橡胶圆柱体的平面外剪切变形分析

利用Gao Y C给出的一类不可压缩的应变能函数,分析了不均匀橡胶圆柱体受平面外剪切变形问题.通过平面外剪切变形问题的变形模式,并结合应力和位移的边界条件以及界面连续条件得到了位移场和应力场在瞬时构型中的解析解,并讨论了材料的不均匀性对位移场及应力场分布的影响.结果表明:不均匀模型可以方便地退化成均匀模型;橡胶圆柱体的不均匀性对位移场和应力场的分布有着重要影响.     

三峡水库应力场对水田坝断裂影响的数学-力学模型研究

水库蓄水后, 在一定空间范围内形成了应力场、应变场和渗流场。我们建立了一个数学一力学模型, 以描述水压应力场的特征。通过运用弹塑性岩土体非线性应力一应变和稳定性静力分析NOLM83二维有限元程序发现, 水库水压应力场的最大主应力从水库中心向两侧、从水库表面向深部逐渐降低。在此基础上, 研究了在未来三峡水库水压应力场影响下, 水田坝断裂的应力、应变和影响范围。研究表明, 平面影响范围为该断裂两侧5～-6km.由于岩体的浮托作用, 地表面的累积位移量少于10mm, 并向下逐渐减小。因此, 水田坝断裂完全能够承受三峡水库蓄水后产生的水压应力, 不会出现中-强度水库诱发地震, 不会影响三峡工程的安全。     

应力诱发界面扩散下夹杂演化的有限元模拟

应力作用下内连导线中的夹杂等缺陷会迁移和变形,从而影响电子器件的可靠性.论文基于应力诱发表面扩散机制下的弱解描述,推导了固-固界面在界面扩散机制下的有限单元控制方程,并数值分析了应力诱发界面扩散下金属内连导线中夹杂的形貌演化.研究结果表明:在拉压应力下,夹杂会发生分节或者圆形化;在双向等值拉应力下,夹杂存在着沿长轴生长...     

渐开线齿轮接触应力测量实验方法研究

采用光弹性三维剪应力差法对接触应力进行了研究.根据相似原理将模型在载荷作用下进行应力冻结;通过模型切片及分析对渐开线齿轮接触应力进行测量,并采用赫兹接触理论和有限元方法分析渐开线齿轮的接触应力.试验结果表明,接触正应力小于Hertz接触理论解及有限元计算结果.因接触点的应力梯度很大,剪应力差法受网格密度的制约,均化了接触点的实际应力梯度.但是,其误差仍在合理范围内,完全可以满足工程需要.试验测量值与赫兹接触应力理论值及有限元结果的比较表明,该方法是合理可行的.     

THE STRESS FIELD AT MODE I CRACK TIP ON STEEL PIPE UNDER AXIAL TENSION

采用弹性断裂力学Westergaard 的方法,分析在轴向拉伸载荷作用下钢管的Ⅰ型裂纹尖端处的应力场. 基于Ⅰ型裂纹钢管应力场的特征,设定尖端处的应力艾雷函数,给出其应力场模型边界条件和应力场的解析函数,并利用裂纹尖端处的切平面研究裂纹尖端局部应力场,建立了钢管裂纹尖端应力场模型. 通过钢管与平板Ⅰ型裂纹应力场模型的对比,结果表明二者明显不同,钢管裂纹尖端处应力峰值影响范围仅与裂纹长度、拉应力相关.     

铁中Ⅰ型裂纹裂尖场与裂尖形变机制分析

应用有限元及连续介质力学计算了平面应交条件下体心立方铁中不同取向裂纹的裂尖应力场和弹性应变能密度分布,从宏微观相结合角度分析了裂尖场分布与裂尖微结构演化的相互关联.指出裂尖塑性变形的具体形式与裂尖滑移面上分切应力的大小密切相关,并从能量角度解释了裂尖相变产生的原因,最后结合相关分子动力学研究成果探讨了裂尖奇异性区域.     

