电磁复合材料中圆弧形界面导电刚性线尖端应力强度研究

研究无穷远处反平面力载荷和平面电磁载荷作用下,电磁智能材料中圆弧形界面导电刚性线尖端应力强度问题。运用复变函数方法,得到该问题的一般解;并得到界面上只有一条刚性线时的封闭形式解,求解基体及夹杂区域复势函数、刚性线尖端的应力、电位移和磁感应强度因子。对于压电基体和压磁夹杂情况下,详细讨论刚性线长度以及无穷远处载荷对刚性线尖端应力强度因子的影响规律。当同时加载力电磁载荷时,刚性线尖端的应力、电位移和磁感应强度因子依赖于复合材料的有效材料常数。     

规则性分布长纤维增强复合材料的等效弹性研究

建立一种用于预测规则性分布长纤维增强复合材料等效力学性能的分析模型。在位移格林函数中通过引入周期性分布几何特征来反映纤维分布和相互作用的影响。另外,利用双夹杂理论引入界面相微结构参数,研究复合材料有效弹性的尺寸效应。最后,通过与有限元计算结果比较,验证本理论模型的合理性。该分析模型可以进一步扩展用于其他的力学问题研究,比如损伤行为、材料弹塑性等。     

层片结构共晶体的残余应力场

层片结构共晶体由同向平行的片状夹杂和基体构成,片状夹杂和基体之间为强约束化学结合界面。首先建立四相模型,根据制备过程的温度变化,基于Eshebly理论得到基体内的残余应力和残余应变;然后在三相胞元应变均匀条件下,通过有效自洽理论得到片状夹杂和界面相的残余应力场;最后在基体、界面相和片状夹杂为各向同性的条件下,得到层片结构共晶体的残余应力分布规律,并分析其尺度效应。     

考虑材料夹杂的接触问题数值分析

金属在冶炼过程中产生的非金属夹杂物以及裂纹等缺陷在交变载荷作用下产生应力集中,形成疲劳源,使部分材料与基体材料脱离产生裂纹,影响材料的疲劳寿命。基于半解析法(Semi-analytical method,SAM),将计算区域离散为若干个微立方体单元,每个夹杂可由不同数量的微立方体单元构成。根据等效夹杂方法(Equivalent inclusion method,EIM),每个单元夹杂均具有一个未知的等效特征应变,通过求解应力-应变本构方程组得到。接触压力通过共轭梯度法求解,进而得到表面残余变形和表层下应力分布等。采用二维和三维快速傅里叶变换(Fast Fourier transform,FFT)算法快速求解变形、特征应力等变量。结果表明,算法稳定,收敛性好;材料夹杂对接触压力和表层应力分布有显著影响;处于接触表面附近的大尺寸夹杂对材料性能影响最大。基于本模型可模拟任意形状和分布的夹杂的影响。     

半空间界面反平面谐振动对界面刚性物的激励效应

利用波函数展开法和格林(Green)函数法研究了半空间界面上的刚性物与半圆形凹陷对半空间界面上反平面稳态点源的动态响应问题。考虑到问题的线性特点应用叠加原理将复杂的双曲偏微分方程定解问题分解为几个子问题写出问题的解,利用问题的位移连续条件得到确定接触力或接触处位移的定解方程组。通过一个算例分析了刚性物的质心位移幅度和转动响应幅度的变化以及半圆形凹陷处的环向动态应力的变化,结果说明方法是可行的,结论可为地面工程结构抗震设计提供理论参考。     

圆柱壳开孔补强的弹性和弹塑性有限元分析

考虑补强圈与圆柱壳作为一个整体子模型和接触子模型，对开孔补强结构的圆柱壳进行了弹性和弹塑性有限元应力分析。比较两个子模型和弹性／弹塑性有限元分析的结果，发现接触子模型和整体子模型的圆柱壳开孔应力分布相似，但接触子模型和整体子模型在壳体和补强圈之间的接触面上的应力分布存在差异。对不同直径的接管和不同倾角的接管进行了有限元分析，分析表明，应力分布及最大应力受倾角的影响较大，受直径变化的影响不大。     

间断式纤维增强热塑性基复合材料应力应变场分析

用有限元法通过引入一个单胞模型和适当的边界条件，分析了间断式纤维增强复合材料在外部载荷作用下复合材料内部应力－应变场的变化规律，比较了基体在弹性和弹塑性条件下纤维、纤维与基体界面应力分布的特点。     

