一维六方准晶弹性层合悬臂梁的解析解

论文利用一维六方准晶的平面本构关系,以及简化为平面问题的物理方程,在悬臂梁的弹性应力解的基础上,假设准晶层和弹性层的应力分布,求出了各自的位移表达式,再利用层间连续条件和放松的边界条件,推导出一维六方准晶层合悬臂梁仅在自由端受集中力作用下声子场和相位子场的位移解析解,为研究准晶涂层材料的力学性质提供参考.     

梯度功能压电悬臂梁的一组基本解及其应用

采用应力函数解法,研究了弹性参数和体积力同时呈梯度变化时压电材料悬臂粱的力-电响应,得到了应力函数和电位移函数的解析表达式及梯度功能压电悬臂梁的一组基本解．作为一种应用形式,给出了梯度功能压电执行器的尖端位移和制动力的确定方法、此外,利用该基本解,可以方便地确定悬臂梁在多种不同典型荷载单独或联合作用下的解答。     

线性分布荷载作用下梯度功能压电悬臂梁的解

采用逆解法求解了上表面受线性分布荷载作用的压电悬臂梁执行器，其中体积力$F_z$ 呈非线性分布. 首先确定了应力函数和电位移函数的多项式表达式，进而研究了该问题的 通解，以及体积力的不同分布对解答的影响. 常体积力和无体力情况下的解可以由上述 解直接得到. 本文为研究其它类型的压电梯度微观结构提供了一种可行的方法.     

压电材料中切口/接头端部平面电弹性场奇异性有限元分析

为了对平面载荷作用下压电材料中切口或接头端部附近电弹性场奇异性问题进行分析，首先以应力平衡方程、Maxwell方程和和边界条件为基础，得到一种求解压电材料特征问题的弱式方程；其次，假定楔形切口或接头端部附近单元内位移和电势沿径向分布为指数形式，而周向方向分布则采用泡函数插值，将其代入弱式方程，建立一种只需对楔形切口或接头端部附近周边进行离散的一维简单有限元方法．压电材料的极化轴可以是任意方向．利用该有限元模型讨论了楔形切口角度、极化轴方向和边界条件对奇性场的影响．通过和其它特定情况下的现有解相比，证实了该文有限元数值方法的有效性，而且精度很高．     

悬臂轴拉杆一阶随机分析的解析解

针对悬臂轴拉杆在自由端受集中力问题进行了随机分析，其中考虑了轴拉杆杨氏模量的变异，在小变异情况下获得了不同相关结构与相关长度下问题的解析解，并就结果对相关结构的敏感性进行了讨论．     

基于MATLAB的悬臂梁大变形分析

主要研究悬臂梁大变形的挠度求解问题.通过推导悬臂梁自由端受集中力时的绕曲线方程,得出一种较为简便的大变形问题求解方法.编写程序利用黎曼积分配合二分法迭代出解,并和传统小变形解法进行了比较.同时,利用ANSYS软件建模证明了本文方法在一定范围的正确性.     

双材料应力分析中的镜像点方法

提出一种分析各类双材料中任一点受集中力作用问题的方法.通过将结合界面或其自由表面看作镜面,将应力函数或位移函数设定成固定于受载点及其镜像点上的局部坐标系下的形式,利用界面连续条件和Dirichlet的单值性原理,所有应力函数或位移函数就可由无限体中集中力的解或半无限体表面集中力的解的应力函数求得.这种方法不仅可适用于单一界面的情况,也可使用于多个界面并存的情况,并且也可适用于具有自由表面的结合材料.这一方法可应用于各类结合材料、涂层薄膜材料、板材等.     

裂纹端部细短纤维的应力分析

基于裂纹端部存在与其裂纹面相垂直的二相细短纤维分析模型，采用叠加原理推导了求解纤维表面应力分布函数的积分方程，通过简化得到了该方程的解析表达显式，该积分方程的特征值方程是纤维几何参数，材料常数以及纤维相对于裂纹位置的相关函数，当材料参数不满足特征方程时，积分方程将具有唯一解；并借助数值方法，给出了纤维剪应力分布算例，和纤维对应力强度因子的影响。     

含固支端梁的解析解

采用弹性力学的应力函数法求含固支端梁的应力和位移时,无法严格满足固支端的实际边界条件,需要采用简化的固支边界条件。本文对已有的简化固支边界条件进行了改进,基于新的简化固支边界条件,推导出了四种含固支端梁的应力和位移的解析解,并进行了相应的数值计算,对几种固支边界条件进行了讨论。由本文方法得到的上表面受均布载荷作用悬臂梁的位移u和v的解析解与有限元解的最大误差分别为3.0%和1.0%,两端固支梁的应力σx的解析解与有限元解的最大误差为5.3%。通过理论与数值结果的比较表明,本文改进的固支边界条件是对固支端一种很好的简化。     

磁头精定位控制中压电致动特征的解析解

利用压电弹性介质的二维本构关系,对于分割电极片状压电致动器在恒定的反平行电场作用下的电-力致动特性,在对自由端边界作圣维南意义下的放松处理后,采用弹性力学的半逆求解方法,导出了其力-电耦合的静态位移和应力分布的解析解.通过将所得解析解与没有简化假设的有限元数值解进行比较,结果表明:所得解析解的致动特性（即自由端位移随外加电压的变化特征）与数值解的结果几乎完全重合,表明其二维解析解是有效和可靠的.     

