残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响．首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式．研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响．     

非完美界面弹性复合材料中的微分几何方法

首次用微分几何方法计算了含一般旋转椭球体嵌入相的非完美界面弹性复合材料的有效模量·用内蕴几何量表出了能量泛函中的全部界面积分项，由此得到了这种统一嵌入相模型的复合材料有效模量的上下界限·在三种极限情况，即球、盘和针状嵌入相下，本文的结果将退化到Ｈａｓｈｉｎ（１９９２）的结果·     

球形涂层粒子增强复合材料的有效模量

本文通过四相球模型和复合材料的等效介质理论,研究了球形涂层粒子增强复合材料的有效模量性质,得到了这种增强复合材料的有效体积模量和有效剪切模量的理论预测公式。这些结果在特殊情况下,可退化到三相球模型确定的球形粒子增强复合材料的有效模量公式。     

一维多介质可压缩流动的守恒型界面追踪方法

本文针对一维问题的ProntTracking方法,提出了一种较易实现的守恒型界面追踪方法.利用双波近似求解Riemann问题来确定界面处的数值通量,在固定的网格上采用统一的有限体积格式进行内点和交界面点的计算,通过守恒插值以及守恒量的重新分配,保证数值解在全场实现一致守恒,将该方法应用于一维多介质可压缩流动的模拟,给出了满意的数值模拟结果.     

压电复合材料圆形夹杂中螺型位错和界面裂纹的干涉分析

研究了无穷远纵向剪切和面内电场共同作用下,压电复合材料圆形夹杂中螺型位错与界面裂纹的电弹耦合干涉作用．运用Riemann-Schwarz 对称原理,并结合复变函数奇性主部分析方法,获得了该问题的一般解答．作为典型算例,求出了界面含一条裂纹时基体和夹杂区域复势函数和电弹性场的封闭形式解．应用广义Peach-Koehler公式,导出了位错力的解析表达式．分析了裂纹几何参数和材料的电弹性常数对位错力的影响规律．结果表明,界面裂纹对位错力和位错平衡位置有很强的扰动效应,当界面裂纹长度达到临界值时,可以改变位错力的方向．该结果可以作为格林函数研究圆形夹杂内裂纹和界面裂纹的干涉效应．其公式的退化结果与已有文献完全一致．     

各向异性双材料中运动螺型位错与界面刚性线的干涉

研究了各向异性双材料中匀速运动螺型位错与界面刚性线的干涉问题.运用Riemann Schwarz解析延拓技术与复势函数奇性主部分析方法,获得了该问题的一般弹性解答,求出了界面含一条和两条刚性线情况下的封闭形式解,并给出了刚性线尖端的应力强度因子和作用于运动位错上的像力的显式表达式.结果表明,位错速度增大可以削弱位错对应力强度因子的反屏蔽效应;位错速度越大,位错平衡点越靠近刚性线,退化结果与已有的解答完全吻合.     

双材料接合半无限体三维矩形界面裂纹应力强度因子分析

基于体积力法,研究了双材料接合半无限体三维矩形界面裂纹的应力强度因子问题．在数值计算中,未知的体积力密度采用基本密度函数和多项式乘积的形式来近似,其中基本密度函数是根据界面裂纹应力的振荡奇异性来选取的．计算结果表明,基于本算法得到的数值结果其收敛精度和计算误差都是令人满意的．算例中,给出了应力强度因子随矩形形状及双材料参数的变化规律．     

具有非均匀界面相的颗粒和纤维增强复合材料弹性静力学问题的解析解

通过将以位移表示的平衡方程转化为黎卡提方程,得到了具有非均匀界面相的颗粒和纤维增强复合材料非均匀界面相内弹性场的解析解·　所得的解析解是弹性模量呈幂次方变化的非均匀界面相解的通用形式·　任意给定1个幂指数,可以得到具有非均匀界面相的颗粒和纤维增强复合材料体积模量的解析表达式·　通过改变幂指数及幂次方项的系数,此解析解可适用于具有多种不同性质的非均匀界面相·　结果表明:界面相模量和厚度对复合材料模量有很大的影响,当界面相存在时,粒子将出现一种"尺寸效应"·     

椭圆型界面问题的破裂再生核方法

本文基于一维椭圆型界面问题提出了一种有效的数值方法.首先,根据模型构建一个崭新的破裂再生核空间.其次,应用破裂再生核方法给出了此类界面问题的近似解,并讨论该方法的收敛性.最后,通过几个有效的数值算例来说明该方法的精确性和稳定性.     

