Exact Solution of Out-of-Plane Problems of an Arch with Varying Curvature and Cross Section

This paper deals with the exact solution of the differential equations for the out-of-plane behavior of an arch with varying curvature and cross section. The differential equations include the shear deformation effect. The cross section of the arch is doubly symmetric. Due to the double symmetry, in-plane and out-of-plane behavior will be uncoupled. However, a coupling of the out-of-plane bending and the torsional response will exist and will be discussed in this study. The governing differential equations of planar arches loaded perpendicular to their plane are solved exactly by using the initial value method. The analytical expressions of the fundamental matrix can be obtained for some cases. It is also possible to use these analytical expressions in order to obtain the displacements and the stress resultants for an arch with any loading and boundary conditions. The examples given in the literature are solved and the results are compared. The analytical expressions of the results are given for some examples.     

Inception Sediment Transport Relationships at High Slopes

This study proposes relationships between mean streamflow depth and cohesionless particle bed characteristics at the beginning of the sediment transport at high slopes in low submergence conditions. The inception of sediment transport is theoretically approached by the incipient motion condition. A previous theoretical analysis of the equilibrium of a gravel particle based on the exposure of the particle itself to the streamflow is generalized by introducing the relative position of the exposed part of the particle with respect to the bottom and by considering the case of a partially submerged particle. Using a low-submergence flow velocity profile in the particle balance of forces at the limit of equilibrium leads to a relationship between the mean flow depth and the sediment size. Another velocity profile of low-submergence flow is added to that used in the previous study, and two analytical expressions of flow depths corresponding to the beginning of sediment transport are obtained for both fully submerged particles and partially submerged particles. The theoretical flow depths given by the analytical expressions are then compared with those from previous experimental tests at the beginning of sediment transport at high slopes with fully submerged particles. The comparison shows a satisfactory agreement between theoretical and experimental values of flow depth corresponding to the degree of exposure and the relative position of the exposed part of the surface layer bed particles.     

Nonlinear Thermoelastic Buckling of Pin-Ended Shallow Arches under Temperature Gradient

This paper presents a nonlinear thermal buckling analysis of circular shallow pin-ended arches that are subjected to a linear temperature gradient field in the plane of curvature of the arch. The linear temperature gradient produces axial expansion and curvature changes in the arch. The bending action produced by the curvature change and the axial compressive action produced by the restrained axial expansion may lead the arch to buckle suddenly in the plane of its curvature. The end reactions resulting from the restrained axial expansion also produce bending actions that are opposite to that produced by the temperature differential and tend to produce deflections on the convex side of the arch. A geometrically nonlinear analysis for thermoelastic buckling has been carried out based on a virtual work technique, and analytical solutions for the critical temperature gradients for the in-plane limit instability and bifurcation buckling are obtained. It is found that antisymmetric bifurcation is the dominant buckling mode for most shallow arches that are subjected to a linear temperature gradient. The limit instability is possible only for slender and shallow arches. It is also found that a characteristic value of the arch geometric parameter exists and that arches whose geometric parameter is less than this characteristic value show no typical buckling behavior. The formula for this characteristic value of the arch geometric parameter is derived.     

Brief Analysis of Shallow Water Equations Suitability to Numerically Simulate Supercritical Flow in Sharp Bends

This work deals with the suitability of two-dimensional shallow water equations for the numerical simulation of supercritical free surface flows in bends, when the usual hypothesis of small width/curvature radius ratio does not hold. Here, a very reliable and accurate finite-volume, Godunov-type scheme is adopted for the numerical integration of the governing equations. Comparison with a selected set of experimental laboratory data and asymptotic analytical solutions shows that several aspects concerning the physics of the phenomenon are well reproduced, such as the blocking of the stream when the Froude number of the undisturbed flow is not large enough and the bend is sufficiently sharp, while maximum water depth in the bend is systematically underestimated.     

