Two-dimensional numerical analyses of double conforming contacts with effect of curvature

Pinned connections and journal bearings with cylindrical conforming contacts are widely used as fundamental building blocks in machines and civil structures of civilization. It is critical to determine their stress fields and contact performances under desired configurations in order to successfully design them. This paper presents a numerical model to deal with such contacts, particularly with the general configuration–double interfaces. Necessary formulae are developed and numerical procedures are described in this paper. Efficient numerical methods, i.e., the discrete convolution-fast Fourier transformation (DC-FFT) method and the conjugate gradient method (CGM), are implemented in the algorithm. Validations are conducted against the Persson’s results and finite element results and demonstrate excellent agreement. This contact analysis can be useful for design engineers to evaluate stress and contact pressure distribution. Furthermore, this efficient method of determining radial displacement can be applied in an elasto-hydrodynamic lubrication analysis.     

Vorticity and curvature at a stream surface

If S is a stream surface in a flow, we show the relationship between the three components of the vorticity field on S and the curvatures of the streamlines (geodesic torsion, normal curvature and geodesic curvature).     

Effect of longitudinal surface curvature on heat transfer

The effect of longitudinal surface curvature on heat transfer has been analysed for laminar forced convection by the method of matched asymptotic expansions. Utilizing the classical solution of boundary layer equations as the first order approximations, the second order perturbation for the velocity and temperature field has been calculated by a similarity analysis. The analysis permits the wall temperature to vary as a power function of distance from the stagnation point. Numerical solutions have been obtained for the resulting coupled ordinary differential equations. The results for the variation in the second order temperature profile and the second order wall temperature gradient due to surface curvature parameter, Prandtl number, wall temperature distribution parameter, and pressure gradient parameters are presented graphically. The variation in a typical temperature profile due to curvature, and percentage variations from the first order theory due to longitudinal surface curvature are also presented graphically.     

The impact of a single drop on a wetted solid surface

 The impact of single drops on a thin liquid film was studied to understand the mechanism of secondary atomisation of sprays colliding on a wetted, cold, solid surface. To span a wide range of conditions various mixtures of water and glycerol were used. The use of Weber number, Ohnesorge number and non-dimensional film thickness to describe the peculiarities of the phenomenon allowed to carry out the experiments under appropriate similarity conditions. The impact of millimetric drops was analysed in detail by photographic means, using both still photography to study impact morphology, and laser sheet visualisation to investigate secondary droplet formation. Two mechanisms of splash were identified, depending essentially on the liquid viscosity (Ohnesorge number), a parameter which appears to play an important role also in defining the splash morphology. A photographic documentation is annexed. The characteristic times of the crown formation, the non-linear evolution of cusps (jet formation) and the surface roughness influence are further discussed. The experimental results allow to propose an empirical correlation for the splashing/deposition limit, for a wide range of conditions, and a comparison to available previous works is presented. The influence of the film thickness and liquid viscosity on the splash is confirmed and quantified. Received: 1 March 1996/Accepted: 12 November 1996     

Flow regimes in a single dimple on the channel surface

The boundaries of the domains of existence of flow regimes past single dimples made as spherical segments on a flat plate are determined with the use of available experimental results. Regimes of a diffuser-confuser flow, a horseshoe vortex, and a tornado-like vortex in the dimple are considered. Neither a horseshoe vortex nor a tornado-like vortex is observed in dimples with the relative depth smaller than 0.1. Transformations from the diffuser–confuser flow regime to the horseshoe vortex regime and from the horseshoe vortex flow to the tornado-like vortex flow are found to depend not only on the Reynolds number, but also on the relative depth of the spherical segment. Dependences for determining the boundaries of the regime existence domains are proposed, and parameters at which the experimental results can be generalized are given.     

Two-dimensional nonstationary gas dissipation into a vacuum from a plane or axisymmetric channel

The nonstationary escape of an ideal polytropic gas from a plane or axisymmetric channel is investigated. It is hence assumed that the gas is initially at rest, and the diaphragm separating it from the vacuum can be at any section of the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–83, January–February, 1976.     

On problems of optimal design of shallow shell with double curvature on elastic foundation

The present paper discusses a method of optimal design of the shallow shell with double curvature on the elastic foundation Substantially we take the initial flexural function as the control function or design variable which will be found and the potential energy of the external loads as the criterion of quality of the optimal design of the shallow shell with double curvature, therefore the functional of the potential energy will be aim function. The optimal conditions and the isoperimetric conditions belong to the constrained conditions. thus we obtain the necessary conditions of the optimal design for the given problems, at the same time the conjugate function is introduced, then the problems are reduced to the solutions of two boundary value problems for the differential equation of conjugate function and the initial flexual function.     

