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1.
A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers. 相似文献
2.
《International Journal of Solids and Structures》1999,36(31-32):4767-4788
The article reports a methodology to synthesize the response of plane strain orthotropic and transversely isotropic half-spaces and full-spaces with arbitrarily oriented symmetry axes and subjected to concentrated and to distributed loads. Numerical results include the response of a half-space and a full-space to a uniform strip load. The examples presented analyze the influence of coordinate axis rotation and of the continuum anisotropy ratios. Stationary dynamic behavior is assumed throughout the article. 相似文献
3.
《International Journal of Solids and Structures》2014,51(23-24):4082-4093
This investigation is concerned with a mathematical analysis of an elastic circular cylindrical pile embedded in a transversely isotropic half-space under lateral dynamic excitations. A combination of time-harmonic horizontal shear force and moment are applied at the top end of the pile. The boundary value problem is formulated by decomposing the pile-medium system into a fictitious pile and an extended transversely isotropic half-space. A Fredholm integral equation of the second kind governs the interaction problem, whose solution is then computed numerically. Selected results for dynamic compliance bending moment, displacement and slope profiles are presented for different transversely isotropic half-spaces to portray the influence of degree of anisotropy of the medium on various aspects of the solution. 相似文献
4.
The contact interaction of two elastic isotropic half-spaces is analyzed. One of the half-spaces has a smooth shallow depression, resulting in an imperfect contact of the surfaces. The contact gap is assumed filled with a real gas. Gas–liquid transition due to variation in the external load and temperature is considered. The plane problem formulated is solved by the method of contact-gap functions. The effect of the filler and its phase transition on the width and depth of the gap and the contact pressure is studied 相似文献
5.
In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials (e.g., BaTiO3), piezomagnetic materials (e.g., CoFe2O4), and multiferroic com-posite materials (e.g., BaTiO3-CoFe2O4 composites) also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displace-ments, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional (3D) dislocation loops with a constant extended Burgers vector in trans-versely isotropic magneto-electro-elastic (MEE) bimaterials (i.e., joined half-spaces). The derived solutions can also be simply reduced to those expressions for piezoelectric, piezo-magnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials. 相似文献
6.
Green’s functions of a transversely isotropic half-space overlaid by a thin coating layer are analytically obtained. The surface coating is modeled by a Kirchhoff thin plate perfectly bonded to the half-space. With the aid of superposition technique and employing appropriate displacement potential functions, the Green’s functions are expressed in two parts; (i) a closed-form part corresponding to the transversely isotropic half-space with surface kinematic constraints, and (ii) a numerically evaluated part reflecting the interaction between the half-space and the plate in the form of semi-infinite integrals. Some limiting cases of the problem such as surface-stiffened isotropic half-space, Boussinesq and Cerruti loadings, and extremely flexible and rigid plates are also studied. For the classical Cerruti problem in transversely isotropic materials, the effects of incompressibility are highlighted. Numerical results are provided to show the effects of material anisotropy, relative stiffness factor, and load buried depth. The obtained Green’s functions play a key role in treating further mixed-boundary-value problems in surface stiffened transversely isotropic half-spaces. 相似文献
7.
H. Bufler 《Archive of Applied Mechanics (Ingenieur Archiv)》2000,70(1-3):103-114
Summary This paper deals with the stationary heat conduction in a solid consisting of planar, isotropic or transversely isotropic
layers. The following cases are considered: (1) arbitrarily layered solid, (2) macroperiodically layered solid, consisting
of equal pairs of different basic layers with finite thicknesses, (3) microperiodically layered solid, consisting of equal
layer groups of two or more different basic layers of infinitesimal thicknesses. Assuming a perfect contact between the layers,
exact solutions for the plane, the axisymmetric and the general three-dimensional problem of macro- and microperiodically
layered semispaces, respectively, are derived using integral transforms and the transfer-matrix method. It is proved that
the microperiodically layered solid with isotropic or transversely isotropic basic layers is equivalent to a homogeneous transversely
isotropic solid.
Received 31 March 1999; accepted for publication 21 May 1999 相似文献
8.