压电螺型位错和含界面裂纹圆形夹杂的电弹干涉效应

研究了在无穷远反平面剪切和面内电场共同作用下压电材料基体中一个压电螺型位错与含界面裂纹圆形弹性夹杂的电弹耦合干涉作用．运用复变函数方法,获得了该问题的一般解答．作为典型算例,求出了界面含一条裂纹时,基体和夹杂区域复势函数的封闭形式解以及裂纹尖端应力和电位移场强度因子．应用扰动技术和广义Peach-Koehler公式,导出了位错力的解析表达式．数值结果表明,界面裂纹对压电螺型位错与夹杂的干涉具有强烈扰动效应,当裂纹长度达到临界值时,可以改变其干涉机理．同时,分析说明压电材料中软夹杂可以排斥基体中的位错．     

Effective bulk moduli of materials containing stochastically distributed nano-inhomogeneities with surface stresses

In the present contribution, a mathematical model for the investigation of the effective properties of a material with randomly distributed nano-particles is proposed. The surface effect is introduced via Gurtin-Murdoch equations describing properties of the matrix/nano-particle interface. They are added to the system of stochastic differential equations formulated within the framework of linear elasticity. The homogenization problem is reduced to finding a statistically averaged solution of the system of stochastic differential equations. These equations are based on the fundamental equations of linear elasticity, which are coupled with surface/interface elasticity accounting for the presence of surface tension. Using Green's function this system is transformed to a system of statistically non-linear integral equations. It is solved by the method of conditional moments. Closed-form expressions are derived for the effective moduli of a composite consisting of a matrix with randomly distributed spherical inhomogeneities. The radius of the nano-particles is included in the expression for the bulk moduli. As numerical examples, nano-porous aluminum and nano-porous gold are investigated assuming that only the influence of the interface effects on the effective bulk modulus is of interest. The dependence of the normalized bulk moduli of nano-porous aluminum on the pore volume fraction (for certain radii of nano-pores) are compared to and discussed in the context of other theoretical predictions. The effective Young's modulus of nano-porous gold as a function of pore radius (for fixed void volume fraction) and the normalized Young's modulus vs. the pore volume fraction for different pore radii are analyzed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

A new reformulation of vibration suppression equations of functionally graded magnetorheological fluid sandwich beam

This article presented a new reformulation of governing equations of functionally graded magnetorheological fluid (FGMRF) sandwich beams using new auxiliary functions. This technique led to the decoupled vibration equations of the FGMRF sandwich beams and also to the analytical solutions for the in-plane and out of plane displacement fields by considering the Euler-Bernoulli beam theory (EBBT). The material properties of top and bottom layers were changed through the layer thickness according to a power-law distribution of the volume fraction of the constituents. Complex shear modulus of the magnetorheological fluid was varied continuously as a quadratic function of magnetic field intensity. Natural frequencies and corresponding loss factors were calculated with high accuracy in comparison with those available in literature. The effects of boundary conditions, geometric and material properties and the magnetic field intensity on vibrational modes were investigated. Results revealed that unlike the natural frequencies, the loss factors were more affected by the magnetic field.     

