直角平面区域内固定圆形刚性夹杂问题的Green函数解

利用复变函数法、多极坐标移动技术研究了直角平面区域内含有固定圆形夹杂时的反平面问题Green函数解.首先构造出不含夹杂的完整直角平面区域内满足边界应力条件的入射位移场;其次,建立直角平面区域内固定圆形夹杂对该入射场产生的满足直角边界应力自由条件的散射波解,并由叠加原理得到介质内的总波场.最后利用夹杂边界处的位移条件确定出散射波解中的未知系数,最终得到问题的Green函数解,还通过算例讨论了夹杂边界处的径向应力和环向应力随不同波数、角度和不同夹杂位置及不同点源位置的变化情况.算例结果表明了该文方法的有效实用性.     

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。     

横观各向同性介质中椭圆夹杂受非弹性剪切变形引起的弹性场的确定

本文求解了横观各向同性介质中椭圆夹杂内受非弹性剪切变形引起的弹性场。采用各向异性弹性力学平面问题的复变函数解法,结合保角变换,获得夹杂内应变能和基体内边界的应力分布和相应的应变能的表达式。进一步,根据最小应变能原理,获得表征夹杂平衡边界的两个特征剪切应变,从而得到了弹性场的解析解。通过应力转换关系,验证了应力解满足夹杂边界上法向正应力和剪应力的连续条件,表明了该解的正确性。本文解可用于复合材料断裂强度的分析中。     

含界面刚性线夹杂与广义压电位错双压电介质的电弹性分析

研究了双压电材料中广义压电位错与分布于界面的刚性共线线夹杂相互作用问题.基于线性压电理论Stroh框架,相应的混合边值问题,可化为常见的Hilbert问题.求解Hilben问题,得到存在界面刚性线夹杂与位错时,压电体内所有场变量的显式表达.给出了由于界面和刚性线夹杂的存在,作用于广义压电位错上的广义Peach-Koehler镜像力.对均匀压电材料这一特殊情况,给出了数值算例,讨论了位错对刚性线夹杂端部场强度因子的干涉和它们之间的相互作用.结果可作为求解界面刚性线夹杂与微裂纹交互作用问题的Green函数,也可作为边界元方法的核函数.     

求弹性半平面问题基本解的一个新方法

本文所提到的弹性半平面问题的基本解是一个满足特殊条件的弹性半平面的应力位移解答。这些条件为:(1)半平面内一点处作用有集中力X,Y或集中力偶M;(2)半平面边界为自由或固定边。利用平面弹性的复变函数方法,文中把弹性半平面基本解的问题归结为下列问题,使一个特定解析函数和另一个解析函数的共轭值在半平面边界上相等。对上述转化后的问题,只要利用复变函数的性质,不难从基本解的第一部分推导出基本解的第二部分。其中,基本解的第一部分是弹性全平面的本基解。从而,半平面问题基本解可以方便地得到。此外,文中还首次给出了:(1)集中力偶作用于半平面内一点时的基本解;(2)当半平面边界固定情况下的基本解。     

完备型二次边界轮廓法的研究及求解断裂力学J_α、L、M积分

对线弹性平面问题的边界轮廓法,选用完备的二次位移形函数,使求解问题的维数降低两维,给出了求解边界位移和面力以及内点应力的求解方法。证明平面弹性断裂力学J_a积分、M积分、L积分方程的被积函数的散度均等于零,将它们分别转化为边界点的位移和面力的线性迭加,无需计算数值积分。算例表明,本文方法具有较高的精度。     

完备型二次边界轮廓法的研究及求解断裂力学Ja,L,M积分

对线弹性平面问题的边界轮廓法，选用完备的二次位移形函数，使求问题的维数降低两维，给出了求解边界位移和面力以及内点应力的求解方法。证明平面弹怀断鲜明力学Ｊａ积分、Ｍ积分、Ｌ积分方程的被积函数的散度均等于零，将它们分别转化为边界点的位移和面力的线性迭加，无需计算数值积分，算例表明，本文方法具有较高的精度。     

二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射

利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切（shearing horizontal, SH）波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂边界产生的能够自动满足直角边应力自由条件的散射波解,从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况,结果表明了算法的有效实用性。     

平面热弹性问题的边界元分析

本文利用位移法由平面热弹性问题的基本方程出发,简要地叙述了边界积分方程的建立及离散化手法,导出了由边界上的位移和表面力直接计算边界应力的公式。作为数值计算例,计算了圆形区域,同心圆区域和具有偏心圆孔的圆形区域的热应力。计算结果与解析解或实验结果进行了比较,两者相当吻合。计算表明,边界元法对求解平面热弹性问题十分有效.本文也适用于有体积力的平面弹性问题.     