Calculation of an axisymmetric turbulent wall jet over a surface of convex curvature

One of the many applications of curved wall jets of engineering importance is the Coanda Flare, which is used for burning waste gases in the petroleum industry and which gave rise to this work. The gas jet flows over an axisymmetric tulip shaped body, entraining ambient air and so promoting clean combustion. The object of this work was to calculate the development of the jet with the extra rates of strain imposed by both longitudinal curvature and divergence. A differential ‘partially-parabolic’ technique was used with uncoupling of the streamwise and cross-stream momentum equations, leading to an efficient computer program. The extra rates of strain were modelled by corrections to a mixing length model with the two effects being assumed to be additive. The calculation method was compared with seven test ccases of experimental data. The first five were from published literature, and included the plane wall jet and axisymmetric free jet, and the separate effects of longitudinal curvature and divergence. The lost two cases were measurements of the wall jet flow over a model Coanda Flare. The calculation method gave generally good results for the main features of the flow such as growth rate and velocity decay. Details of the flow were not so well predicted, particularly the turbulent shear stress, as a result of the relatively simple turbulence model employed. The calculation method should provide a useful engineering tool, but some profitable developments could be made, particularly in the area of turbulence modelling.     

Effect of yield surface curvature and void nucleation on plastic flow localization

The effect of void nucleation is incorporated in a recently proposed material model that accounts for a combination of kinematic hardening and isotropic hardening of a porous ductile material. Since each of plastic dilatancy, void nucleation and yield surface curvature have a strong influence on predictions of plastic flow localization, the present material model can be used to study the interaction of these effects. Nucleation controlled by the plastic strain as well as nucleation controlled by the maximum normal stress on the particle-matrix interface are modelled. The predictions of the material model, for various combinations of parameters, are illustrated by analyses of shear band formation under plane strain or axisymmetric conditions, and by analyses of necking in biaxially stretched sheets.     

Nonlinear stability of a shallow unsymmetrical heated orthotropic sandwich shell of double curvature with orthotropic core

Equations which govern the behavior of an elastic unsymmetrical, orthotropic sandwich shell of double curvature with orthotropic core having different elastic characteristics under uniform heating are derived. The face sheet may be of unequal thickness of different materials. However, a restriction that the radii of curvature of the shell elements be large compared with the overall thickness of the sandwich shell is imposed. The variational procedure has been used to obtain the five equations which govern the behavior of the heated orthotropic sandwich shell for the stability. In case of symmetry the equations resemble with those of Grigolyuk. Finally, the numerical results of a square or a rectangular simply supported curved plate section of a cylindrical shell under thermal loading have been computed and compared with other known results. The graphs have been drawn to show the effects of different sandwich material for immovable and movable edge conditions.     

Two-dimensional motion of a set of particles in a free surface flow with image processing

A method to analyze bed load with image processing was developed. The motion of coarse spherical particles on a mobile bed entrained by a shallow turbulent flow down a steep channel was filmed with a high-speed camera. The water free surface and the particle positions were detected combining classical image processing algorithms. We developed a particle-tracking algorithm to calculate all particle trajectories and motion regimes, rolling or saltation. At constant slope, the contribution of the rolling particles to the solid discharge only slightly differed when the particle supply was increased. At a slope of 10%, it represented about 40%. In contrast, rolling became the major regime when the slope increased, at a slope of 15% it represented up to 80% of the total solid discharge.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

变曲率连续滚滑接触安定性的数值方法研究

针对接触表面变曲率的特点,引入局部坐标系,构造出局部坐标下残余应力应变场的分布状态,建立了变曲率连续啮合过程中安定状态残余应力的计算方法。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,并采用增量映射方法求解特征应变决定的残余问题,可直接得到接触安定状态下的接触残余应力,并随之进行安定极限的判定。采用该数值方法计算了不同曲率处接触点的安定极限,给出了安定极限与摩擦因数之间的关系,并与有关数值结果相比较,验证了该算法的有效性。     

Effects of the curvature radius of a cylindrical shell on the stress intensity factors of surface cracks

The effects of the curvature radius of a cylindrical shell on stress intensity factors are investigated in circumferential (inner and outer) semielliptical surface cracks in a cylindrical shell. What is new in this paper is to have given: (1) The stress intensity factors for surface cracks in a cylindircal shell are determined by photoelastic technique. (2) By a special method photoelastic slices are handled for obtaining a clear caustic curve, and the stress intensity factors for surface cracks in a cylindrical shell are determined by the caustic method. (3) An approximate equation of curvature correction factor F_c is proposed. (4) Effects of the curvature radius R of a cylindrical shell on the stress intensity factors of surface cracks are obtained. The results of this paper are in fair agreement with already existing analytical results. The approximate equation of curvature correction factor F_c can be widely used for engineering purposes.     

