纤维增强复合材料轴对称界面端的奇异应力场

提出了一种分析横观各向同性纤维增强复合材料轴对称界面端的奇异应力场的特征值法。基于横观各向同性弹性材料空间轴对称问题的基本方程和一阶近似假设,利用分离变量形式的位移函数和无网格算法,导出了关于应力奇异性指数和应力角函数的奇异性特征方程。对于纤维/基体轴对称界面端模型,特征值法给出的应力奇异性指数、相应的位移和应力角函数,与通过有限元分析得到的结果非常吻合。利用有限元计算得到的奇异应力场,结合特征值法给出的应力奇异性指数和应力角函数,通过线性外插得到了相应的应力强度系数。特征值法结合有限元分析,可以完全确定横观各向同性纤维增强复合材料轴对称界面端的奇异应力场。     

压电扇形板弯曲的三维精确解

本文利用Ding et al^[1]提出的横观各向同性压电材料三维问题的通解,求得了压电扇形板在表面正应和和电位移或电势作用下的三维精确解,该解可退化为圆板情形。     

关于横观各向同性体在其各向同性面内弹性问题的一个常数

研究了在平面应力和平面应变情况下, 横观各向同性材料在其各向同性面内的应力2应变关系以及用位移表达的平衡方程可以被表示成与各向同性材料完全相同的形式。这种等同关系是通过引入一个与横观各向同性材料的泊松比有关的常数得到的。该常数的引入消除了已发表的文献中求解横观各向同性材料平面问题时出现的矛盾。这个常数的引入也便于正确计算单向纤维增强复合材料的横向切变模量。      

压电材料中渗透性周期共线反平面裂纹问题

本文利用复变函数方法,借助于Riemann-Schwarz延拓技术和保形映照方法,研究了渗透性边界条件下周期共线反平面裂纹问题,获得了解的表达式,得到了力学和电学强度因子。结果表明在裂纹尖端应力和电位移的奇异性都与远场作用的应力载荷和裂纹长度有关,其中应力的奇异性与材料无关,电位移的奇异性则与材料有关,电载荷对裂尖的奇异性没有影响。最后,运用数值算例,给出周期裂纹间的干涉效应和裂纹的尺度效应。     

压电材料中反平面渗透裂纹的解

用复变函数的保角映射法,采用可渗透边界条件,研究了含裂纹的无限大压电材料在平面内电场和反平面荷载作用下的耦合场,得到了精确的解和场强度因子以及能量释放率。结果表明,电场强度在裂尖没有奇异性,应变、应力、电位移具有1/2阶的奇异性,能量释放率总是正的。     

横观各向同性层合压电矩形板稳定问题的三维精确分析

从横观各向同性压电弹性力学的三维基本方程出发,通过引入位移函数和应力函数,构造了两类相互独立的状态空间方程,使原方程解耦成两个低阶方程,有利于具体问题的求解。对于四边简支压电层合矩形板面内双向均匀受压的稳定问题,建立了层合板上下表面状态变量间的关系式,利用边界条件进一步导出特征方程。发现存在两类彼此无关的稳定形式:第一类对应板的纯面内稳定,而第二类则是一般意义上的板的弯曲稳定。给出了数值结果,并考察了相关参数的影响。     

压电材料切口奇性指数计算

利用一种数值方法分析压电材料切口尖端包括奇异应力场和奇异电位移场在内的双重奇异性。基于切口尖端的位移场按幂级数渐近展开假设, 从应力平衡方程和Maxwell方程出发, 推导出关于压电材料切口奇性指数的特征方程组, 同时将切口的力学和电学边界条件转化为奇性指数和特征函数的组合表达, 从而将压电材料双重奇性分析问题转化为在相应边界条件下微分方程组的特征值求解问题, 采用插值矩阵法, 可以一次性地计算出压电材料切口的各阶奇性指数。裂纹作为切口的特例, 其尖端的电弹性奇性指数亦可以根据本法求出。     

压电材料切口奇性指数计算

利用一种数值方法分析压电材料切口尖端包括奇异应力场和奇异电位移场在内的双重奇异性.基于切口尖端的位移场按幂级数渐近展开假设,从应力平衡方程和Maxwell方程出发,推导出关于压电材料切口奇性指数的特征方程组,同时将切口的力学和电学边界条件转化为奇性指数和特征函数的组合表达,从而将压电材料双重奇性分析问题转化为在相应边界条件下微分方程组的特征值求解问题,采用插值矩阵法,可以一次性地计算出压电材料切口的各阶奇性指数.裂纹作为切口的特例,其尖端的电弹性奇性指数亦可以根据本法求出.     

