共查询到20条相似文献,搜索用时 31 毫秒
1.
A static thermoelectroelastic problem for an infinite transversally isotropic body containing a spheroidal cavity is explicitly solved. The symmetry axis of the spheroid coincides with the anisotropy axis of the body. It is assumed that at a rather large distance from the cavity the body is in a uniform heat flow directed along the anisotropy axis. Formulas are derived for the stress components and the projections of the electric displacement vector near the cavity, which depend on the heat-flow value, cavity geometry, and the thermoelectroelastic properties of the material. The solution of the problem for a body with a disk-like crack is obtained as a partial case from the solution of the problem for a piezoceramic body with a spheroidal cavity. The stress intensity factors for the force and electric fields are determined near the crack 相似文献
2.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(11):1263-1271
A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary
shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship
is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite
piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF
and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems.
As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of
the stresses and the normal electric displacement on the crack surface
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005. 相似文献
3.
An explicit solution is constructed for the static problem of thermoelectroelasticity for an infinite transversally isotropic
body with a heat-insulated elliptic crack located in the isotropy plane. It is assumed that at a large distance from the crack
the body is affected by a uniform heat flow perpendicular to the crack plane. Formulas are derived for the stress intensity
factors at the crack end, which depend on the value of the heat flow, crack geometry, and the thermoelectroelastic properties
of the piezoceramic body.
Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 72–82, February, 2000. 相似文献
4.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(3):320-330
The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane
perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress
(SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for
a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find
the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity.
The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface
are found as an example
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008. 相似文献
5.
Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow 总被引:1,自引:0,他引:1
The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote
uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping
and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or
hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the
electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates.
When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The
effect of the heat flow direction and the dielectric constant of air inside the crack on the thermal electroelastic fields
are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results
are valid. 相似文献
6.
A conjugate electroelastic field in a piezoceramic cylinder with a parabolic crack under static loading is investigated. Uniformly
tensile stresses and an electric potential are applied to the end faces of the cylinder. The following two types of electric
conditions are considered at the crack boundary: the electric potential is continuous across the crack and the normal component
of the electric-displacement vector on the crack surface is equal to zero. For each of these cases, expressions for some quantities
characterizing the disturbed field in the crack plane and formulas to calculate the stress intensity factors are presented.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 36, No. 3, pp. 72–80, March, 2000. 相似文献
7.
The electroelastic problem for a transversely isotropic prolate ceramic spheroid is solved explicitly. The spheroid surface
is free from external forces. The case is considered where the piezoceramic body is subjected to a given potential difference
between electrodes partially covering the surface at the vertices. The normal component of electric-flux density is equal
to zero on the noneletroded portion of the surface. Plots of normal stresses in the symmetry plane of the piezoceramic body
are given
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 58–67, July 2005. 相似文献
8.
An exact solution is obtained to the three-dimensional problem of thermoelectroelasticity for a piezoceramic body with a spheroidal
cavity. The solutions of static thermoelectroelastic problems are represented in terms of harmonic functions. Far from the
cavity, the body is in a uniform heat flow perpendicular to the axis of symmetry of the cavity
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 57–66, November 2005. 相似文献
9.
Using the boundary integral equation method, the problem of stationary heat conduction and thermoelasticity for a semi-infinite
body with a crack parallel to its boundary is solved. Temperature or heat flow on the crack is prescribed. The body boundary
is heat-insulated or is at zero temperature. The dependence of the stress intensity factor on the depth of occurrence of a
circular crack at a constant temperature or under a constant heat flow is studied. In contrast to mechanical loading, thermal
loading shows less SIF values than in an infinite body
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 46–54, April 2007. 相似文献
10.
The present paper studies unsteady temperature fields in growing bodies of spherical shape. The growth occurs due to constant accretion of layers of constant thickness on the surface of the main body. In the general case, the temperature of the accreted material is different from that of the main body, which causes a heat flow on the accretion surface. The solution of the initial boundary-value problem of heat conduction is sought as an expansion in the complete system of eigenfunctions of the differential operator generated by the problem. 相似文献
11.
Yu. N. Podil'chuk 《International Applied Mechanics》1999,35(7):713-721
An explicit solution of the static problem of electroelasticity for a transversally isotropic piezoceramic medium containing
a tunneled elliptical recess, one axis of which coincides with the axis of the medium's anisotropy, is constructed in this
study. It is assumed that the surface of the recess is free of mechanical forces, and the normal component of the induction
vector on this surface is equal to zero. Tensile forces act at a sufficient distance from the recess along its axis. The solution
of the corresponding problem for a medium containing an internal crack is obtained as a special case.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 35, No. 7, pp. 77–84, July, 1999. 相似文献
12.
《International Journal of Solids and Structures》2002,39(9):2665-2685
This paper presents an exact solution for the problem of an elliptic hole or a crack in a thermopiezoelectric solid. First, based on the extended version of Eshelby–Stroh's formulation, the generalized 2D problems of an elliptical hole in a thermopiezoelectric medium subject to uniform heat flow and mechanical–electrical loads at infinity are studied according to exact boundary conditions at the rim of the hole. The complex potentials in the medium and the electric field inside the hole are obtained in closed form, respectively. Then, when the hole degenerates into a crack, the explicit solutions for the field intensity factors near the crack tip and the electric field inside the crack are presented. It is shown that the singularities of all the field are dependent on the material constants, the applied heat load and mechanical loads at infinity, but not on the applied electric loads. It is also found that the electric field inside the crack is linearly variable, which is different from the result based on the impermeable crack model. 相似文献
13.