非局部弹性体中的反平面线力问题

本文把经典弹性体中的线力问题推广到非局部弹性体中,得到非局部介质中反平面线力和它的应力场的解析表达式,应力场无经典的奇异性,非局部线力是高斯型分布不再是经典的δ函数,给出非局部线力满足的推广的线力定义。     

INTERACTION OF ELECTRIC CHARGES IN A PIEZOELECTRIC WITH RIGID EXTERNAL CRACKS

IntroductionRecently much attention has been paid to Green’s functions[1 -7]for anisotropic mediabecause of their important applications in boundary element methods used widely inengineering analysis. Generally speaking, it is relatively easy to obtain G…     

Green's functions for a piezoelectric semi-infinite body with a fixed conductor surface

By using Stroh's formalism, simple explicit compact expressions of Green's functions for a piezoelectric semi-infinite body, with a fixed conductor surface electrode, subject to a singularity (i.e., a generalized line dislocation and a generalized line force at a point z°) are presented. Coulomb forces acted on the free line charge at z° due to the boundary polarization charges of the medium and the induction charges of the conductor together with the electromechanical coupling effects inside the region are analyzed in detail. The obtained results are valid not only for plane and antiplane problems but also for the coupled problems between inplane and outplane deformations.     

GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY "HARMONIC FUNCTIONS

I.IntroductionBecauseofthecouplingcharacteristicbetweenthemechanicaldeformationandthee1ectricaleffect,piezoelectricmaterialshavebeenwidelyusedintransducersandsmartstructures.Moreandmoreattentionshavebeenpaidonsuchmaterials,andgreatadvanceshavebeenmadeinva…     

A piezoelectric screw dislocation interacting with a half-plane trimaterial composite

The electro-elastic stress investigation on the interaction between a screw dislocation and a half-plane trimaterial composite composed of three bonded dissimilar transversely isotropic piezoelectric materials is analyzed in the framework of linear piezoelectricity. Each layer is assumed to have the same material orientation with x ₃ in the poling direction. The dislocations are characterized by a discontinuous displacement and electric potential across the slip plane and are subjected to a line force and a line charge at the core. Based on the complex variable and the method of alternating technique, the solution of electric field and displacement field is expressed in terms of explicit series form. The solutions derived here can be applied to a variety of problems, for example, a half-plane bimaterial, a quarter-plane bimaterial, a quarter-plane material and a rectangular strip etc. Numerical results are provided to show the influences of the material combinations and geometric configurations on the electro-elastic fields and image force calculated through the generalized Peach-Koehler formula. The solutions proposed here can be served as Green??s functions for the analyses corresponding piezoelectric cracking problems.     

GREEN＇S FUNCTIONS OF INTERNAL ELECTRODES BETWEEN TWO DISSIMILAR PIEZOELECTRIC MEDIA

The generalized 2-D problem of a half-infinite interfacial electrode layer between two arbitrary piezoelectric half-spaces is studied. Based on the Stroh formalism,exact expressions for the Green‘ s functions of a line force, a line charge and a line electric dipole applied at an arbitrary point near the electrode edge, were presented, respectively.The corresponding solutions for the intensity factors of fields were also obtained in an explicit form. These results can be used as the foundational solutions in boundary element method (BEM) to solve more complicated fracture problems of piezoelectric composites.     

GREEN'S FUNCTIONS OF INTERNAL ELECTRODES BETWEEN TWO DISSIMILAR PIEZOELECTRIC MEDIA

IntroductionPiezoelectricceramicshavefoundwideapplicationinactuators,sensorsandothercomponents.Inthesedevices,themostcost_efficientgeometryisthatofthecofiredmultilayeractuatorswithmetalelectrodes[1].Toimprovethebondstrengthbetweenpiezoelectricmatrices,theelectrodesareoftenplacedwithoneedgeterminatedinsidepiezoelectricmaterialsandanotheredgeconnectedtoanexternalelectrodestrip .Attheinternalelectrodeedge,theelectricfieldconcentrates.Thenon_uniformlocalfieldinducesinturncrackinitiation ,crackgro…     

GREEN''''S FUNCTIONS FOR 2D PROBLEMS OF ANISOTROPIC PIEZOELECTRIC MATERIAL WITH A STRIP REGION

By using Stroh's formalism and the conformal mapping technique, we derive the simple explicit elastic fields of a generalized line dislocation and a generalized line force in a general anisotropic piezoelectric strip with fixed surfaces, which are two fixed conductor electrodes. The solutions obtained are usually considered as Green's functions which play important roles in the boundary element methods. The Coulomb forces of the distributed charges along the region boundaries on the line chargeq atz ⁰ are analysed in detail. The results are valid not only for plane and antiplane problems but also for the coupled problems between inplane and outplane deformations.     

Stress and electric displacement analyses in piezoelectric media with an elliptic hole and a small crack

In this paper, the interactions between an elliptic hole and an arbitrary distributed small crack in plane piezoelectric medium, which are often happened in engineering problems, are discussed. The Green’s functions in a piezoelectric plate with an elliptic hole for a generalized line dislocation and a generalized line force are presented. The small crack is represented by unknown continuous distributed dislocations. By considering traction free conditions on the surface of the small crack, the problem is then reduced to a group of singular integral equations which are solved by using a special numerical technique. Accuracy of the present method is confirmed by comparing the numerical results with those in literatures for PZT-4 when the elliptic hole is degenerated into a crack. The generalized stress intensity factors of cracks and the generalized stress on the edge of the elliptic hole are shown graphically. It is shown that the small crack may have shielding or amplifying effects on the main elliptic hole or crack, which depends on the location and orientation of the small crack. The hole near a crack can significantly reduce the stress intensity factor of the crack. The direction of the electric field is important to shielding effect.     

Two-dimensional electroelastic fundamental solutions for general anisotropic piezoelectric media

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