陶瓷基复合材料低循环拉—拉疲劳寿命预测

采用细观力学方法建立预测纤维增强陶瓷基复合材料低循环拉—拉疲劳寿命的模型。该模型考虑初始加载到疲劳峰值应力时,基体出现裂纹,纤维/基体界面发生脱粘,部分纤维将发生断裂,并采用统计方法得到初始加载到峰值应力时的纤维失效体积分数;在后续循环过程中,考虑纤维相对基体在界面脱粘区滑移造成界面切应力下降,纤维失效模型与Evans界面磨损模型相结合,得到循环过程中纤维失效体积分数与界面切应力、循环数之间的关系;当纤维失效导致剩余强度下降,并小于疲劳峰值应力时,判断材料失效。采用剩余强度方法对陶瓷基复合材料的S-N曲线进行预测,并将预测的S-N曲线与试验数据进行对比,结果吻合较好。     

开孔圆柱壳模拟疲劳试验模型及加载条件的研究

研究受内压开孔圆柱壳与其受拉伸开孔平板模型在结构和受载条件上的相似性，有限元分析表明，开孔圆柱壳与其相应的平板模型在开孔附近的等效应力分布非常相似，分析和试验结果表明，开孔圆柱壳模拟疲劳试验载荷应由控制疲劳寿命的关键部位（即危险点）的等效应力来确定，当开孔圆柱壳与其平板模型在危害点的等效应力水平和分布相同时，可认为二者的疲劳寿命也相同，在正确的加载条件下，开孔平板模型可用于开孔圆柱壳的模拟疲劳试验，并较精确地预测开孔圆柱壳的疲劳寿命。     

界面层对C/SiC复合材料热残余应力影响的模拟及分析

针对平纹编织C/Si C复合材料的C纤维束,通过对其扫描电子显微镜(Scanning electron microscope,SEM)照片的测量,考虑纤维排布以及选择合适的界面模型,建立了包含界面层的三维三相的代表特征体元(Representative volume element,RVE)的有限元模型。采用间接耦合的降温法,在考虑温度对组分弹性常数的影响以及施加合适的周期性边界条件的基础上模拟了C纤维束轴向的热残余应力。分析可知,对于Si C基体的热残余应力,其随着界面层厚度的减小而增大,随着界面层模量的增大而增大。引入一维应力分布轴,将振荡幅值作为选择最佳参数的一个条件,据此可知选用热膨胀系数小的界面层材料可更好的降低组分间热残余应力变化的梯度。     

Analysis of the stress concentration on circular rigid inclusion in a non-linear viscous material

The stress concentration factor of a circular rigid inclusion buried in a non-linear viscous material described by a power law is obtained for various rate hardening exponents. The medium, under a generalized plane condition, is subjected to a bi-axial tension with identical boundary stresses in the horizontal and vertical axes. The stress concentration factor of a circular hole in a non-linear viscous material under a plane strain condition is compared to the stress concentration under generalized plane strain conditions for various rate hardening exponents. The medium is considered to be subjected to the same boundary stress condition as the circular rigid inclusion.The effect of the interaction between the two inclusions on the stress concentration is discussed in terms of the volumetric fraction of the inclusion.     

平面刚性夹杂问题的边界积分方程方法

研究了含刚性夹杂的平面弹性力学问题。由Ｓｏｍｉｇｌｉａｎａ公式出发，将问题归结为一组混合型边界积分方程的求解。其中外侧边界仍为常规的边界积分方程，而夹杂线上则是典型的Ｃａｕｃｈｙ型奇异积分方程，结合使用边界元及奇异积分方程算法［１］．本文对若干具有工程意义的例子作了数值计算，得到了其应力强度因子；有关结果还与文［２］作了比较，从而证明本文方法是完全可靠的，它可进一步用于解决更一般的问题。     

Couette flows of rigid/plastic solids: analytical examples of the interaction of constitutive and frictional laws

The exact analytical solution under plane strain conditions is found for a hollow circular cylinder subjected to rotational friction on the inner surface and an uniform pressure on the outer surface. Two constitutive laws, a rigid/plastic hardening model with a saturation stress (Voce-Palm material) and a rigid/viscoplastic model (Bingham material), are considered as well as three interfacial laws, sticking, Coulomb sliding friction and Tresca shearing friction. The study focuses on general behavior of the solutions for various pairs of constitutive and interfacial models, such as existence and uniqueness and qualitative differences in solution. For the Voce-Palm material, it is shown that solutions do not exist for certain boundary conditions if only sticking or Coulomb friction are permitted. On the other hand, multiple solutions exist for certain boundary conditions if only sticking and Tresca friction are permitted. Existence is achieved under all boundary conditions if sticking and both frictional laws permitted simultaneously. Uniqueness and unambiguity are achieved if two interface selection principles are invoked: (1) sticking must occur if it is possible and (2) Coulomb sliding must occur if it is possible and sticking is not. Geometrical interpretation of results in the form of friction maps is provided to illustrate possible regimes of interfacial behavior for different boundary conditions.     

