含椭圆形刚性夹杂的压电材料平面问题

应用复变函数的Ｆａｂｅｒ级数展开方法，本文研究了含椭圆形刚性夹杂的压电材料平面问题，给出了问题的封闭解。解签表明，夹杂内的电场强度和电位移为常量。并通过算例分析，讨论了正，逆压电效应在基体孔周处的机电行为。     

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.     

General coupled solution of anisotropic piezoelectric materials with an elliptic inclusion

In this investigation, the Stroh formalism is used to develop a general solution for an infinite, anisotropic piezoelectric medium with an elliptic inclusion. The coupled elastic and electric fields both inside the inclusion and on the interface of the inclusion and matrix are given. The project supported by the National Natural Science Foundation of China     

The fundamental solutions for the plane problem in piezoelectric media with an elliptic hole or a crack

1.IntroductionItiswell-knownthatthefundame,ltalsolutionsorGreen'sfunctionsplayanimportantroleilllinearelasticity.Forexample,theycanbeusedtoconstructmanyanalyticalsolutionsofpracticalproblems.Itismoreimportantthattheyareusedasthefundamentalsolutionsintheboundaryelementmethod(BEM)tosolvesomecomplicatedproblem.Withthewidely-increasingapplicationofpiezoelectricmaterialsinengineeringproblems,thestudyregardingtheGreen'sfLlnctionsinpiezoelectricsolidshasreceivedmuchinterest.The3DGreen'sfunctionsi…     

On the electroelastic interaction of a piezoelectric screw dislocation with an elliptical inclusion in piezoelectric materials

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｉｎｔｅｒａｃｔｉｏｎｏｆｄｉｓｌｏｃａｔｉｏｎｓｗｉｔｈｉｎｃｌｕｓｉｏｎｓｉｓｏｆｃｏｎｓｉｄｅｒａｂｌｅｉｍｐｏｒｔａｎｃｅｆｏｒｕｎｄｅｒｓｔａｎｄｉｎｇｔｈｅｐｈｙｓｉｃａｌｂｅｈａｖｉｏｒｏｆｍａｔｅｒｉａｌｓ.Ｓｕｃｈｓｔｕｄｉｅｓｃａｎｐｒｏｖｉｄｅｄｉｎｆｏｒｍａｔｉｏｎｃｏｎｃｅｒｎｉｎｇｃｅｒｔａｉｎｓｔｒｅｎｇｔｈｅｎｉｎｇｏｒｈａｒｄｅｎｉｎｇｍｅｃｈａｎｉｓｍｓｉｎｎｕｍｂｅｒｏｆｔｒａｄｉｔｉｏｎａｌａｎｄｃｏｍｐｏｓｉｔｅｍａｔｅｒｉ…     

Generalized 2D problem of piezoelectric media containing collinear cracks

The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases: one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads. The project supported by the National Natural Science Foundation of China (19772004)     

An exact solution of crack problems in piezoelectric materials

IntroductionInrecentyearscrackproblemsinpiezoelectricmaterialhavereceivedmuchattention.Manytheoreticalanalyseshavebeengivenby[1～16].Itshouldbe,however,notedthatalltheaboveanalysesarebasedonaso-calledimpermeablecrackassumphon,i.e.thecrackfacesareassumedtobeimpermeabletoelectricfield,sotheelectricdisplacementvanishesinsidethecrack.Usingthisassumption,onewillobtainthefollowingresultS[2'3'5,6'9'16]=whentheelectricloadsaresolelyaPPliedatinLfinity,theelectricdisplacementissquare-rootsingularatthe…     

POLYNOMIAL SOLUTIONS TO PIEZOELECTRIC BEAMS (Ⅱ)——ANALYTICAL SOLUTIONS TO TYPICAL PROBLEMS

IntroductionThis paper is a continuation of Ref.[1],in which a series of orthotropic piezoelectricplane problems was solved and the corresponding exact solutions were obtained with the trial-and-error method,on the basis of the general solution expressed …     

压电材料轴对称有限元分析

给出了横观各向同性压电材料轴对称问题有限元法列式,叙述了压电材料有限元法分析中的一些特殊处理步骤,包括无量纲化和特征值问题计算中对电势自由度的凝聚。对压电材料轴对称问题的一些经典静力问题进行有限元计算,同时对压电圆板的轴对称自由振动进行了计算,和解析结果作了比较,二者符合良好。     

