共查询到20条相似文献,搜索用时 482 毫秒
1.
Based on initial nonlinear constitutive equations, we establish the extended displacement and traction boundary integral equations for a piezoelectric medium with a volume electric charge, along with electron and electric current density boundary integral equations for a conductor with a volume electric current. Then, an iterative approach is proposed for investigation of boundary value problems in two-dimensional piezoelectric semiconductors (PSCs). Compared with extended displacements obtained by finite element analysis, this approach is validated via a rectangular PSC under extended external loads. Furthermore, as a numerical example, extended displacements across an elliptical hole in a rectangular PSC are investigated. It is shown that there is a stress concentration near the elliptical hole, which is closely dependent on its shape. 相似文献
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Ming Tao Hao Luo Chengqing Wu Wenzhuo Cao Rui Zhao 《Mathematical Methods in the Applied Sciences》2023,46(2):2773-2800
The complex boundary of the elliptical inclusion rendered it difficult to solve the problem of wave scattering. In this study, the steady-state response was analyzed using the wave function expansion method. Subsequently, the Ricker wavelet was employed as the transient disturbance, and Fourier transform was used to determine the distribution of transient dynamic stress concentration around the elliptical inclusion. The effects of wave number, elliptical axial ratio, and difference in material properties on the distribution of the dynamic stress concentration around the elliptical inclusion were evaluated. The numerical results revealed that the dynamic stress concentration always appeared at both ends of the major axis and minor axis of the elliptical inclusion, and the difference in material properties between the inclusion and medium influenced the variations in the dynamic stress concentration factor with the wave number and elliptical axial ratio. 相似文献
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Guanxixi Jiang Zailin Yang Cheng Sun Baitao Sun Yong Yang 《Mathematical Methods in the Applied Sciences》2020,43(11):6888-6902
Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well. 相似文献
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We investigate the internal thermal stress field of a three-phase inclusion of arbitrary shape which is bonded to an infinite matrix through an interphase layer. The three phases have different thermoelastic constants. It is found that the internal thermal stress field induced by a uniform change in temperature can be uniform and hydrostatic within an inclusion of elliptical or hypotrochoidal shape when the thickness of the interphase layer is properly designed for given material parameters of the three-phase composite. Several examples are presented to demonstrate the solution. The thermal stress analysis of a (Q + 2)-phase inclusion of arbitrary shape with Q ≥ 2 is also carried out under the assumption that all the phases except the internal inclusion share the same elastic constants. It is found that the irregular inclusion shape permitting internal uniform hydrostatic thermal stresses becomes really arbitrary if a sufficiently large number of interphase layers are added between the inclusion and the matrix. 相似文献
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X. Wang L. J. Sudak C. Q. Ru 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(3):488-509
A general method is presented for the rigorous solution of Eshelby’s problem concerned with an arbitrary shaped inclusion
embedded within one of two dissimilar elastic half-planes in plane elasticity. The bonding between the half-planes is considered
to be imperfect with the assumption that the interface imperfections are uniform.
Using analytic continuation, the basic boundary value problem is reduced to a set of two coupled nonhomogeneous first-order
differential equations for two analytic functions defined in the lower half-plane which is free of the thermal inclusion.
Using diagonalization, the two coupled differential equations are decoupled into two independent nonhomogeneous first-order
differential equations for two newly defined analytic functions. The resulting closed-form solutions are given in terms of
the constant imperfect interface parameters and the auxiliary function constructed from the conformal mapping which maps the
exterior of the inclusion onto the exterior of the unit circle.
The method is illustrated using several examples of an imperfect interface. In particular, when the same degree of imperfection
is realized in both the normal and tangential directions between the two half-planes, a thermal inclusion of arbitrary shape
in the upper half-plane does not cause any mean stress to develop in the lower half-plane. Alternatively, when the imperfect
interface parameters are not equal, then a nonzero mean stress will be induced in the lower half-plane by the thermal inclusion
of arbitrary shape in the upper half-plane. Detailed results are presented for the mean stress and the interfacial normal
and shear stresses caused by a circular and elliptical thermal inclusion, respectively. Results from these calculations reveal
that the imperfect bonding condition has a significant effect on the internal stress field induced within the inclusion as
well as on the interfacial normal and shear stresses existing between the two half-planes especially when the inclusion is
near the imperfect interface. 相似文献
7.
含椭圆形夹杂的压电材料平面问题 总被引:3,自引:0,他引:3
应用复变函数的Faber级数展开方法,本文研究了含椭圆形夹杂的压电材料平面问题,给出了问题的封闭解·解答表明,椭圆夹杂内的应力、应变、电场强度和电位移均为常量·通过算例,还讨论了正、逆压电效应在基体孔周处的机电行为· 相似文献
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采用Green函数法、复变函数法研究了SH波对界面附近含有半圆形脱胶的圆柱形弹性夹杂的散射,并给出了动应力集中系数的数值结果.首先,界面将整个空间分成上下两部分.在下半空间,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数.其次,取该位移函数作为Green函数.上下空间连接时在界面处满足连续性条件,构造出半圆形脱胶裂纹,进而求出应力和位移的表达式.最后作为算例,给出了动应力集中系数的数值结果,分析了介质参数和入射波参数对动应力集中的影响情况. 相似文献
10.
The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses. 相似文献
11.