Stress field near circular-arc interface crack tip based on electric saturation concept

Within the framework of nonlinear electroelasticity, the anti-plane problem of a circular-arc interfacial crack between a circular piezoelectric inhomogeneity and an infinite piezoelectric matrix subjected to a far-field uniform loading is investigated by an electrical strip saturation model, the complex variable method, and the method of analytical continuation. Explicit closed form expressions for the complex potentials in both the matrix and the inclusion, and the stress intensity factor at the crack tip are presented. Comparison with some related solutions based on the linear electroelastic theory shows the validity of the present solutions     

Asymptotic simulation of imperfect bonding in periodic fibre-reinforced composite materials under axial shear

An asymptotic approach for simulation of the imperfect interfacial bonding in composite materials is proposed. We introduce between the matrix and inclusions a flexible bond layer of a volume fraction c⁽³⁾ and of a non-dimensional rigidity λ⁽³⁾, derive a solution for such three-component structure, and then set c⁽³⁾→0, λ⁽³⁾→0. In the asymptotic limit depending on the ratio λ⁽³⁾/c⁽³⁾ different degrees of the interface's response can be simulated. A problem of the axial shear of elastic fibre-reinforced composites with square and hexagonal arrays of cylindrical inclusions is considered. The performed analysis is based on the asymptotic homogenization method, the cell problem is solved using the underlying principles of the boundary shape perturbation technique. As a result, we obtain approximate analytical solutions for the effective shear modulus and for the stress field on micro level depending on the degree of the interfacial debonding. Developed solutions are valid for all values of the components’ volume fractions and properties. In particular, they work well in cases of rapid oscillations of local stresses (e.g., in the case of densely packed perfectly rigid inclusions), while many of other commonly used methods may face computational difficulties.     

直角平面内圆形刚性动夹杂对边界出平面点源载荷的动态响应

采用复变函数法和多极坐标移动技术研究二维直角平面区域内可动圆形刚性夹杂在边界出平面点源载荷作用下的动态响应问题.首先构造出直角平面区域内不含有夹杂时满足直角边界应力条件的格林(Green)函数解;其次求解波动方程边值问题,建立直角平面区域内含有夹杂时满足直边界应力自由条件的散射波解,利用叠加原理写出问题的总波场.借助于夹杂边界处的位移条件和夹杂运动的动力学条件,确定夹杂运动的位移幅度和散射波解中的未知系数.给出的算例结果表明本文方法的有效实用性.     

Constrained zones at singular points of inclusion contours

Stress concentration fields at singular points of the boundary of rigid inclusions in an elastic matrix under conditions of generalized plane stress were investigated by the method of caustics. Inclusion shapes were simulated by closed curves exhibiting cuspidal points, generated from the unit circle by means of a suitable transformation. It was proved that caustics developed at such points are generalized epicycloids, whose size is directly proportional to the respective stress intensity factor, while their orientation corresponds to the directions of the principal stress axes. A straightforward method for the experimental determination of these parameters was developed, important for the design of actual composites.     

An EM algorithm for dynamic estimation of interfacial boundary in stratified flow of immiscible liquids using EIT

Estimation of interfacial boundary between two immiscible liquids in two-phase flows through pipe line provides information about the flow characteristics and thus can aid in design and monitoring of the flow process. The interfacial boundary can be represented in several ways, one such method is the front point approach. Front points describe the location and the shape of the interfacial boundary separating the immiscible liquids. During the flow process, due to fluctuations the interfacial boundary and so the front points which describe the boundary changes with time. The time-varying interfacial boundary can be estimated using dynamic inverse algorithms based on Kalman filter. However, algorithms based on Kalman filter require complete knowledge of model parameters (initial states, state transition matrix, and noise covariance matrices) for implementation. In processes involving complex flow pattern such as two-phase flows, it is difficult to represent the model parameters in a prior form. This uncertainty in model parameters causes suboptimal performance of the Kalman type filters. In this paper, we employ expectation maximization algorithm (EM) to estimate model parameters along with the interfacial boundary using electrical impedance tomography (EIT). The estimation of model parameters reduces the modeling uncertainty and thus results in improving the tracking of interfacial boundary. Numerical and experimental studies are performed to validate the performance of the proposed method.     

Modeling of Coriolis mass flow meter of a general plane-shape pipe

The vibration of a general plane tube with a flowing fluid, which is the measuring element in a Coriolis mass flow meter (CMF), is studied. The dynamic stiffness matrix method is used to model such a tube. The tube is divided into straight and circular elements. The elements dynamic stiffness matrices are derived from the equations of motion. By assembling the elements matrices into a global matrix the natural frequencies are obtained. The mode shapes are obtained by applying the boundary conditions at the supports and the compatibility conditions at the nodes. The effects of the flow velocity on the natural frequency and the relative phase difference are modeled. The method is applied to different tube shapes. The results are compared to the published data which reveals good agreement.