一般各向异性单侧接触界面上波的反射和折射

研究简谐弹性波在一般各向异性介质单侧接触界面上的反射和折射问题．利用Fouier分析方法将非线性Coulomb摩擦接触边界波动问题化为一组代数方程．给出了确定局部分离、滑移和粘着区的思路和方法及各区域的解；讨论了出现界面局部分离和滑移的条件．对特定材料组合情况进行了详细数值计算，给出了界面力、相对滑移速度、张开位移、高频谐波的反射折射系数等特征参量；考察了平面和反平面波动的耦合及整体滑移等．其中关于高频谐波的结果可对已有实验结果给出很好的定性解释．在大多数情况下，即使对摩擦系数无穷大的粘滞接触界面，分离区端部也总是存在一个很小的滑移区。     

垂直入射弹性波在压电体单侧接触界面上的传播特性

弹性波与压电材料接触界面的相互作用问题是工程应用中常见而复杂的问题,入射波足够强会引起界面出现滑移和分离,但滑移和分离的边界未知,边界条件具有非线性特性。通过Fourier分析,将混合边值问题的求解转化为非线性代数方程,利用软件通过迭代修正的方法进行了求解;给出3种状态边界的求解,分析入射波强度、外加应力及电场对界面状态的影响,并对高频谐波的特性进行分析,通过实例对理论推导进行验证,结果显示:入射波强度、外加荷载和电场的大小及摩擦因数均会影响到界面,通过改变这些条件可以控制界面状态,另外检测高频谐波的信号也可以反映界面状态。     

弹性波作用下压电体摩擦接触界面滑移特性分析

弹性波与压电体摩擦接触界面相互作用会引起界面滑移或分离,滑移和分离位置的分布与外加压力、剪力、电场及入射波的条件有关。应用Fourier分析及matlab软件给出了滑移范围的解,给出了粘着、滑移或分离的判定条件,通过算例分析了滑移和分离出现的影响因素和条件,为工程应用提供了理论依据。     

垂直入射弹性波在一般各向异性压电材料单侧接触界面上的传播

弹性波垂直于压电材料摩擦接触界面入射会引起界面局部滑移或分离,导致问题具有边界非线性。应用傅里叶分析技术将问题的求解转化为一组代数方程,通过迭代-修正的方法确定粘着、滑移、分离区的分布位置,给出了各种状态产生的条件及规律。由于边界非线性导致波形畸变并诱发高频谐波,对某些各向异性压电材料,在某些条件下单一入射波遇到界面产生再极化,导致耦合P波及SV波产生,文中给出了高频谐波解及波形极化的产生条件。外加荷载和外加电场通过机电耦合效应对界面产生影响,通过实例分析,给出了外加作用力和电场对一般各向异性材料的影响规律,并分析了因为材料常数不同而引起的影响规律的不同。     

各向异性介质中SH波引起的裂纹扩展

本文利用Green函数法,求解各向异性介质中半无限长裂纹在SH波作用下,以任意速度扩展的问题。首先,利用Laplace变换和Cagniard-de Hoop反演法求解各向异性介质中反平面问题的Green函数,并利用它建立了求解裂纹扩展问题的积分方程。因为方程为Abel型的,所以可得到在SH波作用下,半无限长裂纹扩展问题的解析解。还可求得裂纹端点附近的应力和裂纹表面上位移的表达式。并对裂纹端点附近的奇异性进行讨论。最后讨论了裂纹尖端附近任一点的能量关系。并应用Griffith的能量准则,对裂纹扩展规律进行了讨论。     

二维各向异性弹性力学的Stroh公式及其推广

Stroh公式是解决各向异性弹性体二维变形的强有力的工具。该公式形式上简洁优美、应用上方便有力。它的推广形式也日益在混合边值问题、压电材料、非对称弯曲板、三维各向异性弹性体、稳态运动、多自由度系统振动等方面得到广泛应用。本文简要介绍Stroh公式及其推广形式的研究状况与进展。     

各向异性层状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质位移位，应力传播矩阵，给出了直角坐标系各向异性层状介质中弹性波的传播矩阵解法，该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题，数值结果表明，计算效率，准确性及稳定性均较好。     

各向异性展状介质中弹性波的传播矩阵解法

基于广义胡克定律及混和变量弹性波方程，解析求得各层介质内位移、应力传递矩阵，给出了直角坐标系下各向异性层状介质中弹性波的传播矩阵解法．该方法适用于非轴对称各向异性和点源作用，较好地解决了数值计算中有效数字精度损失问题．数值结果表明，计算效率、准确性及稳定性均较好．     

各向异性介质的弹性波散射问题的边界元方法

本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.     

