钢丝绳捻制成形接触问题的有限元分析

基于虚功原理建立了钢丝绳捻制成形过程中考虑接触摩擦时的刚度方程,将小球分裂算法用于接触搜索,Augmented Lagrange法用于计算接触力．以钢丝绳一次捻制成形过程为例,分析了摩擦系数和自扭转系数对接触应力和加工应力域变的影响．研究结果表明。摩擦系数对剪应力的影响比对等效应力和等效塑性应变的影响大;考虑摩擦时钢线表面的轴向残余应力计算结果比无摩擦条件下的计算结果更接近实验结果．     

Effect of interfacial contact forces in radial contact wire strand

A new mathematical model has been developed to predict the behaviour of a stranded cable assembly under the influence of interfacial radial contact forces and radial contraction of the core. A single layered cable assembly with six helical wires and a straight cylindrical core, all made with the same material, Steel has been chosen to explain this phenomenon when the assembly is under the influence of core–wire radial contact. An attempt is made in this paper to model the strand with a radial (core–wire) contact and deduce its equations of equilibrium. Numerical analysis of strand force, twisting moment, strand stiffness, contact force and contact stresses is carriedout based on the equilibrium of thin rods, and the results are compared with the earlier research work. The importance of the inclusion of interfacial forces at the contact locations and their associated effects of axial and twist slip of the helical wires on the core, is highlighted. The behaviour of the stranded cable assembly due to the contact force in the radial direction and its associated effects on the axial strain of the core due to Poisson’s effect is one more additional feature incorporated in the present work.     

含芯拧绞绳非线性弯曲动力学特性分析与研究

建立细长缆索大柔性多体动力学模型时,现实存在的复杂捻制几何构型多不予考虑,而是将柔索简化为材料均匀梁进行描述,致使运动仿真模型与物理实际存在一定差距. 为此,研究一种典型非线性拧绞绳股的大变形等效动力学建模方法,考虑准静态与大范围运动情况下绳股内的线接触,计算了受摩擦力及弯曲曲率影响的绳股可变弯曲刚度,通过等效梁模型避免了绳股精细建模时的大规模计算消耗. 基于连续介质力学与绝对节点坐标方法,建立了拧绞绳惯性广义坐标下的多柔体动力学模型. 为了验证等效模型的可行性,与基于有限段方法建立的精细模型进行对比仿真分析,通过位形验证了等效模型的精度. 进一步地,根据力载作用下的准静态构型,研究了特定构型绳股弯曲刚度沿轴向的分布规律;通过自重力下一端固定柔性绳摆自由运动仿真并与传统均匀梁模型相比,研究了模型弯曲特性的差异. 最后,根据能量守恒原理分析了摩擦耗散系统内各种能量间的相互转化. 拧绞绳大变形等效动力学模型能够提高绳索动力系统运动预测的仿真计算效率,还能为钢丝绳参数与构型设计提供依据.      

Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties

A multi-layered model for frictionless contact analysis of functionally graded materials (FGMs) with arbitrarily varying elastic modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be linear function while the Poisson’s ratio is assumed to be a constant. With the model, the frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically.     

Statically indeterminate contacts in axially loaded wire strand

This paper is concerned with the analysis of simple wire strands made from one layer of circular wires helically wrapped around a circular straight core wire. The undeformed configuration is the special case in which each of the surrounding helical wires touches its two adjacent neighbouring helical wires as well as touching the core wire. This forms a statically indeterminate contact problem. A simple finite element model is developed to analyse this situation. Numerical results show that contacts can occur simultaneously at all possible contact points when the strand is subjected to extension with both ends fixed against rotation.     

General axial response of stranded wire helical springs

The large static deflection of an axially loaded helical spring formed of a twisted strand of smooth circular wires is considered. Contact between the wires in the strand may or may not be maintained upon loading, depending upon the type of construction and the type of loading. It is found that the making or breaking of wire contact within the strand has a drastic ettect upon the extension and twist of a wire and upon the extension of the strand, but has practically no effect upon the twist of the strand, and only a moderate effect upon the overall response of the spring. Limited experimental data tend to verify the theory. It is found that a good engineering approximation for the axial stiffness of a twisted m-wire spring in which contact is maintained can be made by treating the spring as m untwisted helical wires acting independently, provided the strand twist is not too severe.     

闭孔泡沫铝泊松比及三轴压缩变形模式

在闭孔泡沫铝的唯象本构模型中, 泊松比是一个非常关键的参数, 为了探究闭孔泡沫铝泊松比变化规律研究结果存在分歧的原因, 认识闭孔泡沫铝泊松比变化规律中特征点的物理意义, 采用数值模拟方法, 建立了闭孔泡沫铝的3D-Voronoi模型及2D-Voronoi模型, 对模型进行侧面位移耦合单轴压缩边界条件下的仿真分析; 基于闭孔泡沫铝本构模型的唯象特性, 对闭孔泡沫铝变形模式的研究同样十分重要, 为明确其三轴压缩下的变形模式, 对闭孔泡沫铝的3D-Voronoi模型进行侧面位移受限轴向压缩边界条件下的仿真分析. 研究结果表明, 常规壳单元接触中的厚度减薄特性是闭孔泡沫铝泊松比变化规律的研究结论存在分歧的原因, 但厚度减薄不影响泡沫铝模型致密前胞孔结构的变形模式; 闭孔泡沫铝泊松比的准确变化规律为“增高?降低?再增高”的“S”型曲线, 并且, 曲线极大值对应闭孔泡沫铝吸能效率的增速下降点; 等比压缩应力状态下, 闭孔泡沫铝存在四种侧面变形模式, 分别为“(短期)压缩变形→膨胀变形”、“压缩变形→膨胀变形→压缩变形→膨胀变形”、“压缩变形→(短期)膨胀变形”及“压缩变形”.      