Piezothermoelastic analysis of a piezoelectric material with an elliptic cavity under uniform heat flow 总被引:1,自引:0,他引:1
Summary The problem of a two-dimensional piezoelectric material with an elliptic cavity under a uniform heat flow is discussed, based
on the modified Stroh formalism for the piezothermoelastic problem. The exact electric boundary conditions at the rim of the
hole are introduced in the analysis. Expressions for the elastic and electric variables induced within and outside the cavity
are derived in closed form. Hoop stress around the hole and electric fields in the hole are obtained. The limit situation
when the hole is reduced to a slit crack is discussed, and the intensity factors for the problem are obtained.
Received 14 April 1998; accepted for publication 25 June 1998 相似文献
14.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(2):150-157
The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric
loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for
an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is
an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along
the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations
of the crack
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008. 相似文献
15.
Qun Li Andreas Ricoeur Meinhard Kuna 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(6):685-700
The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered.
A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of
electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory
when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces.
Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection
with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an
applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover,
compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric
load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics. 相似文献
16.
The oscillation and dissipative heating of an infinitely long piezoceramic cylinder polarized along the radius is considered
in the case of partial heat depolarization, with harmonic quasi-static loading of the cylinder by a potential difference.
The inner surface of the cylinder is thermally insulated; there is heat transfer at the outer surface. An analytical solution
is obtained, and numerical calculations are performed for a TsTStBS-2 piezoceramic. The conditions in which the depolarized
zone appears are examined, along with the stress-strain state of the cylinder.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya
Mekhanika, Vol. 35, No. 3, pp. 42–48, March, 1999. 相似文献
17.
We determine the electrostressed state of a piezoceramic medium with an arbitrarily oriented triaxial ellipsoidal inclusion
under homogeneous mechanical and electric loads. Use is made of Eshelby’s equivalent inclusion method generalized to the case
of a piezoelectric medium. Solving the problem for a spheroidal cavity with the axis of revolution aligned with the polarization
axis demonstrates the high efficiency of the approach. A numerical analysis is carried out. The stress distribution along
the surface of the arbitrarily oriented triaxial ellipsoidal inclusion is studied 相似文献
18.
Norio Hasebe Christian Bucher Rudolf Heuer 《International Journal of Solids and Structures》2010,47(1):138-147
A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate. 相似文献
19.
《International Journal of Solids and Structures》2003,40(22):6143-6162
The weight function in fracture mechanics is the stress intensity factor at the tip of a crack in an elastic material due to a point load at an arbitrary location in the body containing the crack. For a piezoelectric material, this definition is extended to include the effect of point charges and the presence of an electric displacement intensity factor at the tip of the crack. Thus, the weight function permits the calculation of the crack tip intensity factors for an arbitrary distribution of applied loads and imposed electric charges. In this paper, the weight function for calculating the stress and electric displacement intensity factors for cracks in piezoelectric materials is formulated from Maxwell relationships among the energy release rate, the physical displacements and the electric potential as dependent variables and the applied loads and electric charges as independent variables. These Maxwell relationships arise as a result of an electric enthalpy for the body that can be formulated in terms of the applied loads and imposed electric charges. An electric enthalpy for a body containing an electrically impermeable crack can then be stated that accounts for the presence of loads and charges for a problem that has been solved previously plus the loads and charges associated with an unsolved problem for which the stress and electric displacement intensity factors are to be found. Differentiation of the electric enthalpy twice with respect to the applied loads (or imposed charges) and with respect to the crack length gives rise to Maxwell relationships for the derivative of the crack tip energy release rate with respect to the applied loads (or imposed charges) of the unsolved problem equal to the derivative of the physical displacements (or the electric potential) of the solved problem with respect to the crack length. The Irwin relationship for the crack tip energy release rate in terms of the crack tip intensity factors then allows the intensity factors for the unsolved problem to be formulated, thereby giving the desired weight function. The results are used to derive the weight function for an electrically impermeable Griffith crack in an infinite piezoelectric body, thereby giving the stress intensity factors and the electric displacement intensity factor due to a point load and a point charge anywhere in an infinite piezoelectric body. The use of the weight function to compute the electric displacement factor for an electrically permeable crack is then presented. Explicit results based on a previous analysis are given for a Griffith crack in an infinite body of PZT-5H poled orthogonally to the crack surfaces. 相似文献
20.
The general solution of the electroelastic problem for a transversely isotropic hyperboloid of revolution is used to find the stress concentration near a hyperboloidal neck in a piezoceramic body subjected to bending. The solution is a sum of four partial solutions for the case where the forces and the normal component of the induction vector on the neck surface are equal to zero. Numerical examples are given for specific external loads and properties of the body. The stress components and normal component of the induction vector near the neck vertex are plotted as a function of the external load and neck curvature 相似文献