Mathematical model for on-line heat treatment of steel bars

A mathematical model to predict steel bar thermal behaviour during continuous quenching after the finishing mill has been developed. The model includes process variables, such as finishing rolling speed, finishing temperature, rod size and chemical composition, water flowrate and mechanical design of the cooling device. It was found that empirical correlations for the heat-transfer coefficient belonging to water spray systems are suitable to simulate fast cooling employing submerged water-cooling tubes. Martensite depth is strongly influenced by the bar diameter and water velocity inside the submerged tube. Mist spray systems are not as effective as submerged tubes for cooling steel bars, although, the initial cooling rates are higher. The % volume of martensite is a direct function of the self-tempering temperature, and independent of the fast cooling device.     

LCAK钢CAS精炼过程的物理模拟

针对CAS精炼过程中罩外有大量气泡溢出的问题,在相似性原理的基础上建立了CAS钢包的水模型.研究了CAS精炼过程中底吹气量、浸渍罩插入深度和不同底吹位置对钢包混匀时间的影响.实验发现:浸渍罩的中心与底吹气孔的中心同轴时,能有效地防止罩外气泡溢出.对于300 t钢包,底吹方案优化后,底吹位置选在距钢包中心0.3r~0.4r(r为钢包底部半径),精炼时底吹气量为600 L·min-1,排渣时底吹气量选在500 L·min-1左右,浸渍罩浸入深度选为180~225 mm.工业试验表明,优化后的底吹方案有效地解决了罩外气泡溢出的问题,并且提高了LCAK钢液的洁净度和可浇注性.      

宽板坯连铸结晶器内钢液流动的数值模拟

结合水模型实验,应用商业软件Phoenies模拟230 mm×2 000 mm连铸坯结晶器内钢液流场。研究了浸入式水口底型、插入深度、出口倾角等工艺参数对钢液面波动及流股对结晶器窄面冲击力的影响,并用水模型实验进行验证。结果表明,合理的浸入式水口结构尺寸和工艺参数为:凹底结构、插入深度120 mm、倾角15°。     

Erosion of Sand by Circular Impinging Water Jets with Small Tailwater

This technical note presents the results of an experimental study of the erosion of loose cohesionless sand beds by impinging circular water jets with a minimum depth of tailwater. Measurements were made of both the maximum dynamic and static scour depths and the radius of the scour hole. It was found that the dynamic scour depth is about three times that of static scour at the asymptotic state. Dimensional arguments and experimental results are used to show that the main dimensions of the scour hole at the asymptotic state are a function of the densimetric Froude number F0′ = U0′/, where U0′ = velocity of the jet at the original level of the sand bed; g = acceleration due to gravity; D = mean diameter of the sand particles; ρ = density of the eroding fluid; and Δρ = difference between particle and fluid densities. Useful correlations have been developed to estimate the size of the scour holes. Also included is a comparison between the erosion caused by submerged and unsubmerged impinging circular jets.     

Drainage of Ponded Surface by an Array of Ditches

A comprehensive analytical solution for the quantity of seepage into an array of fully penetrating ditches from a ponded surface has been obtained using hodograph and Schwarz–Christoffel transformation. The solution includes equations for the quantity of seepage from the seepage face part as well as the water depth part of the ditch. The solution also comprises expressions for the velocity potential at the stagnation point and the variation in seepage velocity. The variation in seepage quantity is like the shape of a curved channel whose boundary maps along a circle onto the hodograph plane. This shape is average of a semiellipse and a parabola. The seepage contribution from the nonseepage face is maximum for half full condition and it is half of the total seepage in an empty ditch (full seepage face). Irrespective of the spacing between ditches the quantities of seepage from the seepage face part and the nonseepage part are equal for one third full ditch. The solution also deals with special cases like single ditch, unequal spacing between ditches, and unequal depth of water in adjacent ditches. The expressions the quantity of seepage have been simplified in explicit algebraic equations through minimization of errors. The simplified expressions, which are near exact, result in answers in single step computations. Also, an example and graphs have been included to demonstrate the sensitivity of the parameters.     