复杂界面(界面层)条件下的弹性波传播问题研究综述

界面（界面层）广泛存在于各种材料和结构中,并具有千差万别的形态．各种界面条件下的波动问题有着重要的理论与实际意义．综述了完好粘接界面、弱连接界面（或界面层）以及接触界面等复杂界面模型下弹性波传播问题的研究现状,主要集中于界面模型的建立、波传播问题的研究方法及主要结论．并提出了值得进一步研究的问题．     

Optimal Fiber-Mesh Layout for a Composite Anisotropic Elastic Wedge

We consider a homogeneous orthotropic elastic wedge in plane stress loaded by a concentrated force at the apex. The orthotropic material is conceived of to be formed by a matrix reinforced by a triangular net of elastic fibers, so that the fiber size and the net shape determine the average elastic moduli of the composite material. It is found that maintaining fixed the amount of material used for the reinforcement, there exists a particular fiber disposal which maximizes the stiffness of the wedge. The optimal disposal is different-in-type for diverse opening-angles of the wedge. This revised version was published online in July 2006 with corrections to the Cover Date.     

On Inclusions at a Bi-Material Elastic Interface

Paper considers idealised problems relating to the axial stiffness of an anchor imbedded at the interface between dissimilar elastic halfspaces. The two halfspaces are bonded to each other in the region outside a circle. A thin rigid circular disc is embedded between the halfspaces and is bonded to one or both of them. The stiffness is obtained in closed form by the systematic application of Fourier and Abel transforms to the governing integral equations.     

New Explicit Expression of Barnett-Lothe Tensors for Anisotropic Linear Elastic Materials

The three Barnett-Lothe tensors H, L, S appear often in the Stroth formalism of two-dimensional deformations of anisotropic elastic materials [1–3]. They also appear in certain three-dimensional problems [4, 5]. The algebraic representation of H, L, S requires computation of the eigenvalues p^v(v=1,2,3) and the normalized eigenvectors (a, b). The integral representation of H, L, S circumvents the need for computing p ^v(v=1,2,3) and (a, b), but it is not simple to integrate the integrals except for special materials. Ting and Lee [6] have recently obtained an explicit expression of H for general anisotropic materials. We present here the remaining tensors L, S using the algebraic representation. They key to our success is the obtaining of the normalization factor for (a, b) in a simple form. The derivation of L and S then makes use of (a, b) but the final result does not require computation of (a, b), which makes the result attractive to numerical computation. Even though the tensor H given in [6] is in terms of the elastic stiffnesses C^μ v while the tensors L, S presented here are in terms of the reduced elastic compliances s′ _μv , the structure of L, S is similar to that of H. Following the derivation of H, we also present alternate expressions of L, S that remain valid for the degenerate cases p ₁ p ₂ and p₁=p₂ = p ₃. One may want to compute H, L, S using either C _μv or s′ _μv v, but not both. We show how an expression in C^μ v can be converted to an expression in s′ _μv v, and vice versa. As an application of the conversion, we present explicit expressions of the extic equation for p in C^μ v and s′ _μv v. This revised version was published online in August 2006 with corrections to the Cover Date.     

On Thermal Contact of Two Axially Symmetric Elastic Solids

A contact problem of two elastic convex and axially symmetric solids heated (or cooled) to temperatures of different values is considered. Pertinent formulae have been derived for relations between the contact pressure, geometrical characteristics of the solids and distributions of heat flux over the contacting region. We have analysed: 1. The problem of the loss of the contact between two solids pressed together with active heat fluxes. We discuss the cases for which the contact of the axially symmetric solids can take the form of a circle, or an annulus. 2. The problem of a paradox when the mathematically well posed contact problem of thermoelasticity leads to a physically unacceptable solution with a region of overlapping materials. Here we discuss a generalization of the cooled sphere paradox. The heat flux functions are continuously differentiable, of constant sign. The conditions have been derived for the cases when the paradox can be avoided.     

Contact Interaction Between a Laminated Shell of Revolution and a Rigid or Elastic Foundation

A method is proposed to solve the contact problem for laminated anisotropic shells of revolution. The method is based on a two-dimensional model that accounts for transverse shears and reduction. Also the method is based on the method of successive approximations, the generalized pseudo-force method, and a numerical-analytical method of solving boundary-value problems. The results obtained for a cylindrical shell of complex thickness structure are compared with those obtained in three-dimensional formulation__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 68–75, May 2005.     