均匀分布荷载作用下压电悬臂梁弯曲问题解析解

对由横观各向同性电介质构成的悬壁梁在均匀分布荷功作用下的弯曲问题进行了研究，采用逆解法，建立了问题的应力函数与电势分布函数，进而得到问题的精确多项式解析解。     

PLANE STRAIN PROBLEM OF PIEZOELECTRIC SOLID WITH ELLIPTIC INCLUSION

By using the complex variables function theory, a plane strain electro-elastic analysis was performed on a transversely isotropic piezoelectric material containing an elliptic elastic inclusion, which is subjected to a uniform stress field and a uniform electric displacement loads at infinity. Based on the present finite element results and some related theoretical solutions, an acceptable conjecture was found that the stress field is constant inside the elastic inclusion. The stress field solutions in the piezoelectric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric boundary conditions.     

Penny-shaped crack in transversely isotropic piezoelectric materials

Using a method of potential functions introduced successively to integrate the field equations of three-dimensional problems for transversely isotropic piezoelectric materials, we obtain the so-called general solution in which the displacement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. In order to analyse the mechanical-electric coupling behaviour of penny-shaped crack for above materials, another form of the general solution is obtained under cylindrical coordinate system by introducing three quasi-harmonic functions into the general equations obtained above. It is shown that both the two forms of the general solutions are complete. Furthermore, the mechanical-electric coupling behaviour of penny-shaped crack in transversely isotropic piezoelectric media is analysed under axisymmetric tensile loading case, and the crack-tip stress field and electric displacement field are obtained. The results show that the stress and the electric displacement components near the crack tip have (r ^−1/2) singularity. The project supported by the Natural Science Foundation of Shaanxi Province, China     

A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator

This paper investigates the electro-mechanical behaviour of a thick, laminated actuator with piezoelectric and isotropic lamina under externally applied electric loading using a new two-dimensional computational model. The elastic core is relatively thick and thus it is modelled by Timoshenko thick-beam theory. Although the piezoelectric lamina is a beam-like layer, it is formulated via a two-dimensional model because of not only the strong electro-mechanical coupling, but also of the presence of a two-dimensional electric field. It is shown in this paper that a one-dimensional model for the piezoelectric beam-like layer is inadequate. The piezoelectric model is constructed within the scope of linear piezoelectricity. The actuation response is induced through the application of external electric voltage. Under the strong coupling of elasticity and electricity, the strain energy and work of electric potential are presented. The electro-mechanical response of the laminated Timoshenko beam is formulated and determined via a variational energy principle. Numerical examples presented illustrate convincing comparison with finite element solutions and existing published data. New numerical solutions are also presented to investigate the geometric effect on the electro-mechanical bending behaviour.     

Analytical solution for the electroelastic dynamics of a nonhomogeneous spherically isotropic piezoelectric hollow sphere

Summary By introduction of a special dependent variable and separation of variables technique, the electroelastic dynamic problem of a nonhomogeneous, spherically isotropic hollow sphere is transformed to a Volterra integral equation of the second kind about a function of time. The equation can be solved by means of the interpolation method, and the solutions for displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are presented at the end.The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016).     

Finite-part integral and boundary element method to solve three-dimensional crack problems in piezoelectric materials

Using the hypersingular integral equation method based on body force method, a planar crack in a three-dimensional transversely isotropic piezoelectric solid under mechanical and electrical loads is analyzed. This crack problem is reduced to solve a set of hypersingular integral equations. Compare with the crack problems in elastic isotropic materials, it is shown that for the impermeable crack, the intensity factors for piezoelectric materials can be obtained from those for elastic isotropic materials. Based on the exact analytical solution of the singular stresses and electrical displacements near the crack front, the numerical method of the hypersingular integral equation is proposed by the finite-part integral method and boundary element method, which the square root models of the displacement and electric potential discontinuities in elements near the crack front are applied. Finally, the numerical solutions of the stress and electric field intensity factors of some examples are given.     

Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack

Based on the complex potential approach, the two-dimensional problems in a piezoelectric material containing an elliptic hole subjected to uniform remote loads are studied. The explicit, closed-form solutions satisfying the exact electric boundary condition on the hole surface are given both inside and outside the hole. When the elliptic hole degenerates into a crack, the field intensity factors are obtained. It is shown that the stress intensity factors are the same as that of isotropic material, while the electric displacement intensity factor depends on both the material properties and the mechanical loads, but not on the electric loads. In other words, the uniform electric loads have no influence on the field singularities. It is also shown that the impermeable crack assumption used previously to simply the electric condition is not valid to crack problems in piezoelectric materials.     

Almansi-type boundary conditions for electric potential inducing flexure in linear piezoelectric beams

Using the recent results found in [1, 2] we prove that it is possible to induce flexure in linear piezoelectric beams by means of quadratic Almansi type boundary conditions for the electric potential. Beams constituted by transversely isotropic piezoelectric materials whose symmetry axis is parallel to the axis of the beam are considered. Our choice of boundary conditions for the electric potential has been suggested by the results found in [1, 3]. An explicit expression of material parameters that influence flexure is given in terms of piezoelectric moduli. Received: October 21, 1996     

横观各向同性压电材料中裂纹问题的边界元法

采用Somigiliana公式给出了三维横观各向同性压电材料中的非渗漏裂纹问题的一般解和超奇异积分方程，其中未知函数为裂纹面上的位移间断和电势间断．在此基础上，使用有限部积分和边界元结合的方法，建立了超奇异积分方程的数值求解方法，并给出了一些典型数值算例的应力强度因子和电位移强度因子的数值结果，结果令人满意．     

THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

I. INTRODUCTIONBecause of the widespread application and intrinsic brittleness of piezoelectric ceramics, significantattention is being paid to the crack problems of piezoelectric ceramics. The last decade has seen a lotof three-dimensional studies of crack in piezoelectric ceramics[1??9]. In addition, the electroelastic fieldin a transversely isotropic piezoelectric space with a half-plane crack subjected to symmetric normalpoint forces, antisymmetric tangential point forces and point ch…