Isaac Harris 《Mathematical Methods in the Applied Sciences》2019,42(18):6741-6756
In this paper, we derive a sampling method to solve the inverse shape problem of recovering an inclusion with a generalized impedance condition from electrostatic Cauchy data. The generalized impedance condition is a second order differential operator applied to the boundary of the inclusion. We assume that the Dirichlet‐to‐Neumann mapping is given from measuring the current on the outer boundary from an imposed voltage. A simple numerical example is given to show the effectiveness of the proposed inversion method for recovering the inclusion. We also consider the inverse impedance problem of determining the impedance parameters for a known material from the Dirichlet‐to‐Neumann mapping assuming the inclusion has been reconstructed where uniqueness for the reconstruction of the coefficients is proven. 相似文献
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《Applied Mathematical Modelling》2014,38(5-6):1710-1728
In this paper, a lattice Boltzmann model for the Maxwell’s equations is proposed by taking separate sets of distribution functions for the electric and magnetic fields, and a lattice Boltzmann model for the Maxwell vorticity equations with third order truncation error is proposed by using the higher-order moment method. At the same time, the expressions of the equilibrium distribution function and the stability conditions for this model are given. As numerical examples, some classical electromagnetic phenomena, such as the electric and magnetic fields around a line current source, the electric field and equipotential lines around an electrostatic dipole, the electric and magnetic fields around oscillating dipoles are given. These numerical results agree well with classical ones. 相似文献
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We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field on the geometry of the conductive rod. In particular, we accurately characterize the localization of the gradient field (i.e., the electric current) near the boundary of the rod where the curvature is sufficiently large. We develop layer‐potential techniques in deriving the quantitative estimates and the major difficulty comes from the anisotropic geometry of the rod. The result complements and sharpens several existing studies in the literature. It also generates an interesting application in EIT (electrical impedance tomography) in determining the conductive rod by a single measurement, which is also known as the Calderón's inverse inclusion problem in the literature. 相似文献
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《Journal of Applied Mathematics and Mechanics》1998,62(3):435-442
An elastic bounded anisotropic solid with an elastic inclusion is considered. An oscillating source acts on part of the boundary of the solid and excites oscillations in it. Zero displacements are specified on the other part of the solid and zero forces on the remaining part. A variation in the shape of the surface of the solid and of the inclusion of continuous curvature is introduced and the problem of the theory of elasticity with respect to this variation is linearized. An algorithm for constructing integral representations for such linearized problems is described. The limiting properties of the linearized operators are investigated and special boundary integral equations of the anisotropic theory of elasticity are formulated, which relate the variations of the boundary strain and stress fields with the variations in the shape of the boundary surface. Examples are given of applications of these equations in geometrical inverse problems in which it is required to establish the unknown part of the body boundary or the shape of an elastic inclusion on the basis of information on the wave field on the part of the body surface accessible for observation. 相似文献
15.
应用Stroh理论,研究了两压电介质之间的刚性介电线夹杂问题。首先该问题被化为Hilbert问题,然后分别给出了压电介质内的复势函数解、夹杂内的电场解和夹杂尖端场的解析表达式。结果表明,在夹杂尖端附近,所有的场变量均呈现奇异性和振荡性,且其强度取决于介质的材料常数和无限场远处的应变。此外,结果还表明,当从夹杂内部趋近夹杂尖端时,夹杂内的电场也呈现奇异性和振荡性。 相似文献
16.
Two dissimilar, homogeneous and istropic, elastic half-spacesare bonded together over thier infinite plane of contract. Anarbitrarily shaped finite part of one of them (an inclusion)tends spontaneously to undergo a unifrom infinitesimal strain,but, as it remains attached to and restrained by the surroundingmaterial, an equilibrated state of stress and strain is establishedeverywhere instead. By adopting a convenient expression forthe fundamental field of a point force, we transformed inclusion.For a general shape of the inclussion and for particular sphericaland finite cylindrical shapes in detail, we consider the evaluationof the elastic strain energy, especially of the interactionterm which depends on the location of the inclusion and bothpairs of elastic moduli, and which is of great significancein physical applications. 相似文献
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应力偶对孔洞附近应力集中的影响 总被引:1,自引:0,他引:1
将求解无限弹性平面中孔洞附近应力集中问题的复变函数方法,推广到微极弹性介质的应力集中问题上去,在复平面上给出了二维微极弹性理论应力集中问题的一般解,它可由解析函数与“域函数”构造出来,并利用保角映射的方法来满足非圆孔洞的边界条件。在此基础上建立了求解微极弹性理论中应力集中问题的一般求解方法。最后,对圆形孔洞附近的应力集中系数作了数值计算,并给出了具体结果。 相似文献
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Harn C. Chen 《Finite Elements in Analysis and Design》1993,13(4):249-258
Special finite elements are developed for efficient evaluation of stress concentration around a hole in complex structures. The complex variable formulation is used to derive a special set of stress functions which embody the stress concentration effects of a hole. The stress functions in combination with an independent displacement field assumed along the element boundary are used to construct the special elements with the hybrid displacement finite element method. Several numerical examples are presented to show that the used of special finite elements to model critical regions around a hole, together with conventional finite elements to model other regions away from the hole, is not only very convenient but also highly accurate. 相似文献
20.
The solutions of a three-dimensional rectangular limited-permeable crack or two three-dimensional rectangular limited-permeable cracks in the piezoelectric/piezomagnetic composite materials were investigated by using the generalized Almansi’s theorem and the Schmidt method. Finally, the relations among the electric field, the magnetic flux field and the stress field near the crack tips were obtained and the effects of the electric permittivity, the magnetic permeability of the air inside the crack, the shape of the rectangular crack on the stress, the electric displacement and magnetic flux intensity factors in the piezoelectric/piezomagnetic composite materials were analyzed. 相似文献