子午线轮胎接触变形的结构有限元分析

针对195／60R14子午线轮胎建立了三维非线性有限元模型，着重研究了额定充气压力及静载荷作用下帘线承受拉应力和剪应力的基本特征。计算结果表明，接地区域摩擦力呈斜对称分布，反映了轮胎中帘线-橡胶复合材料存在变形耦合效应；冠带层、带束层、胎体帘线应力分布较为复杂，载荷变化对其应力水平和分布影响较大；在胎肩部位应力较高，且随载荷变化局部帘线应力变化剧烈，在承受交变载荷时，易形成层间剥落。分析结果有助于预测轮胎的使用性能，可以针对性地应用于因轮胎结构设计引起的质量损坏，某些对轮胎使用性能不利的受力状态可通过结构的优化设计来克服。     

The Brazilian disc under parabolically varying load: Theoretical and experimental study of the displacement field

The displacement field in an intact Brazilian disc under the influence of a parabolically varying radial pressure distribution acting along two symmetric arcs of its periphery is studied. The specific loading type closely approaches the actual load-distribution as obtained by considering the specimen and the load platen as a system of two elastic bodies in contact. The problem is solved adopting the complex potentials method and a closed form full-field solution is proposed. The results of the theoretical analysis for discs made either from Dionysos marble or PMMA are considered in juxtaposition to the respective ones obtained for uniform radial pressure as well as for concentrated point load. Critical points related to the variation of the displacement field in the immediate vicinity of the load platen-specimen interface are enlightened. The accuracy of the solution is assessed by comparing the analytic results with the experimental ones obtained from series of Brazilian-disc tests carried out using the standardized device suggested by the international society for rock mechanics. The specimens were made from PMMA and the 3D digital image correlation technique was employed for measuring the components of the displacement field developed. It is proved that the experimental results are in very good qualitative and quantitative agreement with the theoretical predictions.     

Fourier series based FE analysis of a disc under prescribed displacements–elastic stress study

This paper examines the numerical displacements and stresses developed around a disc under horizontal prescribed displacements and at the interface separating it from the surrounding elastic soil. Since the geometry of the problem exhibits axial symmetry and the loading is non-axisymmetric, the semi-analytical FE approach is used as it proves to be efficient and economical. First, both analytical and numerical expressions for soil reaction are established and compared. Results of comparison show a very good agreement. Then, for different values of the soil Poisson’s ratio, normal radial stresses, orthoradial stresses and shear stresses distributions along radial distance reaching 20r _d (r _d is the disc radius) are presented for a disc that has either perfectly smooth or perfectly rough interfaces with the elastic medium. The paper finishes by showing the effect of the soil Poisson’s ratio as well as the relative soil/interface stiffness on the stresses developed at the interface locations.     

Mechanics and full-field deformation study of the Ring Hoop Tension Test

We investigate the mechanics of the Ring Hoop Tension Test (RHTT), as a means to assess the properties of anisotropic tubes in the hoop direction. This test involves placing a ring extracted from the tube over two close-fitting D-shaped mandrels that are then parted using a universal testing machine. Since the curvature of the ring does not change during loading, the ring undergoes only stretching. We determine the effects of contact pressure, radial stress, and friction between the tube and mandrels using FEA simulations. The effects of the pre-existing thickness eccentricity and of the specimen-making procedure on the recorded RHTT response are also assessed with a combination of experiments and analysis. We tested tubes from Al-6061-T4 with a diameter/thickness ratio of 20. We found that as the friction increases beyond 0.1–0.15, the state of uniaxial tension is deteriorated, indicating that care must be taken to minimize the tube-mandrel friction. We determined that although these tubes have a relatively large thickness eccentricity (±4% of the nominal thickness), this had no effect on the recorded results. We showed that the tubes should not be turned to remove that eccentricity, as the machining process induces damage that is noticeable in the results. We found that the contact pressure and the contact-induced radial stress cause limited deviations from uniaxial tension, comparable to the case of a tube under axial load and internal pressure which is often used for assessing the material properties in the hoop direction. Central in our analyses is the knowledge of the hoop strain field, which was assessed using 3D Digital Image Correlation. We propose a data reduction procedure for RHTT that accounts for all the above effects. Finally, with all effects accounted for, we establish the anisotropy of the extruded Al-6061-T4 tubes studied.     

Elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient

The elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient has been analyzed by using Seth’s transition theory and generalized strain measure. It has been observed that disc made of beryl and magnesium materials requires higher angular speed to yield at the inner surface in comparison to the disc made of brass material. The radial stress has a maximum at the internal surface of the disc made of beryl, magnesium and brass materials, but circumferential stress neither maximum nor minimum at this surface. With the introduction of thermal effect, the value of circumferential stress has a maximum at the external surface of the disc made of the beryl and magnesium, but the reverse results are obtained for the disc made of brass material. The combined impacts of temperature and angular speed have been displayed numerically and depicted graphically.

     

Cracked elastic layer under compressive mechanical loads

We consider boundary value problem in which an elastic layer containing a finite length crack is under compressive loading. The crack is parallel to the layer surfaces and the contact between crack surfaces are either frictionless or with adhesive friction or Coulomb friction.Based on fourier integral transformation techniques the solution of the formulated problems is reduced to the solution of a singular integral equation, then, using Chebyshev’s orthogonal polynomials, to an infinite system of linear algebraic equations. The regularity of these equations is established. The expressions for stress and displacement components in the elastic layer are presented. Based on the developed analytical algorithm, extensive numerical investigations have been conducted.The results of these investigations are illustrated graphically, exposing some novel qualitative and quantitative knowledge about the stress field in the cracked layer and their dependence on geometric and applied loading parameters. It can be seen from this study that the crack tip stress field has a mode II type singularity.     

Mechanics of advancing pin-loaded contacts with friction

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.     

Constitutive Model Calibration for Powder Compaction Using Instrumented Die Testing

Calibration procedures for constitutive models for powder compaction are presented. A practical calibration method based on a die compaction experiment is presented. A newly developed apparatus consisting of a die instrumented with radial stress sensors is described. The paper proposes two contributions to account for errors present in instrumented die testing, which are due to 1) elastic compliance of the testing frame, influencing the measurement of axial strain and 2) the presence on non-homogeneous stress state in the test specimen. It is shown that system compliance is important for generating an accurate stress-strain curve for compression. The effect of different compliance correction methods is evaluated with regard to the accuracy of models predicting pressing forces. The system compliance becomes more significant during unloading in the die; this information is used to determine the elastic properties. A new compliance correction method is introduced following a detailed analysis of the forces and deformations of different parts of the loading frame. In instrumented die compaction the axial and radial stresses are measured at fixed locations and the specimen is subject to non-homogeneous stresses and strains due to the effect of friction between the powder and die wall. Starting from the Janssen-Walker method of differential slices a method to account for non-homogeneous stress and strain is developed.     

A BEM solution to transverse shear loading of composite beams

In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of composite beams of arbitrary constant cross-section. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson’s ratio and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross-section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear centre of the cross-section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson’s ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ‘exact’ elastic beam theory is remarkable.     

Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials

This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials(FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier's equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement,strains, and stresses are determined by the exact solution to Navier's equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.     

The ability of agricultural tyres to distribute the wheel load at the soil-tyre interface

Bigger tyres with lower inflation pressure at equivalent wheel loads are expected to reduce the stresses transmitted to the soil. We measured the contact area and the vertical stress distribution near the soil-tyre interface for five agricultural implement tyres at 30 and 60 kN wheel load and rated inflation pressures. Seventeen stress transducers were installed at 0.1 m depth in a sandy soil at a water content slightly lower than field capacity and covered with loose soil. The recently developed model FRIDA was successfully fitted to the experimental stress data across the footprint. The contact area reflected the size of the tyres. The small tyres had identical contact area at the two loads, while it increased with load for the two biggest tyres. The small tyres presented uneven stress distributions with high peak stresses. Across the tests, the tyre inflation pressure described well the measured peak stress as well as the modelled maximum stress. The latter seems to be appropriate in evaluating vehicle trafficability. We found significant differences among tyres for the slope of a linear regression between the mean ground pressure and the inflation pressure, while the tyres displayed the same interception on the mean ground pressure axis. Our results therefore suggest that the slope of this relation is the most sensitive expression of tyres’ ability to deflect and transfer stresses to the soil. The two small tyres performed poorer in this respect than the larger tyres. Tests were limited to one soil strength, with future research directed toward a broader spectrum of soil strengths.     