Giovanni Menditto Lucia Quattrini Angelo Marcello Tarantino 《Journal of Elasticity》1993,33(2):167-190
The contact problem between two orthotropic solids is examined. The problem is solved by using Lodge's method, which permits the transformation of the boundary-value problem of an anisotropic solid to a form identical with the corresponding problem of an isotropic medium. The proposed solution is then compared with known results of certain cases and it is observed that it producesHertz's solution when used for an isotropic case,Lodge's solution when applied to contact between an orthotropic solid and a rigid plane and, finally,Love's solution if the solid is transversely isotropic with the axis of material symmetry perpendicular to the rigid plane of contact. 相似文献
9.
Olesya I. Zhupanska 《Journal of Elasticity》2010,99(2):147-161
In this work a contact problem for a transversely isotropic half-space indented by a rigid sphere is considered. The axis
of symmetry of the half-space is orthogonal to the axis of the applied contact load, which makes the problem fully three-dimensional.
An exact solution to this contact problem is constructed. Stresses and strains are obtained in the form of contour integrals
in the complex plane with explicitly determined dimensionless integrands. As an illustrative application of the constructed
solution, failure beneath the indenter in a unidirectional composite is analyzed. 相似文献
10.
The effect of a thin isotropic coating on the edge effect zone in a representative element of a coated material is examined.
Isotropic and transversely isotropic materials are considered. The transversely isotropic material has the elastic properties
of unidirectional glass-fiber-reinforced plastic. The decay of the edge effect in the directions perpendicular to the coating
plane and to the plane of isotropy is studied. A boundary-value problem of elasticity for piecewise-homogeneouse orthotropic
bodies and a quantitative edge effect decay criterion for normal stresses are used as a design model. The problem is solved
using the finite-difference method and base schemes. The results of evaluation of the edge effect zone in homogeneous and
inhomogeneous materials are presented. It is shown that the presence of a thin isotropic coating blocks the edge effect, that
is, decreases the edge effect zone in both isotropic and transversely isotropic materials
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 61–67, December 2007. 相似文献
11.
Rajneesh KUMAR Rajeev KUMAR 《应用数学和力学(英文版)》2010,31(9):1153-1172
The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of a transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived after developing a mathematical model for welded and smooth contact boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficient via wave number are plotted graphically to depict the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction field, the normal stress, and the temperature change for welded contact are obtained and shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation. 相似文献
12.
Priza Kayestha Elizabete Rodrigues Ferreira Anil C. Wijeyewickrema 《International Journal of Solids and Structures》2013,50(22-23):3586-3596
The propagation of finite-amplitude time-harmonic shear horizontal waves, in a pre-stressed compressible elastic layer of finite thickness embedded between two identical compressible elastic half-spaces, is investigated. This is accomplished by combining finite-amplitude linearly polarized inhomogeneous transverse plane wave solutions in the half-spaces and finite-amplitude linearly polarized unattenuated transverse plane wave solutions in the layer. The layer and half-spaces are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. The special case where the interfaces between the layer and the half-spaces are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the shear horizontal wave speed with the pre-stress and the propagation angle. 相似文献
13.
D. A. Pozharskii 《Journal of Applied Mechanics and Technical Physics》2018,59(3):491-497
Within the framework of the anisotropic theory of elasticity, a three-dimensional contact problem of interaction of two massive transversely isotropic bodies, whose dimensions substantially exceed the size of the contact region, is investigated. In this case, the isotropy planes of contacting elastic bodies are mutually perpendicular. Exact and numerical solutions of the problem are determined. Calculations for various transversely isotropic materials are carried out. 相似文献
14.
A. A. Kalyakin 《Journal of Applied Mechanics and Technical Physics》2006,47(3):446-454
Plane and axisymmetric contact problems for a three-layer elastic half-space are considered. The plane problem is reduced
to a singular integral equation of the first kind whose approximate solution is obtained by a modified Multhopp-Kalandiya
method of collocation. The axisymmetric problem is reduced to an integral Fredholm equation of the second kind whose approximate
solution is obtained by a specially developed method of collocation over the nodes of the Legendre polynomial. An axisymmetric
contact problem for an transversely isotropic layer completely adherent to an elastic isotropic half-space is also considered.
Examples of calculating the characteristic integral quantities are given.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 165–175, May–June, 2006. 相似文献
15.
