Two-Dimensional Magnetoelastic Problem for a Multiply Connected Piezomagnetic Body

A general method based on complex variable theory is proposed to determine the magnetic and elastic fields of a piezomagnetic body. This method is used to derive the basic relations for complex potentials in the two-dimensional problem of magnetoelasticity, their general representations for a multiply connected domain, expressions for stresses, displacements, vectors of magnetic field intensity and magnetic flux density, and magnetic field potential. A closed-form solution is obtained for a body with an elliptic (circular) hole or crack subjected at infinity to the action of a constant magnetoelastic field. Numerical results for a piezomagnetic plate with a circular hole are presented __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 64–74, October 2005.     

Interacting circular inclusions in antiplanepiezoelectricity

The problem of multiple piezoelectric circular inclusions, which are perfectly bondedto a piezoelectric matrix, is analyzed in the framework of linear piezoelectricity. Both the matrixand the inclusions are assumed to possess the symmetry of a hexagonal crystal in the 6 mm classand subject to electromechanical loadings (singularities) which produce in-plane electric fieldsand out-of-plane displacement. Based upon the complex variable theory and the method ofsuccessive approximations, the solution of electric field and displacement field either in theinclusions or in the matrix is expressed in terms of explicit series form. Stress and electric fieldconcentrations are studied in detail which are dependent on the mismatch in the materialconstants, the distance between two circular inclusions, and the magnitude of electromechanicalloadings. It is shown that, when the two inclusions approach each other, the oscillatory behaviorof the stress and electric field can be induced in the inclusion as the matrix and the inclusions arepoled in the opposite directions. This important phenomenon can be utilized to build a verysensitive sensor in a piezoelectric composite material system. The present derived solution canalso be applied to the inclusion problem with straight boundaries. The problem associated withthree-material media under electromechanical sources is also considered.     

Elastic interaction of partially debonded circular inclusions. I. Theoretical solution

A complete solution has been obtained of the elasticity problem for a plane containing a finite array of partially debonded circular inclusions, regarded as the open-crack model of fibrous composite with interface damage. A general displacement solution of the single-inclusion problem has been derived by combining the complex potentials technique with the newly derived series expansions. This solution is valid for any non-uniform far load and is finite and exact in the case of polynomial far field. Applying the superposition principle expands this theory to the multiple inclusion problem and provides a simple and rapidly convergent iterative algorithm. The presented numerical data show an accuracy and numerical efficiency of the proposed method and discover the way and extent to which the elastic interaction between the partially debonded inclusions affects the local fields, stress intensity factors and the energy release rate at the interface crack tips.     

电磁弹性复合材料双圆柱夹杂问题

研究了双圆柱压电夹杂嵌于无限大压磁基体中的力学问题，获得了基体受到无究远处电，磁，力载荷作用下的解析解。利用复变函数呆角变换和解析延拓，以及圆环域内的洛朗级数展开和Cauchy积分公式等得到了基体和两个夹杂中的复位势。由所获得的复位势继而得到了应力，电位移和磁通密度等物理量的解析表达式。并给出了算例分析，以此来表明夹杂对系统电磁弹性耦合行为的影响，以及验证所得解的正确性和实用性。     

平面弹性中双圆柱夹杂问题的格林函数

通过复势法并结合共形映射、解析开拓、奇点分析、Cauchy积分公式、圆环域上的Laurent级数展开等技术的联合运用,给出了含有双圆柱异相夹杂的无限大弹性基体这种三相复合系统在受到面内集中力和刃型位错作用时的级数形式的精确解答。该奇点可以作用于基体上或两夹杂内部,当一刃型位错作用于基体上时,也推导了该位错与双圆柱夹杂的交互作用能以及作用于位错上的广义。所给出的算例验证了该弹性解答的正确性并直观显示出奇点与双圆柱夹杂的相互作用。     

Magnetoelastic problem for a bodywith periodic elastic inclusions

A general approach based on complex variable theory is proposed to determine the magnetoelastic state of a body with an infinite row of elliptic inclusions under the action of magnetic and elastic fields. Numerical solutions to a two-dimensional problem for a body made of Terfenol-D magnetostrictive material and piezomagnetic ceramic material and having circular, elliptic, and rectilinear inclusions made of a different material are presented depending on the geometry of the inclusions, their material characteristics, the spacing between them, and the type of applied load __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 32–40, September 2006.     