The Remarkable Nature of Radially Symmetric Deformation of Spherically Uniform Linear Anisotropic Elastic Solids

Antman and Negron-Marrero [1] have shown the remarkable nature of a sphere of nonlinear elastic material subjected to a uniform pressure at the surface of the sphere. When the applied pressure exceeds a critical value the stress at the center r=0 of the sphere is infinite. Instead of nonlinear elastic material, we consider in this paper a spherically uniform linear anisotropic elastic material. It means that the stress-strain law referred to a spherical coordinate system is the same for any material point. We show that the same remarkable nature appears here. What distinguishes the present case from that considered in [1] is that the existence of the infinite stress at r=0 is independent of the magnitude of the applied traction σ0 at the surface of the sphere. It depends only on one nondimensional material parameter κ. For a certain range of κ a cavitation (if σ0>0) or a blackhole (if σ0<0) occurs at the center of the sphere. What is more remarkable is that, even though the deformation is radially symmetric, the material at any point need not be transversely isotropic with the radial direction being the axis of symmetry as assumed in [1]. We show that the material can be triclinic, i.e., it need not possess a plane of material symmetry. Triclinic materials that have as few as two independent elastic constants are presented. Also presented are conditions for the materials that are capable of a radially symmetric deformation to possess one or more symmetry planes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Backward Transfer-Matrix Method for Elastic Analysis of Layered Solids with Imperfect Bonding

This paper presents a backward transfer-matrix method for the elastic analysis of layered solids with an imperfect bonding at the layer interfaces. Literature review reveals that the conventional transfer-matrix method has an intrinsic fault which leads to ill-conditioned matrices for thick layers and accumulative numerical errors for a large number of layers and that there are a few publications available in the relevant literature regarding analytical analysis of layered solids by taking into account the effects of imperfectly bonded interfaces. The backward transfer-matrix method adopted in this paper completely overcomes the ill-posedness associated with the conventional transfer-matrix method and fully retains the highest efficiency of the classical transfer-matrix concept for analytical formulation of solutions in layered elastic solids with imperfectly bonded interfaces. Numerical results indicate that there is no problem in the numerical evaluation of the solutions with high accuracy and efficiency, and that the interfacial bonding conditions have a significant effect on the elastic response of layered solids due to external loading. This revised version was published online in August 2006 with corrections to the Cover Date.     

表面形貌变形对塑性成形滑动接触界面摩擦的影响

为了更好地理解塑性成形滑动接触界面的摩擦行为,构建了一种新型的摩擦试验装置,运用表面纹理化技术制备了两类表面形貌的1050铝材试件,在不同的接触压力和滑动速度条件下进行一系列拉伸摩擦试验.对试验前后试件三维表面形貌进行了测量;提取真实接触面积比、封闭空体面积比和开放空体面积比等三维表面参数,来描述试件表面形貌的变化.试验发现:摩擦系数随名义接触压力和滑动速度增加而逐渐减小;试件初始表面形貌对摩擦有明显的影响;试件表面形貌和参数随接触条件出现了规律性变化.基于机械流变模型的分析表明:随着试件表面形貌变形,不同的机理决定界面摩擦行为,摩擦系数对名义接触压力和滑动速度的依赖性可分别归因于微观塑性流体动压润滑效应和入口区流体动压牵引效应.     

弹性杆与结构接触冲击的冲击力计算研究

本文提出了一种将杆与结构的接触冲击问题简化为集中力与集中阻尼的常规结构动力学问题的计算模型。对于大型结构，可采用一种特殊的人工边界，只需对人工边界域内的结构用有限元法进行计算。这种人工边界是齐次的，可根据冲击影响区的大小人为地确定     

On the Elastic Field of a Shpherical Inhomogeneity with an Imperfectly Bonded Interface

This study is devoted to the development of a unified and explicit elastic solution to the problem of a spherical inhomogeneity with an imperfectly bonded interface. Both tangential and normal displacement discontinuities at the interface are considered and a linear interfacial condition, which assumes that the tangential and the normal displacement jumps are proportional to the associated tractions, is adopted. The elastic disturbance due to the presence of an imperfectly bonded inhomogeneity is decomposed into two parts: the first is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion, while the second is formulated in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined in this paper.