The elastic displacements, stresses and interaction energy of arbitrarily shaped dislocation loops with general Burgers vectors in transversely isotropic bimaterials (i.e. joined half-spaces) are expressed in terms of simple line integrals for the first time. These expressions are very similar to their isotropic full-space counterparts in the literature and can be easily incorporated into three-dimensional (3D) dislocation dynamics (DD) simulations for hexagonal crystals with interfaces/surfaces. All possible degenerate cases, e.g. isotropic bimaterials and isotropic half-space, are considered in detail. The singularities intrinsic to the classical continuum theory of dislocations are removed by spreading the Burgers vector anisotropically around every point on the dislocation line according to three particular spreading functions. This non-singular treatment guarantees the equivalence among different versions of the energy formulae and their consistency with the stress formula presented in this paper. Several numerical examples are provided as verification of the derived dislocation solutions, which further show significant influence of material anisotropy and bimaterial interface on the elastic fields and interaction energy of dislocation loops. 相似文献
16.
Baljeet Singh 《Continuum Mechanics and Thermodynamics》2013,25(5):675-683
The present paper is concerned with the propagation of plane waves in a transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The governing equations are solved in x–z plane to show the existence of three plane waves. Reflection of these plane waves from thermally insulated as well as isothermal stress-free surfaces is studied to obtain a system of three non-homogeneous equations in reflection coefficients of reflected waves. For numerical computations of speeds and reflection coefficients, a particular material is modeled as transversely isotropic dual-phase-lag generalized thermoelastic solid half-space. The speeds of plane waves are computed numerically for a certain range of the angle of propagation and are shown graphically against the angle of propagation for the cases of dual-phase-lag (DPL) thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity. Reflection coefficients of various reflected plane waves are computed numerically for thermally insulated as well as isothermal cases and are shown graphically against the angle of incidence for the cases of DPL thermoelasticity, coupled thermoelasticity and Lord–Shulman generalized thermoelasticity. 相似文献
17.
V. I. Zubko 《International Applied Mechanics》2003,39(3):332-338
A mechanical and mathematical bending model for a stack of transversely isotropic plates is developed. The resolving equations for deflections and tangential displacements are supplemented with a system of differential equations for normal and tangential contact stresses. It is demonstrated that for stacks consisting of an arbitrary number of identical plates with no friction between them, the initial system of equations for contact stresses can be reduced to Helmholtz equations. This transition allows obtaining the complete eigenvalue spectrum for the Laplasian of the problem and, in special cases, eigenfunctions. They are Krylov functions when bending is cylindrical and Bessel functions when bending is axisymmetric 相似文献
18.
I.IntroductionDuetotheirintrinsiccouplingeffectbetweenmechanicalandelectricalfields,piezoelectricmaterialshavebeenwidelyusedintechnologyastransducersandsensorsand,morerecently,asactuatorsinsmartstructures.lnordertooptimizetheirmicrostructuresandunderstand… 相似文献
19.
Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy 总被引:1,自引:0,他引:1
Jiangying Chen Haojiang Ding Weiqiu Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(4):241-251
Based on the basic equations for axisymmetric problems of transversely isotropic elastic materials, the displacement components
are expressed in terms of polynomials of the radial coordinate with the five involved coefficients, named as displacement
functions in this paper, being undetermined functions of the axial (thickness) coordinate. Five equations governing the displacement
functions are then derived. It is shown that the displacement functions can be found through progressive integration by incorporating
the boundary conditions. Thus a three-dimensional analytical solution is obtained for a transversely isotropic functionally
graded disc rotating at a constant angular velocity.The solution can be degenerated into that for an isotropic functionally
graded rotating disc. A prominent feature of this solution is that the material properties can be arbitrary functions of the
axial coordinate. Thus, the solution for a homogeneous transversely isotropic rotating disc is just a special case that can
be easily derived. An example is finally considered for a special functionally graded material, and numerical results shows
that the material inhomogeneity has a remarkable effect on the elastic field. 相似文献
20.
Haimin Yao Shaohua Chen Pradeep R. Guduru Huajian Gao 《International Journal of Solids and Structures》2009,46(5):1167-1175
Recently, Chen and Gao [Chen, S., Gao, H., 2007. Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. solids 55, 1001–1015] studied the problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic solid subjected to an inclined pulling force. An implicit assumption made in their study was that the contact region remains symmetric with respect to the center of the cylinder. This assumption is, however, not self-consistent because the resulting energy release rates at two contact edges, which are supposed to be identical, actually differ from each other. Here we revisit the original problem of Chen and Gao and derive the correct solution by removing this problematic assumption. The corrected solution provides a proper insight into the concept of orientation-dependent adhesion strength in anisotropic elastic solids. 相似文献