of a shrouded blade

To investigate the nonlinear vibration behavior of a shrouded blade with friction dynamic contact interface, a friction contact stiffness model is proposed to describe the friction force at different rough interfaces and different normal loads. In the proposed model, the friction contact interface is discretized to a series of friction contact pairs and each of them can experience stick, slip, or separate states. Fractal geometry is used to simulate the topography of contact surfaces. The contact stiffness is calculated using the Hertz contact theory and fractal geometry, which is related to contact interfaces parameters including normal load, roughness, Young??s modulus, and Poisson??s ratio. The trajectory tracking method is used to predict the friction force and it is not necessary to judge the transition condition among stick, slip, and separate states. It is suitable for complicated periodic motion of the contact interfaces. The forced response of a real shrouded blade is predicted using the proposed model and the multi-harmonic balance method. The effect of surface roughness, initial normal load, and contact area on the forced response of a shrouded blade is studied. It is shown that contact stiffness increases with normal load and fractal dimension. The resonant amplitude is sensitive to the initial normal load and contact surface roughness. The response can be influenced by the contact area, which is an important parameter for blade designers.     

Contact angle calculations from the contact/maximum diameter of sessile drops

This paper presents two algorithms for computing the contact angle of sessile liquid drops given data about the drops. The first yields the contact angle given the volume, surface tension and maximum diameter (or contact diameter) of a single drop. This algorithm is an extension of existing algorithms based on knowledge of the maximum diameter or of the contact diameter of a drop. A sensitivity analysis is included for this algorithm, allowing estimates to be made of the error in computed contact angle caused by errors in the measurement of the volume and/or diameter. The second algorithm requires only the volume and maximum or contact diameter of two different drops as input, and it produces both the contact angle and surface tension as output. Both algorithms are based on Newton's method applied to a function whose value is computed by solving a system of ordinary differential equations obtained from the Laplace equation of capillarity. The techniques are applicable to both hydrophobic and hydrophilic surfaces. Copyright © 2000 John Wiley & Sons, Ltd.