钢丝绳捻制成形的空间几何模型与有限元分析

根据钢丝绳捻制成形原理，在考虑钢丝绳空间几何形状的基础上，建立了引入自扭转系数时钢丝绳的几何结构计算模型和钢丝绳捻制成形有限元计算边界条件模型。进而编制了相应的有限元建模程序，生成可被ANSYS直接调用的数据文件。分析了钢丝绳一次捻制和二次捻制的加工应力应变变化情况，并讨论了自扭转系数对加工应力应变的影响。     

Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods

We consider a geometrically accurate model for a helically wound rope constructed from two intertwined elastic rods. The line of contact has an arbitrary smooth shape which is obtained under the action of an arbitrary set of applied forces and moments. We discuss the general form the theory should take along with an insight into the necessary geometric or constitutive laws which must be detailed in order for the system to be complete. This includes a number of contact laws for the interaction of the two rods, in order to fit various relevant physical scenarios. This discussion also extends to the boundary and how this composite system can be acted upon by a single moment and force pair. A second strand of inquiry concerns the linear response of an initially helical rope to an arbitrary set of forces and moments. In particular we show that if the rope has the dimensions assumed of a rod in the Kirchhoff rod theory then it can be accurately treated as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions similar to those of a Kirchhoff rod. Finally we derive the bending and twisting coefficients of this effective rod.     

The mechanical behavior of a wire rope with an independent wire rope core

A new model for simulating the mechanical response of a wire rope with an independent wire rope core is presented. The rope is subjected to both an axial load and an axial torque. In contrast with previous models that consider the effective response of wound strands, the present model fully considers the double-helix configuration of individual wires within the wound strand. This enables to directly relate the wire level stress to the overall load applied at the rope level. The model assumes a fiber response of individual wires. Two alternative kinematics of the wires are considered, and are used to predict the elastic response of the rope. The postulated kinematics are theoretically validated and the predicted rope response is in agreement with new experimental data. The new model enables the extraction of the stress at the wire level that can be used in turn to estimate global features of the rope such as force interaction between wires, rope stiffness, strength, and fatigue life.     

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.     

The effect of contact conditions and material properties on the elasticity terminus of a spherical contact

The fundamental problem of elastic–plastic normally loaded contact between a deformable sphere and a rigid flat is analyzed under perfect slip and full stick conditions for a wide range of the sphere mechanical properties. The effect of these properties on failure inception is investigated by finding the critical interference and normal loading as well as the location of the first plastic yield or brittle failure. The analysis is based on the analytical Hertz solution under frictionless slip condition and on a numerical solution under stick condition. The failure inception is determined by using either the von Mises criterion of plastic yield or the maximum tensile stress criterion of brittle failure. For small values of the Poisson’s ratio the behavior in stick, when high tangential stresses prevail in the contact interface, is much different than in slip. For high values of the Poisson’s ratio the tangential stresses under stick condition are low and the behavior of the failure inception in stick and slip is similar.     

Effect of axial load on the propagation of elastic waves in helical beams

Helical structures are designed to support heavy loads, which can significantly affect the dynamic behaviour. This paper proposes a physical analysis of the effect of axial load on the propagation of elastic waves in helical beams. The model is based on the equations of motion of loaded helical Timoshenko beams. An eigensystem is obtained through a Fourier transform along the axis. The equations are made dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain). A parametric study is conducted. The effect of loading is quantified in high, medium and low-frequency ranges. Noting that the effect is significant in low frequencies, dispersion curves of stretched and compressed helical beams are presented for different helix angles and radii. This effect is greater as the helix angle increases. Both the effects of stress and geometry deformation are shown to be non-negligible on elastic wave propagation.     

The effect of contact conditions and material properties on plastic yield inception in a spherical shell compressed by a rigid flat

The onset of plastic yielding in a spherical shell loaded by a rigid flat is studied for stick and slip contact conditions using finite element analysis. The effect of various material properties on the critical normal load, critical interference and critical contact area at the onset of plastic yielding is investigated and the location where plastic yielding first occurs is determined. A comparison is made with results obtained previously for slip contact condition. Substantial differences are found at low to medium Poisson’s ratio values, while some similarities are found to occur for high Poisson’s ratio values. In particular, a spherical shell is more prone to yield under stick than under slip contact condition.     

Low-velocity impact response of sandwich beams with functionally graded core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young’s modulus is represented by a polynomial in the thickness coordinate, but the Poisson’s ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel—the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of the beam with graded core increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load are reduced considerably due to grading of the core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.     