含椭圆孔压电材料的电弹场

采用复变函数的方法,研究了含椭圆孔的压电材料在无限远处受力电荷载作用的平面问题。与已有文献不同,通过求解10元一次方程,得到了满足可导通和不可导通电边界条件,孔内和压电材料体内电弹场的通解。以PZT一4压电陶瓷为例,给出了孔内的电场、压电材料体内电弹场沿孔边和坐标轴向的分布情况。得出了以下新的结论:含椭圆孔压电材料的电弹场与边界条件、力电荷载的方向、椭圆孔的形状有关,但在水平方向的拉伸载荷和电位移的作用下,椭圆孔的形状对长半轴处的环向电位移和正应力的最大值没有影响。     

功能梯度压电层/压电半空间结构中Love波的传播:一种改进的拉盖尔多项式方法

使用传统的拉盖尔多项式方法求解层状半空间结构时,存在因层间材料差异所造成的应力、电位移不连续的现象。为了克服此方法的不足,提出了一种改进的拉盖尔多项式方法,研究了功能梯度压电层状半空间中Love波的传播特性。与文献中应用WKB法得到的结果进行对比,验证了该方法的正确性。计算和分析了相应的频散曲线、应力和电位移分布曲线。结果表明:该方法能够避免因层间材料差异所造成的应力、电位移不连续现象的出现;高频Love波的应力和电位移主要分布在功能梯度压电层中速度较低的一侧。该研究为基于Love波传感器的设计与优化奠定了一定的理论基础。     

Dynamic response for non-homogeneous piezoelectric medium with multiple cracks

A general procedure to analyze the dynamic response of non-homogeneous piezoelectric medium containing some non-collinear cracks is developed. It is assumed that all the material properties only depend on the coordinates y (along the thickness direction). The assumption is made that the non-homogeneous medium is composed of numerous laminae with their surfaces perpendicular to the thick direction. The solution method is based upon the Fourier and Laplace transforms to reduce the boundary value problem to a system of generalized singularity equations in the Laplace transform domain. The singular integral equations for the problem are derived and numerically solved by weight residual value method. The time-dependent full field solutions are obtained in the time domain. As numerical illustration, the stress and electric displacement intensity factors for a three-layer plate specimen with two cracks are presented. It is found that the stress and electric fields are coupled in the crack plane ahead of the crack tip for non-homogenous piezoelectric materials.     

Coupled 2D electric and mechanical fields in piezoelectric solids containing cracks and thin inhomogeneities

This paper develops integral equations and boundary element method for determination of 2D electro-elastic state of solids containing cracks, thin voids and inclusions. It proves that stress and electric displacement field near the tip of thin inhomogeneity possesses square root singularity. Thus, for determination of electromechanical fields near thin defects new special base functions are introduced. The interpolation quadratures along with the polynomial transformations are adopted for efficient numerical evaluation of singular and hypersingular integrals. Presented numerical examples show high efficiency and accuracy of the proposed approach.     

Electroelastic analysis of an electrically dielectric Griffith crack in a piezoelectric layer

The fracture analysis of an electrically dielectric Griffith crack embedded in a piezoelectric layer is made under in-plane electro-mechanical loadings. To simulate an opening crack full of a dielectric interior, the energetically consistent crack-face boundary conditions are utilized. Applying the Fourier transform technique, the boundary-value problem is reduced to solving two coupling singular integral equations. The intensity factors of stress, electric displacement, crack opening displacement (COD) and electric potential are further determined by the Lobatto-Chebyshev collocation method. The variations of the electric displacement at the crack surfaces are investigated by using the energetically consistent and semi-permeable boundary conditions respectively. The observations show that the electric displacement inside the crack is decreasing with an increase of the ratio between the crack length and piezoelectric layer width. Numerical computations are further carried out to compare the intensity factors of stress and electric potential, and the energy release rate using the energetically consistent boundary conditions with those using the semi-permeable boundary conditions. The obtained results reveal that the stress induced by a dielectric inside a crack has great effects on the stress intensity factor and energy release rate, but little influence on the electric potential difference across the crack.     

Antiplane Permeable Edge Cracks in a Piezoelectric Strip of Finite Width

A piezoelectric strip with permeable edge cracks normal to the strip boundaries is analyzed. Under uniform antiplane mechanical shear and inplane electric loading, the distribution of the entire electroelastic field in a cracked piezoelectric strip is determined in explicit analytic form via the conformal mapping technique. It is found that the strain and the electric displacement exhibit the same singularity as the stress near the crack tips, while the electric field is always uniform. The field intensity factors and the energy release rate are independent of the applied electric load for prescribed stress, and related to the applied electric load for prescribed strain.     

铆接界面端三维奇异性应力场的研究

针对铆接结构的特点,应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式,并根据铆钉/被铆接件接触界面端的位移和应力边界条件,建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比,验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题,考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。     

Evaluation of power-logarithmic singularities, T-stresses and higher order terms of in-plane singular stress fields at cracks and multi-material corners

The scaled boundary finite-element method is extended to analyze the in-plane singular stress fields at cracks and multi-material corners. A complete singular stress field is represented semi-analytically as a series of matrix power functions of the radial coordinate originating from the singular point. This method is capable of directly evaluating orders of singularity, stress intensity factors, T-stresses, higher order terms, angular distributions of stresses for each term and, if present, power-logarithmic singularities. In this method, the singular functions are represented analytically and are not evaluated close to the singular point. Numerical examples are calculated to demonstrate the simplicity and to evaluate the accuracy of the scaled boundary finite-element method.     

Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials

From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular displacement boundary integral equations (BIEs) are applied on the external boundary of the cracked solid, while the hypersingular traction BIEs are used on the crack faces. Three numerical examples are presented to show the path independence and the high accuracy of the J-integral in piezoelectric materials and to analyze the pros and cons of these approaches in evaluating the field intensity factors.