多模微波场中玄武岩加热及内部损伤机理研究

随着微波加热技术的兴起,该技术被广泛应用于岩石破碎中.借助玄武岩研究了微波场中岩石内部温度场和应力场的分布规律,分析了岩石内部损伤机理.采用试验常用频率的工业微波炉对玄武岩试样进行微波照射,利用SEM分析微波照射前后岩石试样内部微裂纹演化规律;结合COMSOL 5.5建立岩石均匀模型分析微波场中岩石表面升温速率,建立岩...     

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对具有不同拉压模量的厚壁球壳,采用双剪统一强度理论推导了其扩张问题的应力及位移的 统一解. 分析了不同模量、不同模型控制参数对厚壁球壳扩张时的扩张压力和应力场的影响. 结果表明：厚壁球壳弹性极限压力、应力场、位移场等均随着模量控制参数、模型参数的变 化而变化,在$\alpha<1$的情况下(即$E^ + < E^ - $),可以明显提高球壳的弹 性极限压力$p_e $; 厚壁球壳塑性极限压力与材料的拉压模量无关,与模型参数$\eta $有关,且随$\eta$的增加,先增大后减小. 因此若采用经典的弹性理论和单一的 模型参数对厚壁球壳进行设计计算,会带来较大的误差.     

带裂纹三维二十面体准晶平面弹性的无摩擦接触问题

利用平面弹性复变方法,通过求解边值问题,研究了单个刚性压头作用在带任意形状裂纹的三维二十面体准晶下的无摩擦接触问题,求得了应力函数封闭解的表达式,同时得到了裂纹左右端点处应力强度因子和压头下方任意点处声子场接触应力的显式表达式。理论结果表明,声子场接触应力在压头边缘具有-1/2阶奇异性。如果忽略相位子场作用,本文得到的结果可退化为已有文献中弹性材料相应结论。数值结果用于分析带水平直裂纹三维二十面体准晶下半平面与单个平底刚性压头无摩擦接触时量纲为一的应力强度因子和量纲为一的接触应力的分布规律;量纲为一的应力强度因子在裂纹距边界垂直距离和压头半宽度之比约为0.3和1.5处取得最大值;量纲为一的接触应力呈对称分布,在压头中心处最小,在压头边缘处达到峰值且具有奇异性;相位子场弹性常数、耦合系数与Lamé常数的比值对量纲为一的声子场接触应力的大小和分布规律几乎无影响。     

含有多个涂层压电纤维复合材料的平面问题研究

压电纤维在未来的复合材料结构健康监测中具有重要作用．本文基于横观各向同性压电材料位移和应力连续条件以及经典的复势函数理论,讨论了同时受到平面内机械载荷和出平面电载荷作用时含有多个带涂层压电纤维的无限大线弹性基体的平面力学问题．首先将线弹性基体、涂层和压电纤维的应力场、位移场表示成复势函数,然后通过横观各向同性压电材料和线弹性材料的位移和应力连续条件确定复势函数表达式．将得到的复势函数表达式代入线弹性基体、涂层和压电纤维的的应力场、位移场公式可确定其应力场和位移场．最后,通过定量的案例讨论了涂层的材料属性对线弹性基体应力场的影响．案例分析表明涂层的材料属性对压电复合材料的应力场有重要的影响．     

粗糙面在梯度表面层上滑动接触的应力分布

对粗糙面在梯度表面层上的滑动过程进行应力分布研究,以模拟实际摩擦过程中,考虑塑性变形情况下,梯度覆层体中的应力分布规律,同时与均质体及单覆层体进行比较研究,分析了在表面载荷相同时滑动接触的应力分布。结果表明覆层体出现塑性变形后,在接触表面上的压力分布与弹性变形时有很大变化,在界面处梯度层的应力分布比单层膜更为理想,其应变梯度也较小;受相同表面载荷作用下产生塑性变形时,梯度层膜在基体产生塑性变形较小     