Primary spacing in directional solidification

A new analytical model is developed to explain the variation in primary spacing λ with growth velocity V. In this model, dendrite growth is resolved into two parts: the growth of the center core and that of the side arms, which are separately treated. In contrast to the assumption in the current models, it is only the dendrite core, not the entire dendrite, whose curvature radius at the tip is directly related to dendrite tip radius R. The primary spacing is considered to be the sum of core diameter and twice the sidearm length. As long as the growth of side arms is suppressed, it becomes cellular growth. As a result, this model gives a reasonable dependence of cell and dendrite spacing on the process parameters. The proposed model has been applied to several alloys to compare its predictions both with experimental data and with the analytical expression of the Hunt-Lu model.     

Primary spacing in directional solidification

A new analytical model is developed to explain the variation in primary spacing λ with growth velocity V. In this model, dendrite growth is resolved into two parts: the growth of the center core and that of the side arms, which are separately treated. In contrast to the assumption in the current models, it is only the dendrite core, not the entire dendrite, whose curvature radius at the tip is directly related to dendrite tip radius R. The primary spacing is considered to be the sum of core diameter and twice the sidearm length. As long as the growth of side arms is suppressed, it becomes cellular growth. As a result, this model gives a reasonable dependence of cell and dendrite spacing on the process parameters. The proposed model has been applied to several alloys to compare its predictions both with experimental data and with the analytical expression of the Hunt-Lu model.     

Tensile Strength of Unsaturated Sand

A theory that accurately describes tensile strength of wet sand is presented. A closed form expression for tensile strength unifies tensile strength characteristics in all three water retention regimes: pendular, funicular, and capillary. Tensile strength characteristically increases as soil water content increases in the pendular regime, reaches a peak in the funicular regime, and reduces with a continuing water content increase in the capillary regime. Three parameters are employed in the theory: internal friction angle (at low normal stress) ?t, the inverse value of the air-entry pressure α, and the pore size spectrum parameter n. The magnitude of peak tensile strength is dominantly controlled by the α parameter. The saturation at which peak tensile strength occurs only depends on the pore size spectrum parameter n. The closed form expression accords well with experimental water retention and tensile strength data for different sands.     

Hydration force in the atomic force microscope: A computational study

Using a hard sphere model and numerical calculations, the effect of the hydration force between a conical tip and a flat surface in the atomic force microscope (AFM) is examined. The numerical results show that the hydration force remains oscillatory, even down to a tip apex of a single water molecule, but its lateral extent is limited to a size of a few water molecules. In general, the contribution of the hydration force is relatively small, but, given the small imaging force ( approximately 0.1 nN) typically used for biological specimens, a layer of water molecules is likely to remain "bound" to the specimen surface. This water layer, between the tip and specimen, could act as a "lubricant" to reduce lateral force, and thus could be one of the reasons for the remarkably high resolution achieved with contact-mode AFM. To disrupt this layer, and to have a true tip-sample contact, a probe force of several nanonewtons would be required. The numerical results also show that the ultimate apex of the tip will determine the magnitude of the hydration force, but that the averaged hydration pressure is independent of the radius of curvature. This latter conclusion suggests that there should be no penalty for the use of sharper tips if hydration force is the dominant interaction between the tip and the specimen, which might be realizable under certain conditions. Furthermore, the calculated hydration energy near the specimen surface compares well with experimentally determined values with an atomic force microscope, providing further support to the validity of these calculations.     

Setting and realizing process plan for straightening thin- walled tube by multiple cross rolls of equal curvature

Since it was difficult to setting the plan and the unifying curvature- radius precisely when the thin- walled tubes were straightened continuously by the rolls of equal curvature. Therefore, based on the mechanism of unifying- straightening for the multiple cross- rolls straightening machine, the judgment method of the unifying curvature- radius was presented firstly in view of the bending and springback equation of the thin- walled tube, and then the searching method of the minimum unifying curvature- radius was presented subsequently, finally the straightening plans were drawn up for different thin- walled tubes with different initial curvature radii, especially for the thin- walled tube with the large initial deformation which could not be unified by the two cross rolls, the new method was pre- bending, unifying, and straightening, and it was also presented whether a thin- walled tube could be straightened. Some procedures were developed by VB to calculate the example, which is shown that the methods are effective, meanwhile it is found that if the unifying curvature- radius exist for an initial curvature- radius, it will not be sole and will be within a scope, and it is also found that there must be a scope of the initial curvature- radius within which the thin- walled tubes can??t be unified by the two cross rolls.     