考虑塑性屈服的井下弹道式煤矸分离理论研究

为完善井下弹道式煤矸分离方法的理论体系,对煤和矸石碰撞反弹过程中的弹塑性行为进行研究。以Hertz接触理论为基础,结合Drucker-Prager准则确定了煤和矸石碰撞过程中初始屈服点相对位置的表达式,指出该位置与泊松比近似呈线性关系,并得到初始屈服时相对变形量、接触力和相对速度的数学模型。基于线性强化弹塑性模型,得到接触力与变形量的函数关系,并依据能量守恒定律,确定碰撞分离时刻的相对速度,进而得到反弹距离的理论模型。在单颗粒冲撞实验台上对煤和矸石进行碰撞反弹试验,试验表明：反弹距离随初始速度的增加基本呈增大趋势,当初始速度较小、煤和矸石破碎较少时,采用材料参数平均值计算得到的反弹距离理论解与试验平均值的一致性较好,当煤和矸石有破碎产生时,由于能量的损失,试验平均值小于理论解。     

Contact analysis in presence of spherical inhomogeneities within a half-space

This paper presents a fast method of solving contact problems when one of the mating bodies contains multiple heterogeneous inclusions, and numerical results are presented for soft or stiff inhomogeneities. The emphasis is put on the effects of spherical inclusions on the contact pressure distribution and subsurface stress field in an elastic half-space. The computing time and allocated memory are kept small, compared to the finite element method, by the use of analytical solution to account for the presence of inhomogeneities. Eshelby’s equivalent inclusion method is considered in the contact solver. An iterative process is implemented to determine the displacements and stress fields caused by the eigenstrains of all spherical inclusions. The proposed method can be seen as an enrichment technique for which the effect of heterogeneous inclusions is superimposed on the homogeneous solution in the contact algorithm. 3D and 2D Fast Fourier Transforms are utilized to improve the computational efficiency. Configurations such as stringer and cluster of spherical inclusions are analyzed. The effects of Young’s modulus, Poisson’s ratio, size and location of the inhomogeneities are also investigated. Numerical results show that the presence of inclusions in the vicinity of the contact surface could significantly changes the contact pressure distribution. From a numerical point of view the role of Poisson’s ratio is found very important. One of the findings is that a relatively ‘soft’ and nearly incompressible inclusion – for example a cavity filled with a liquid – can be more detrimental for the stress state within the matrix than a very hard inclusion with a classical Poisson’s ratio of 0.3.     

定、变载弯曲疲劳钢丝绳失效机理对比研究

为对比揭示定、变载弯曲疲劳钢丝绳断裂机理及磨损演化特性，运用自制钢丝绳弯曲疲劳试验机开展钢丝绳定载、变载弯曲疲劳试验，通过人工拆股统计法和VW-9000系列高速度数码显微系统对比研究钢丝绳断丝分布、断丝数、断口和磨痕形貌等断裂机理，对比分析钢丝绳未断钢丝和断丝的磨痕尺寸演化特性. 结果表明:与钢丝绳定载弯曲疲劳相比，变载弯曲疲劳钢丝绳断丝出现较晚，芯股、螺旋股外层断丝数分别较多、较少，芯股外层钢丝断口挤压变形较大，芯股各层钢丝断口裂纹扩展区占比较低，芯股和螺旋股的各层钢丝磨痕尺寸总体较小，钢丝绳更易达到报废水平.      

Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space

In previous work about axisymmetric adhesive contact on power-law graded elastic materials, the contact interface was often assumed to be frictionless, which is, however, not always the case in practical applications. In order to elucidate the effect of friction and the coupling between normal and tangential deformations, in the present paper, the problem of a rigid punch with a parabolic shape in non-slipping adhesive contact with a power-law graded half-space is studied analytically via singular integral equation method. A series of closed-form analytical solutions, which include the frictionless and homogeneous solutions as special cases, are obtained. Our results show that, compared with the frictionless case, the interfacial friction tends to reduce the contact area and the indentation depth during adhesion. The magnitude of the coupling effect depends on both the Poisson ratio and the gradient exponent of the half-space. This effect vanishes for homogeneous incompressible as well as for linearly graded materials but becomes significant for auxetic materials with negative Poisson’s ratio. Furthermore, influence of mode mixity on the adhesive behavior of power-law graded materials, which was seldom touched in literature, is discussed in details.     

钢筋混凝土结构破坏过程的近场动力学模拟

采用近场动力学(Peridynamics,PD)方法对钢筋混凝土结构破坏过程进行模拟,在"键"型近场动力学模型的基础上,考虑物质点对间的转动以突破泊松比的限制,采用能够描述混凝土材料的拉压异性和断裂特征的损伤模型,引入动态松弛、分级加载、平衡收敛准则和冲击接触等算法,建立了能准确描述钢筋混凝土结构破坏的近场动力学模型。模拟了钢筋混凝土梁在不同荷载作用下破坏的全过程,裂纹扩展路径以及最终破坏形式均与试验结果吻合,为解决工程结构破坏问题提供了一种有效的方法。