基于微凸体接触压力分布的粗糙表面法向接触建模

提出一种考虑微凸体弹塑性接触变形影响的粗糙表面法向接触力学模型。采用有限元模拟微凸体弹塑性接触过程,分析不同塑性屈服条件对微凸体接触载荷和实际接触面积的影响。再根据微凸体接触面上压力分布的变化规律,将微凸体的接触状态分为完全弹性接触阶段、弹塑性接触阶段、完全塑性接触阶段。分析接触面压力变化规律对微凸体法向接触载荷-变形的影响,再利用GW模型的数理统计分析的方法得到粗糙表面的法向接触载荷。将本文提出的模型与完全弹性模型、CEB模型、ZMC模型、KE模型、JG模型进行对比,并且研究了塑性指数对粗糙面接触载荷-平均高度距离的影响。结果表明,本文提出的模型能够更好地描述微凸体法向接触载荷与接触变形的变化趋势,模型预测粗糙表面法向载荷与ZMC、KE模型具有较好的一致性;粗糙面接触载荷随着平均接触距离增加而减少,随着塑性指数的增加,不同模型预测的法向接触载荷差异逐渐增大。     

Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior

A contact stress analysis is presented for a layered elastic half-space in contact with a rough surface exhibiting self-affine (fractal) behavior. Relationships for the mean contact pressure versus representative strain and the real half-contact width versus elastic properties of the layer and the substrate, asperity radius, layer thickness, and truncated half-contact width were derived from finite element simulations of a layered medium compressed elastically by a rigid cylindrical asperity. These relationships were incorporated in a numerical algorithm that was used to obtain the contact pressure distributions and stresses generated by the asperity contacts formed at the interface of the layered medium and the fractal surface. Analytical solutions illustrate the significance of the elastic material properties, layer thickness, and surface topography (roughness) on global parameters such as normal load and real contact area. Results for the contact pressure distribution and the surface and subsurface stresses provide insight into the initiation of yielding and the tendency for cracking in the layered medium. It is shown that cracking at the surface and the layer/substrate interface is more likely to occur in the case of a stiff layer, whereas surface cracking is more prominent for a relatively compliant layer.     

固定接触界面切向静弹性刚度问题研究

根据两球体单峰同时受法向、切向载荷时微滑切向应力的分布以及MB模型,给出了界面的总切向接触静弹性条件刚度、总条件法向载荷的解析解。将切向接触静弹性条件刚度的解析解嵌入到有限元软件中,获得了整机的理论模态。以一款八四七厂华中工学院XHK5140型自动换刀计算机数控立式镗铣床上的结合部为研究对象,通过实验对解析解进行了定量验证。研究结果表明：在理论振型与实验振型一致的条件下,界面模型的相对误差在-19．2％～16．8％之间。     

Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space

Many materials contain inhomogeneities or inclusions that may greatly affect their mechanical properties. Such inhomogeneities are for example encountered in the case of composite materials or materials containing precipitates. This paper presents an analysis of contact pressure and subsurface stress field for contact problems in the presence of anisotropic elastic inhomogeneities of ellipsoidal shape. Accounting for any orientation and material properties of the inhomogeneities are the major novelties of this work. The semi-analytical method proposed to solve the contact problem is based on Eshelby’s formalism and uses 2D and 3D Fast Fourier Transforms to speed up the computation. The time and memory necessary are greatly reduced in comparison with the classical finite element method. The model can be seen as an enrichment technique where the enrichment fields from the heterogeneous solution are superimposed to the homogeneous problem. The definition of complex geometries made by combination of inclusions can easily be achieved. A parametric analysis on the effect of elastic properties and geometrical features of the inhomogeneity (size, depth and orientation) is proposed. The model allows to obtain the contact pressure distribution – disturbed by the presence of inhomogeneities – as well as subsurface and matrix/inhomogeneity interface stresses. It is shown that the presence of an inclusion below the contact surface affects significantly the contact pressure and subsurfaces stress distributions when located at a depth lower than 0.7 times the contact radius. The anisotropy directions and material data are also key elements that strongly affect the elastic contact solution. In the case of normal contact between a spherical indenter and an elastic half space containing a single inhomogeneity whose center is located straight below the contact center, the normal stress at the inhomogeneity/matrix interface is mostly compressive. Finally when the axes of the ellipsoidal inclusion do not coincide with the contact problem axes, the pressure distribution is not symmetrical.     