压电材料反平面应变状态的任意形状夹杂问题

应用复函数的Ｆａｂｅｒ级数展开方法，分析了含任意形状夹杂的压电材料反平面应变问题，给出了问题的复势函数解。利用这个解，具体讨论了椭圆形夹杂及其极限（几何方面与物理方面）问题。并给出了三角形、正方形夹杂的近似结果。其特例结果与早期工作一致     

Inclusion of an arbitrary polygon with graded eigenstrain in an anisotropic piezoelectric half plane

This paper presents an exact closed-form solution for the Eshelby problem of a polygonal inclusion with graded eigenstrains in an anisotropic piezoelectric half plane with traction-free on its surface. Using the line-source Green’s function, the line integral is carried out analytically for the linear eigenstrain case, with the final expression involving only elementary functions. The solutions are applied to the semiconductor quantum wire (QWR) of square, triangular, and rectangular shapes, with results clearly illustrating various influencing factors on the induced fields. The exact closed-form solution should be useful to the analysis of nanoscale QWR structures where large strain and electric fields could be induced by the non-uniform misfit strain.     

Two-dimensional electroelastic fundamental solutions for general anisotropic piezoelectric media

I.IntroductionDuetotheirintrinsiccouplingeffectbetweenmechanicalandelectricalfields,piezoelectricmaterialshavebeenwidelyusedintechnologyastransducersandsensorsand,morerecently,asactuatorsinsmartstructures.lnordertooptimizetheirmicrostructuresandunderstand…     

On determining stresses in rigid inclusions. Plane problems

Plane problems of determining the stress-strain state of an isotropic elastic domain with a rigid inclusion are considered. It is shown that the stress field in the inclusion is uniquely determined. This field is uniform for a plane with an elliptic inclusion, and the stresses at infinity and in the inclusion are related by mutually single-valued formulas. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 183–186, July–August, 2009.     

压电介质平面问题的基本解

应用复变函数的方法,对于压电介质平面问题,分析导出了无限介质或半无限介质受任意 集中载荷作用时的复势函数基本解;这些结果可作为边界元法的基本解,以求解具有复杂边界压电体的平面问题。     

POLYNOMIAL SOLUTIONS TO PIEZOELECTRIC BEAMS (Ⅰ)——SEVERAL EXACT SOLUTIONS

IntroductionDue to its excellent piezoelectric properties,composites made of piezoelectric materialsare found widespread applications and attracted more attentions[1-10].Because of materialanisotropy and couplingbetween mechanical deformation and electric…     

Analyzing the viscoelastic state of a plate with elliptic or linear elastic inclusions

A method is proposed for studying the stress state of a viscoelastic multiply connected isotropic plate with aligned elastic inclusions. The viscoelastic state of a plate with a finite or infinite number of circular and linear inclusions is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 88–98, February 2007. For the centenary of the birth of G. N. Savin.     

GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY “HARMONIC FUNCTIONS”

First, based on the basic equations of two-dimensional piezoelectroelasticity, a displacement function is introduced and the general solution is then derived. Utilizing the generalized Almansi's theorem, the general solution is so simplified that all physical quantities can be expressed by three harmonic functions. Second, solutions of problems of a wedge loaded by point forces and point charge at the apex are also obtained in the paper. These solutions can be degenerated to those of problems of point forces and point charge acting on the line boundary of a piezoelectric half-plane.Project supported by the National Natural Science Foundation of China     

含共线刚性线夹杂各向异性体的平面问题

应用复变函数方法,给出了含共线刚性线夹杂各向异性体平面问题的一般解;对于一个或二个夹杂的情形,给出了封闭形式的应力奇异性系数解;结果表明,应力奇异性系数与材料常数和ε∞ｘ 有关,这里ε∞ｘ 为无限远处ｘ 方向的线应变     

A conductive rigid spheroidal inclusion in a transversely isotropic piezoelectric body subjected to an axial pull

The exact axisymmetric solution is derived for an infinite transversely isotropic piezoelectric body containing an electrically conductive, rigid spheroidal inclusion under an axial pull. A simple general solution is employed in which three quasi-harmonic functions are involved and can be assumed in a closed form. The arbitrary constants are determined from the continuity conditions at the surface of the inclusion. The load-deflection and load-potential relations are derived, especially for two degenerated cases that are very important in the strength analysis of composite piezoelectric materials.