深埋隧洞围岩应力的精确解与近似解的对比分析

对不同断面形状的深埋隧洞进行了分析,比较了隧洞围岩应力解析解与通过当量半径方法得到的近似解之间的差别.首先,应用复变函数的基本理论,给出圆形、椭圆、矩形、直墙拱形等几种常见深埋隧洞围岩应力的解析表达式.其次,应用当量半径的折算形式,将其任意形状的边界转化为标准圆形断面,利用Lamé解答得到了各围岩应力分量.最后,考虑隧洞断面形状参数的变化,通过数值算例对精确解和近似解进行了比较,分析了当量半径折算形式的精确度.在此基础上,应用有限元方法验证了复变函数解析解的精确性,以椭圆、矩形和直墙拱形的复变函数解验证当量半径精确度.结果表明,当量半径的折算形式解答与精确解答之间相似程度与隧洞的断面形状和几何参数之间有着密切的关系.     

A circular inhomogeneity with a mixed-type imperfect interface in anti-plane shear

We present a rigorous study of the problem associated with a circular inhomogeneity embedded in an infinite matrix subjected to anti-plane shear deformations. The inhomogeneity and the matrix are each endowed with separate and distinct surface elasticities and are bonded together through a soft spring-type imperfect interphase layer. This combination is referred to in the literature as a ‘mixed-type imperfect interface’ due to the fact that the soft interphase layer (described by the spring model) is bounded by two stiff interfaces arising from the separate surface elasticities of the inhomogeneity and the matrix. The entire composite is subjected to remote shear stresses and we allow for the presence of a screw dislocation in either the inhomogeneity or the matrix. The corresponding boundary value problem is reduced to two coupled second-order differential equations for the two analytic functions defined in the two phases (as well as their analytical continuations) leading to solutions in either series or closed-form. The analysis indicates that the stress field in the composite and the image force acting on the screw dislocation can be described completely in terms of three size-dependent parameters and a size-independent mismatch parameter. Interestingly, in the absence of the screw dislocation, the size-dependent stress field inside the inhomogeneity is uniform. Several numerical examples are presented to demonstrate the solution for a screw dislocation located inside the matrix. The results show that it is permissible for the dislocation to have multiple equilibrium positions.     

Buckling of laminated plates - A simple finite element based on higher-order theory

A four-noded rectangular element with seven degrees of freedom at each node is developed for buckling analysis of laminated plate structures having any number of layers with a constant thickness of individual layers. The displacement model is so chosen that it can explain adequately the parabolic distribution of transverse shear stresses and the non-linearity of in-plane displacements across the thickness. A geometrical stiffness matrix is developed using in-plane stresses. A wide range of plates from thick to thin are examined under uniaxial loading conditions. The results are compared with the existing analytical and numerical solutions. The present formulations confirm its applicability for buckling analysis of a wide range of plates.     

On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite

The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses.     

Shear of orthogonally reinforced spherofibrous composites

The problem of determining the shear characteristics and interphase stress concentration of fibrous composites with spherical inclusions is examined on the basis of a three-phase model. Stress fields caused by diffusion interaction of phases are neglected. The elastic moduli of the composite are investigated and compared with those obtained from a two-phase model. The general formula for determination of the shear modulus of triorthogonally reinforced compsites is derived using previously investigated relationships for averaged stress fields. The matrix of these compsites contained spherical cavities. The dependence of integral characteristics of three-phase composites on their bulk phase concentration was investigated. The stresses between phases were studied as a function of composite structure.A. A. Blagonravov Machine-Science Institute, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, 104–111, January–February, 1997.     

Two-dimensional viscous flow between circular cylinders: application to damping devices for seismic isolation

A detailed analysis of the fluid dynamics of the two-dimensional viscous flow between circular cylinders is dealt with in this paper. Analytic solutions are found on the basis of asymptotic expansions with respect to a small parameter defined by the ratio between the difference of the radii and the radius of the internal cylinder. The analysis is related to the study of recently developed devices for seismic isolation of buildings based on modified pile foundation, separated from the soil, in which a viscous fluid is inserted in the void space between the pile and the lining of the surrounding soil. The availability of this analytical solution contributes to obtaining accurate predictions of the force on the pile.