Flow about a circular cylinder with a single large-scale surface perturbation

An experimental study of the flow around a cylinder with a single straight perturbation was conducted in a wind tunnel. With this bluff body, positioned in a uniform crossflow, the vortex shedding frequency and other flow characteristics could be manipulated.The Strouhal number has been shown to be a function of the perturbation angular position, _p , as well as the perturbation size and Reynolds number. As much as a 50% change in Strouhal number could be achieved, simply by changing _p by 1°. The perturbation size compared to the local boundary layer thickness, , was varied from approximately 1 to about 20 . The Reynolds number was varied from 10,000 to 40,000. For perturbation sizes approximately 5 to 20 and Reynolds numbers of 20,000 to 40,000, a consistent Strouhal number variation with _p was observed.A detailed investigation of the characteristic Strouhal number variation has shown that varying _p had a significant influence on the boundary layer separation and transition to turbulence. These significant changes occurring in the boundary layer have been shown to cause variations in the spacing between the shear layers, base pressure, drag, lift, and the longitudinal spacing between the vortices in the vortex street.List of Symbols a longitudinal spacing of vortices in the vortex street - C _d drag coefficient - C _dc drag coefficient corrected for blockage effect - C _l lift coefficient - C _p pressure coefficient, p _i –p /q - C _pb base pressure coefficient - C _pbc base pressure coefficient corrected for blockage effect - d perturbation diameter - d ^* spacing between the shear layers; defined as conditionally averaged spacing between points in the shear layers corresponding to 0.99u _max/U - D cylinder diameter; diameter of the circumscribing circle for a cable - f _v vortex shedding frequency - H wind tunnel test section cross-sectional width - L spanwise length of the cylinder - p _i tap pressure - p free stream static pressure - q free stream dynamic pressure - Re Reynolds number based on cylinder diameter - rms root-mean-square - S Strouhal number, f _v D/U - S _max maximum value of S - S _min minimum value of S - t time - u _c vortex convection velocity - u _max maximum velocity in the shear layer - U free stream velocity - U _c free stream velocity, corrected for blockage effect - x streamwise dimension referenced from the back of the cylinder - z lateral wake dimension, i.e., perpendicular to the free stream velocity vector and cylinder axis, referenced from the cylinder axis - x spacing between two hot wire probes aligned streamwise - phase difference between two hot wire probes aligned streamwise - boundary layer thickness - angle from stagnation point in degrees - _p perturbation angular position - _{b p} where S drops back to about the S of a cylinder - _c critical angle, angular position where S drops steeply with 1° change in - _{m p} where S was minimum - _{r p} after S recovers from drop in value - _{t p} where S starts to increase from about the S of a cylinder     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

Influence of the transverse curvature of the lower surface on the conical supersonic flow field on a delta vehicle

The inviscid flow on a delta supersonic flying vehicle model, whose lower surface is formed by the surface of a circular cone and has the shape of an elliptical segment in cross section, is computed and investigated in a linear formulation by the method of through-computation. A flow mode with two stream runoff lines and three spreading lines is detected on the lower surface. The spreading characteristics, affecting the conditions for laminar boundary-layer transition into turbulent, are obtained for this surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 3, pp, 103–110, May–June, 1978.The authors are grateful to G. I. Maikapar for proposing the investigation of the dependence of vehicle quality on the parameter k_R.     

A simple meso-macro model based on SQP for the non-linear analysis of masonry double curvature structures

A 3D model for the evaluation of the non-linear behavior of masonry double curvature structures is presented. In the model, the heterogeneous assemblage of blocks is substituted with a macroscopically equivalent homogeneous non-linear material. At the meso-scale, a curved running bond representative element of volume (REV) constituted by a central block interconnected with its six neighbors is discretized through of a few six-noded rigid wedge elements and rectangular interfaces. Non linearity is concentrated exclusively on joints reduced to interface, exhibiting a frictional behavior with limited tensile and compressive strength with softening. The macroscopic homogenous masonry behavior is then evaluated on the REV imposing separately increasing internal actions (in-plane membrane actions, meridian and parallel bending, torsion and out-of-plane shear). This simplified approach allows to estimate heuristically the macroscopic stress–strain behavior of masonry at the meso-scale. The non-linear behavior so obtained is then implemented at a structural level in a novel FE non-linear code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and non-linear interfaces, exhibiting deterioration of the mechanical properties.Several numerical examples are analyzed, consisting of two different typologies of masonry arches (a parabolic vault and an arch in a so-called “skew” disposition), a ribbed cross vault, a hemispherical dome and a cloister vault. To fully assess numerical results, additional non-linear FE analyses are presented. In particular, a simplified model is proposed, which relies in performing at a structural level a preliminary limit analysis – which allows to identify the failure mechanism – and subsequently in modeling masonry through elastic elements and non-linear interfaces placed only in correspondence or near the failure mechanism provided by limit analysis. Simulations performed through an equivalent macroscopic material with orthotropic behavior and possible softening are also presented, along with existing experimental evidences (where available), in order to have a full insight into the capabilities and limitations of the approach proposed.     

Two-dimensional problem concerning the impact of a rigid body onto a thin elastic plate lying on the surface of a compressible fluid

Institute of Mechanics, Academy of Sciences of the UkrSSR, Kiev. Kiev Autorail Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 59–66, September, 1991.