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IntroductionQuasicrystalasanewstructureofsolidmatter[1,2 ]bringsprofoundnewideastothetraditionalcondensedmatterphysicsandencouragesconsiderabletheoreticalandexperimentalstudiesonthephysicalandmechanicalpropertiesofthematerial,includingtheelasticitytheoryofthequasicrystal,manyvaluableresultsweregiven[3~ 5 ].Defectsinthematerialwereobservedsoonafterthediscoveryofthequasicrystal[6 ,7].Cracksareonetypeofdefects,theirexistencegreatlyinfluencesthephysicalandmechanicalpropertiesofthequasicrystalinem… 相似文献
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十二次对称二维准晶中的无摩擦接触问题 总被引:1,自引:0,他引:1
利用积分变换的方法讨论了在一个刚性压头作用下十二次对称二维准晶的无摩擦接触问题. 通过引入位移势函数,将数量巨大而复杂的偏微分方程转化为两个独立的双调和方程,应用Fourier分析与对偶积分方程理论解决了十二次对称二维准晶材料的无摩擦接触问题,得到了相应的接触应力解析表达式,结果表明:如果接触位移是一常数,则接触应力在接触区域边缘具有-1/2阶奇异性;反之,如果接触应力在接触区域边缘具有-1/2阶的奇异性,则接触位移一定为一常数,这为准晶材料的接触变形提供了重要的力学参数. 相似文献
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提出了一种分析双材料轴对称界面端的应力奇异行为的特征值法.基于弹性力学空间轴对称问题的基本方程和一阶近似假设,利用分离变量形式的位移函数和无网格算法,导出了关于应力奇异性指数的离散形式的奇异性特征方程.由奇异性特征方程的特征值和特征向量,即可确定应力奇异性指数、位移角函数和应力角函数.数值求解了纤维/基体轴对称界面端模型的奇异性特征方程, 结果表明:尺寸效应参数δ(奇异点与轴对称轴的距离和应力奇异性支配区域大小的比值)影响着应力奇异性的强弱与阶次, 准一阶近似解析解只是δ>>1时的一个特例. 相似文献
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Wang Zikun 《Acta Mechanica Sinica》1994,10(1):49-60
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 相似文献
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特征值为二重根的压电材料异材界面端奇异性 总被引:1,自引:0,他引:1
横观各向同性压电材料的特征值的不同,其一般解的形式也不同,压电结合材料问题的求解,可以归结为寻找合适的调和函数,针对材料特征值为二重根(s1^2≠s2^2=s3^2)的情况,将变量分离形式的调和函数作特征展开,推导了横观各向同性压电材料轴对称异材界面端附近的奇民异应力场和奇异电位移场,给出院 决定奇异性的特性方程,结果表明,电位移场和应力场具有相同的奇异性,奇异性次数不仅与界面端形状以及材料的机械性质有关。也与材料的压电特性有关。 相似文献
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THEPLANESTRESSCRACK-TIPFIELDFORANINCOMPRESSIBLERUBBERMATERIALGaoYu-chen(高玉臣),ShiZhi-fei(石志飞)(HarbinShipbuildingEngneeringInst... 相似文献
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A.R. Shahani 《Journal of Elasticity》1999,56(1):17-32
The antiplane deformation of an anisotropic wedge with finite radius is considered in this paper within the classical linear
theory of elasticity. The traction-free condition is imposed on the circular segment of the wedge. Three different cases of
boundary conditions on the radial edges are considered, which are: traction-displacement, displacement-displacement and traction-traction.
The solution to the governing differential equation of the problem is accomplished in the complex plane by relating the displacement
field to a complex function. Several complex transformations are defined on this complex function and its first and second
derivatives to formulate the problem in each of the three cases of the problem corresponding to the radial boundary conditions,
separately. These transformations are then related to integral transforms which are complex analogies to the standard finite
Mellin transforms of the first and second kinds. Closed form expressions are obtained for the displacement and stress fields
in the entire domain. In all cases, explicit expressions for the strength of singularity are derived. These expressions show
the dependence of the order of stress singularity on the wedge angle and material constants. In the displacement-displacement
case, depending upon the applied displacement, a new type of stress singularity has been observed at the wedge apex.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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The present study develops the fracture theory for a two-dimensional octagonal quasicrystals. The exact analytic solution of a Mode Ⅱ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate were determined, the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystal and quasicrystal were figured out. These provide important information for studying the deformation and fracture of the new solid phase. 相似文献
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Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional(3D) icosahedral quasicrystals are discussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhesive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regulation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason coupling constant impact is barely perceptible. The validity of the conclusions is verified. 相似文献
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本文从弹性力学三维问题柱坐标下以位移分量表示的平衡方程出发,用小参数摄动技术提出了平面轴对称变温场下包覆金属层压板孔边层间应力奇异性的具体分析方法,得到了确定奇异性阶次的特征方程,并对两种工程实际中应用的含圆孔的层压板作出了数值算例。 相似文献
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A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon’s solution for the axisymmetric punch problem, Boussinesq’s solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D-n model can all be explicitly recovered by the current general solution. 相似文献
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E.E. Theotokoglou I.H. Stampouloglou 《International Journal of Solids and Structures》2008,45(25-26):6535-6552
The plane axisymmetric problem with axisymmetric geometry and loading is analyzed for a radially nonhomogeneous circular cylinder, in linear elasticity. Considering the radial dependence of the stress, the displacements fields and of the stiffness matrix, after a series of admissible functional manipulations, the general differential system solving the problem is developed. The isotopic radially inhomogeneous elastic axisymmetric problem is also analyzed. The exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio and of power law Young’s modulus and constant Poisson’s ratio. For the isotropic elastic axisymmetric problem, a general expression of the stress function is derived. After the satisfaction of the biharmonic equation and making compatible the stress field’s expressions, the stress function and the stress and displacements fields of the axisymmetric problem are also deduced. Applications have been made for a radially nonhomogeneous hollow cylinder where the stress and displacements fields are determined. 相似文献
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Summary The smooth contact of a rubber half-space dented by a rigid cone apex is analyzed based on the large deformation theory.
The problem is treated as an axially symmetric case, and the material is assumed to be incompressible. The asymptotic equations
for the domain near the apex are derived. They are solved analytically for the shrinking domain, while a numerical solution
is found for the expanding domain in the vicinity of the stress singularity. The purpose of this paper is not only to solve
a typical problem but also to provide an analytical method to solve a large-strain problem with a singular point.
Received 10 July 2001; accepted for publication 24 January 2002 相似文献
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Propagation of a semi-infinite crack along the interface between an elastic half-plane and a rigid half-plane is analyzed. The crack advances at constant subsonic speed. It is assumed that, ahead of the crack, there is a finite segment where the conditions of Coulomb friction law are satisfied. The contact zone of unknown a priori length propagates with the same speed as the crack. The problem reduces to a vector Riemann–Hilbert problem with a piece-wise constant matrix coefficient discontinuous at three points, 0, 1, and ∞. The problem is solved exactly in terms of Kummer's solutions of the associated hypergeometric differential equation. Numerical results are reported for the length of the contact friction zone, the stress singularity factor, the normal displacement u2, and the dynamic energy release rate G. It is found that in the case of frictionless contact for both the sub-Rayleigh and super-Rayleigh regimes, G is positive and the stress intensity factor KII does not vanish. In the sub-Rayleigh case, the normal displacement is positive everywhere in the opening zone. In the super-Rayleigh regime, there is a small neighborhood of the ending point of the open zone where the normal displacement is negative. 相似文献
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In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed. 相似文献