Energy Dissipation on Submerged Block Ramps

Block ramps represent structures that produce high energy dissipation and have a unique characteristic of preserving the ecological balance in a river restoration project. The energy dissipation of a block ramp changes with the tailwater level. In this technical note the relative energy dissipation in submerged flow conditions has been investigated. The experiments were conducted at the Hydraulic Laboratory of the University of Pisa, Pisa, Italy on ramps characterized by different block materials, submergence conditions, and ramp slopes. The study shows that the relative energy loss, varying the hydraulic jump location on the ramp, is essentially a function of the scale roughness, the ramp slope, the ratio between the critical water depth, and the ramp height and the ratio between the ramp length and the reduced length in submerged conditions. The differences in energy dissipation for a submerged hydraulic jump in different bed conditions are also investigated.     

Theoretical limits for the penetration depth of intracavitary applicators

We present an approximated analytical model for calculating the attenuation features of the wavefront power density, or SAR, for linear radiators inside a coaxial cylindrical cavity in both non-lossy and lossy tissues. The results are evidencing the determinant role of the cavity radius in affecting the SAR radial decay and the associated penetration depth. A further explicit finding is that the upper limit for the penetration depth in endocavitary radiative heating is equal to the cavity radius, a limit of general validity which holds in both lossy and non-lossy media for any radius value, and is not affected by the approximated nature of the model. Thus, a simple exponential equation allows a straightforward predictive evaluation of both the penetration depth intrinsic upper limit and the approximate penetration depth values, with only the knowledge of the cavity radius and the operating frequency required, without the need to refer to time-consuming electromagnetic field calculations.     

厚板坯连铸结晶器流场数值模拟

针对鞍钢新轧钢第一炼钢厂厚板坯连铸结晶器建立了三维湍流数学模型和三维实体模型.应用有限元软件对厚板坯连铸结晶器内的流场进行了模拟,计算了铸机拉速、浸入式水口出口倾角和水口浸入深度等工艺参数对结晶器内钢液流动的影响.对比表明,数值模拟结果与水模实验结果相符.     

Scour at Submerged Cylindrical Obstacles under Steady Flow

Results of an experimental study on clear-water scour at submerged cylindrical obstacles (circular cylinders) in uniform bed sediments under steady flow are presented. The scour depths at submerged circular cylinders are compared with the scour depths at corresponding unsubmerged cylinders (extended above the free surface of flow) of the same diameters under similar flow and bed sediment conditions. The scour depth decreases with an increase in submergence ratio. A submergence factor is introduced to determine the scour depth at a submerged cylinder from the information of the scour depth at an unsubmerged cylinder of the same diameter. In addition, the flow fields along the upstream vertical plane of symmetry of unsubmerged and submerged cylinders are presented through vector plots, which reveal that the dimension and strength of the horseshoe vortex decreases with an increase in submergence ratio. The horseshoe vortex circulations, which decrease with an increase in submergence ratio, are computed from the vorticity contours by using the Stokes theorem.     

Experimental Behavior of FRP Strengthened Masonry Arches

This paper deals with the experimental behavior of solid clay brick masonry arches strengthened with glass fiber-reinforced polymer composites. Twelve half-scaled segmental masonry arches subjected to a load applied at the quarter span were tested under displacement control up to failure. The arches were built using handmade low strength bricks and a commercial lime-based mortar, trying to mimic ancient structures. Besides reference unreinforced arches, five different strengthening arrangements, including the use of spike anchors, were studied. The experimental results provide significant information for validation of advanced numerical models and analytical tools and for code drafting. The experimental results also show that (1) only continuous strengthening strategies are able to prevent typical local failure mechanisms of unreinforced arches; (2) strengthening at the intrados is the most effective option to increase strength; and (3) strengthening applied at the extrados provides the higher deformation capacity prior to failure, endowing arches with considerable ductility behavior.