全长粘结式锚杆的非局部摩擦分析

本文对Oden等提出的非局部摩擦模型进行了修正,得到了修正后的非局部摩擦模型.并应用于全长粘结式锚杆问题.文中利用Mindlin问题的位移解导出的全长粘结式锚杆沿杆体表面所受的剪应力的弹性解,对全长粘结式锚杆进行非局部摩擦分析,得到了在修正后的非局部摩擦模型下的全长粘结式锚杆的侧剪应力.文中修正的非局部摩擦模型下的全长粘结式锚杆的剪应力分布规律与试验得到的结果以及局部摩擦模型(库仑模型)下的计算结果进行了对比,结果表明修正的非局部摩擦模型下的计算结果与实验更符合.因此在描述此锚杆剪应力时,非局部摩擦模型比局部摩擦模型(库仑模型)更接近的实际.     

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     

表面纹理磁盘滑动接触的温度和应力及退磁临界条件的研究

采用应力场和温度场耦合的有限元方法,计算磁头/磁盘滑动接触下铝基磁盘磁层内瞬态温度场和应力场及退磁临界条件,分析接触压力、滑动速度、摩擦系数以及磁盘表面纹理对磁层内最大摩擦温升值和最大应力值的影响.结果表明:波形纹理表面瞬间滑动接触所产生的温度分布呈波形特征,表面纹理越尖锐,磁层内的温度和应力越大;滑动速度对磁层内温度的影响大于对应力的影响;当磁层最大应力小于1.2 GPa时,所对应的速度和压力为安全工况;当温升大于180 K时所对应的工况将导致磁盘退磁.     

A Prestressed Elastic Strip with Elastic Reinforcements

A contact problem is studied for a prestressed elastic strip with an elastic reinforcement. The integral Fourier transform is used to construct an influence function for an infinite strip with one face fixed. A unit concentrated force is applied to the strip at an arbitrary angle. The contact problem on force transfer from a thin infinite stringer to the prestressed strip is solved. The problem is mathematically formulated as a system of integro-differential equations for the unknown contact stresses on the assumption that the beam bending model and the uniaxial stress model are valid for the stringer, which is subjected to both vertical and horizontal forces. This system is solved in a closed form using the integral Fourier transform. The contact stresses are expressed in terms of Fourier integrals in a quite simple form. The influence of the initial stresses on the contact stress distribution is analyzed, and effects of concentrated load are revealed     

Agricultural tire deformation in the 2D case by finite element methods

The mechanical characteristics of the rubber tire and the interaction between a tire and a rigid surface were investigated by a two-dimensional (2D) finite element (FE) model. The FE model consists of a rigid rim and a rigid contact surface which interact with the elastic tire. Four distinct sets of elastic parameters are used to represent beads, sidewall, tread and lugs. Several sets of tire loads and inflation pressures were applied to the FE model as boundary conditions, together with various displacements and friction conditions. The deformation of the tire profile, the tire displacements in the vertical and lateral directions, the normal contact pressures, the frictional forces and the stress distribution of the tire components were investigated by the 2D FE model under the above boundary conditions. The calculated tire deflections were compared with the measured data. The results show a good fit between calculated and measured data, especially at high load and inflation pressure. The comparison shows that the FE analysis is suitable to predict aspects of the tire performance like its deflection and interactions with the contact surface. Compared with the experimental methods, the FE methods show many advantages in the prediction of tire deformation, contact pressure and stress distribution.