Diffraction of elastic waves in the plane multiply-connected region and dynamic stress concentration

This paper deals with the problem of diffraction of elastic waves in the plane multiply-connected regions by the theory of complex functions. The complete function series which approach the solution of the problem and general expressions for boundary conditions are given.’ Then the problem is reduced to the solution to infinite series of algebraic equations and the solution can be directly obtained by using electronic computer. In particular, for the case of weak interaction, an asymptotic method is presented here, by which the problem ofp waves diffracted by a circular cavities is discussed in detail. Based on the solution of the diffracted wave field the general formulas for calculating dynamic stress concentration factor for a cavity of arbitrary shape in multiply-connected region are given.     

Interacting elliptic inclusions by the method of complex potentials

An accurate series solution has been obtained for a piece-homogeneous elastic plane containing a finite array of non-overlapping elliptic inclusions of arbitrary size, aspect ratio, location and elastic properties. The method combines standard Muskhelishvili’s representation of general solution in terms of complex potentials with the superposition principle and newly derived re-expansion formulae to obtain a complete solution of the many-inclusion problem. By exact satisfaction of all the interface conditions, a primary boundary-value problem stated on a complicated heterogeneous domain has been reduced to an ordinary well-posed set of linear algebraic equations. A properly chosen form of potentials provides a remarkably simple form of solution and thus an efficient computational algorithm. The theory developed is rather general and can be applied to solve a variety of composite mechanics problems. The advanced models of composite involving up to several hundred inclusions and providing an accurate account for the microstructure statistics and fiber–fiber interactions can be considered in this way. The numerical examples are given showing high accuracy and numerical efficiency of the method developed and disclosing the way and extent to which the selected structural parameters influence the stress concentration at the matrix–inclusion interface.     

Two circular inclusions with inhomogeneously imperfect interfaces in plane elasticity

This paper is concerned with the problem of two circular inclusions with circumferentially inhomogeneously imperfect interfaces embedded in an infinite matrix in plane elastostatics. Infinite series form solutions to this problem are derived by applying complex variable techniques. The numerical results demonstrate that the interface imperfection, interface inhomogeneity, and interaction among neighboring inclusions (fibers) will exert a significant influence on the stresses along the interfaces and average stresses within the inclusions.     

On a bounded elliptic elastic inclusion in plane magnetoelasticity

The problem of an elliptic inclusion embedded in an infinite matrix subjected to a uniform magnetic induction is considered in this paper. Basing upon the two-dimensional magnetoelastic formulation, the technique of conformal mapping, and the method of analytical continuation, a general solution of magnetic field quantities and the magnetoelastic stresses are obtained for both the matrix and the inclusion. Comparison is made with several special cases of which the analytical solutions can be found in the literature, which shows that the solutions presented here are general and exact. Moreover, the magnetoelastic stresses at the interface between the inclusion and the matrix are presented with figures.     

螺型位错偶极子与圆形界面刚性线的干涉效应研究

本文重点研究螺型住错偶极子和圆形夹杂界面刚性线的弹性干涉效应。利用复变函数方法,得到了该问题的一般解;此外还求出了只含一条界面刚性线时的封闭解答,得到了刚性线尖端的应力强度因子以及作用在螺型位错偶板子中心的像力和像力偶矩。研究结果表明：位错偶板子对应力强度因子具有很强的屏蔽或反屏蔽效应;软夹杂吸引位错偶极子,而刚性线排斥位错偶板子,在一定条件下,位错偶极子在刚性线附近出现一个平衡位置;当刚性线的长度争材料剪切模量比达到临界值时,可以改变偶极子和界面之间的干涉机理;刚性线长度对位错偶极子中心像力偶矩也有很大的影响。     

Antiplane problem of circular ARC interfacial rigid line inclusions

The antiplane problem of circular arc rigid line inclusions under antiplane concentrated force and longitudinal shear loading was dealt with. By using RiemannSchwaz‘s symmetry principle integrated with the singularity analysis of complex functions, the general solution of the problem and the closed form solutions for some important practical problems were presented. The stress distribution in the immediate vicinity of circular arc rigid line end was examined in detail. The results show that the singular stress fields near the rigid inclusion tip possess a square-root singularity similar to that for the corresponding crack problem under antiplane shear loading, but no oscillatory character. Furthermore, the stresses are found to depend on geometrical dimension, loading conditions and materials parameters. Some practical results concluded are in agreement with the previous solutions.     