Multi-scale modeling of grouted sand behavior

The mechanical properties of sand: stiffness, cohesion and, to a less extent, friction angle can be increased through the process of grouting. A constitutive model adapted for cohesive-frictional materials from a homogenization technique which allowed us to integrate constitutive relations at the grain level has been developed to obtain constitutive equations for the equivalent continuous granular medium. A representative volume was obtained by mobilizing particle contacts in all orientations. Thus, the stress–strain relationship could be derived as an average of the behavior of these local contact planes. The local behavior was assumed to obey a stress-dependent elastic law and Mohr–Coulomb’s plastic law. The influence of the cement grout was modeled by means of adhesive forces between grains in contact, which were added to the contact forces created by an external load. The intensity of these adhesive forces is a function of nature and amount of grout present inside the material and can be reduced due to a damage mechanism at the grain contact during loading. In this paper, we present several examples of simulation which show that the model can reproduce with sufficient accuracy the mechanical improvement induced by grouting as well as the damage of the grain cementation during loading.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields

In this article, an analytical method is developed to obtain the response of magnetothermoelastic stress and perturbation of the magnetic field vector for a thick-walled spherical functionally graded materials (FGM) vessel. The vessel, which is placed in a uniform magnetic field, is subjected to an internal pressure and transient temperature gradient. Using the Hankel and Laplace transform techniques, the dynamic equation of magnetothermoelastic is solved and the radial and circumferential stresses as well as the perturbation of the magnetic field vector for a typical material are obtained. Moreover, the effect of magnetic field vector and material inhomogeneity on the stresses is investigated.     

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.     

Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure

In this paper, an analytical solution is developed to determine deformations and stresses in circular disks made of functionally graded materials subjected to internal and/or external pressure. Taking mechanical properties of the materials of circular disks to be linear variations, the governing equation is derived from basic equations of axisymmetric, plane stress problems in elasticity. By transforming the governing equation into a hypergeometric equation, an accurate analytical solution of deformations and stresses in circular disks is obtained. The comparison with the numerical solution indicates that both approaches give very agreeable results, indicating correctness of the proposed analytical solution. The obtained analytical solution is employed to determine the radial displacement and stresses in circular disks subjected to external pressure, internal pressure, and internal and external pressure, respectively. How the radius ratio of circular disks affects deformations and stresses is also investigated.     

Interfacial slip and creep in rolling contact incorporating a cylinder with an elastic layer

A systematic approach for investigating the interfacial behaviour of tyred systems is proposed. A two-dimensional contact model of an elastic strip, shrink-fitted onto a wheel, and subjected to different rolling contact conditions, has been adopted to illustrate the method. The model combines existing techniques to explore individual elastic contact problems and it enables us to characterise the behaviour at the strip/substrate interface caused by loads induced by a quasi-static application of stationary and moving loads on the surface of the layer. The solution is compared to the stationary load case and regimes of local slip, full stick, separation and frictional creep are identified and collated for a variety of loading conditions, materials and geometries. Further, this article presents an investigation of frictional shakedown for layered systems subjected to periodic contact loading. The term shakedown is here referred to as the possibility of developing interfacial residual stresses at the layer/substrate interface such that frictional slip, originally activated by the applied external contact load, ceases after a few loading cycles. The possible applicability of the Melan’s theorem for elastic frictional system is investigated and preliminary results presented.     

A new look at the bending strength of gear teeth

This paper reports on an extensive two-dimensional photoelastic study of the basic deformation behavior of gear teeth under load. Limitations of existing bending-strength design procedures are used to formulate a test program which considers the magnitude of the critical root-fillet stresses, the effects of varying the load position on the flank, the effects of friction forces at contact and the relationship between bending and shearing deformations. Particular interest is devoted to a study of the observed movement of the maximum-stress position around the fillet as load moves up the tooth flank and to the associated variation in stress-concentration factors (around the fillets) due to radial, bending and shear loads. Note is also made of the problems associated with observed ‘proximity effects’ and of the procedures carried out in an attempt to qualify the nature of the effect. The results of the program have been used to, explain certain anomalies observed in earlier three-dimensional photoelastic model tests^1.7 and reference is made to the development of a new design procedure for the bending strength of helical gears.     

轮胎与地面接触问题的非线性有限元分析

考虑轮胎的材料非线性、几何非线性、橡胶帘线复合材料各向异性、以及橡胶材料本身的不可压缩特性等,分析了9．00R20子午线轮胎静态下与地面的接触问题,考察了不同下沉量、不同内压及静摩擦系数与因素对轮胎静态接地面内应力应变场的影响,得出了对工程设计有指导意义的结论。     

盘式制动器摩擦界面接触压力分布研究

在考虑具有可变效应的移动热源影响、制动盘与片的弹性影响以及界面摩擦热流影响等的耦合作用下,建立了一个三维瞬态盘式制动器热-结构耦合模型,利用大型有限元软件ANSYS的非线性多场耦合分析方法,分别数值模拟了不同状态下的制动器摩擦接触界面上的压力场分布情况.发现制动接触压力并非均匀分布,而是与制动盘和片的变形、摩擦力以及摩擦热-结构耦合有关.