PLANE ELASTIC PROBLEM ON RIGID LINES ALONG CIRCULAR INCLUSION

The plane elastic problem of circular-arc rigid line inclusions is considered. The model is subjected to remote general loads and concentrated force which is applied at an arbitrary point inside either the matrix or the circular inclusion. Based on complex variable method, the general solutions of the problem were derived. The closed form expressions of the sectionally holomorphic complex potentials and the stress fields were derived for the case of the interface with a single rigid line. The exact expressions of the singular stress fields at the rigid line tips were calculated which show that they possess a pronounced oscillatory character similar to that for the corresponding crack problem under plane loads. The influence of the rigid line geometry, loading conditions and material mismatch on the stress singularity coefficients is evaluated and discussed for the case of remote uniform load.     

The growth of the thermal boundary layer at the inlet to a circular tube

Summary The problem considered is that of the heat transfer occurring at the inlet to a circular tube. Using the method of a previous paper we solve the energy equation in the form of a power series, instead of transforming the equation into an eigenvalue problem by separation of variables, as is usual in such cases. We thus obtain information concerning the temperature distribution at the inlet to the tube which is not provided by the latter method. A sufficient number of coefficients of the power series has been computed to allow the present solution to be joined to one of the second type, thus completing the solution of the problem for all values of the longitudinal variable.     

刃型位错和圆弧形刚性线夹杂的干涉效应

位错和夹杂的干涉效应对于理解材料的强化和韧化机理具有十分重要的意义。文中研究了晶体材料中刃型位错和多条共圆弧刚性线夹杂的干涉作用。利用Riemann—Schwarz反照原理和复势函数的奇性主部分析技术，得到了问题的一般解答；对于只含一条刚性线夹杂的情况，给出了复势函数的封闭形式解。由Peach-Koehler公式求出了作用在刃型位错上的位错力，并讨论了圆弧形刚性线夹杂对位错力的影响规律，发现弧形刚性线对刃型位错有很强的排斥作用。本文解答不但可作为格林函数获得任意分布位错的相应解答，而且可以用于研究刚性线夹杂和任意形状裂纹的干涉效应问题。     

An embedding method for modeling micromechanical behavior and macroscopic properties of composite materials

This paper presents a numerical method for modeling the micromechanical behavior and macroscopic properties of fiber-reinforced composites and perforated materials. The material is modeled by a finite rectangular domain containing multiple circular holes and elastic inclusions. The rectangular domain is assumed to be embedded within a larger circular domain with fictitious boundary loading represented by truncated Fourier series. The analytical solution for the complementary problem of a circular domain containing holes and inclusions is obtained by using a combination of the series expansion technique with a direct boundary integral method. The boundary conditions on the physical external boundary are satisfied by adopting an overspecification technique based on a least squares approximation. All of the integrals arising in the method can be evaluated analytically. As a result, the elastic fields and effective properties can be expressed explicitly in terms of the coefficients in the series expansions. Several numerical experiments are conducted to verify the accuracy and efficiency of the numerical method and to demonstrate its application in determination of the macroscopic properties of composite materials.     

On the stress concentration in thick cylindrical shells with an arbitrary cutout

1.IntroductionThefocusofmuch'researcllforalongtimehasbeenontheinvestigationofstressconcentrationsofthincylindricalshellsll--41.Thestressproblemisdiscussedinreferences[5,6].Whentheratioofthicknesshofshellstothecutoutsizeroisnotrathersmall,thegoverningequationofReissuer'sshallowshellincludingtheeffectoftransversesheardeformationsmustbeusedl7-sl.Thethickshelltheorymakesupweaknessesoftheclassicaltheoryofthinshells.Thetheoryofthickshellscanbeusedforanalyzingstressconcentrationsofcircularcylindrica…     

软铁磁材料平面裂纹问题的耦合场

由磁弹性问题的线性化理论导出磁场下平面软铁磁体问题的控制方程和复势解。利用复势解和奇异积分方程方法,对面内磁场和远场载荷作用下的含裂纹无限大软铁磁平面问题进行了求解,得到耦合场的解。并对不同磁力模型的结果和磁场与机械载荷共同作用下的裂尖应力强度因子进行了讨论。     

Solution of the disk compression problem in the three-dimensional setting

We use three complex potentials to solve the compression problem for a thin circular plate loaded along the external contour. We present the solution in series form and compare the obtained solution with the classical solution.     

Thermal stresses in an isotropic trimaterial interacted with a pair of point heat source and heat sink

A general analytical solution for an isotropic trimaterial interacted with a point heat source is provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to heat conduction and thermoelasticity problems for three dissimilar media are first derived. A rapidly convergent series solution for both the temperature and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. As a numerical illustration, the distributions of thermal stresses along the interface are presented for various material combinations and for different positions of the applied heat source and heat sink.