共查询到20条相似文献,搜索用时 31 毫秒
1.
S. Ueda 《Engineering Fracture Mechanics》2007,74(8):1255-1273
The mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip with a penny-shaped crack is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. The thermal and electromechanical problems are reduced to singular integral equations and solved numerically. The stress and electric displacement intensity factors are presented for different crack size, crack position and material nonhomogeneity. 相似文献
2.
S. Ueda 《Engineering Fracture Mechanics》2008,75(5):1204-1222
Transient response of a penny-shaped crack in a plate of a functionally graded piezoelectric material (FGPM) is studied under thermal shock loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are completely insulated. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations which are solved numerically. The intensity factors vs. time for various crack size, crack position and material nonhomogeneity are obtained. 相似文献
3.
In this paper, the mixed-mode fracture problem of a functionally graded piezoelectric material strip with two penny-shaped or annular cracks is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under electric loading. The problem is formulated in terms of a system of singular integral equations, which are solved numerically. Numerical calculations are carried out, and the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity. 相似文献
4.
Summary A laminate model is employed to solve the elastodynamic problem of a collinear crack in an inhomogeneous material. The inhomogeneous material is treated as a series of thinner layer. The Laplace and Fourier transforms are used to reduce the problem to a set of singular integral equations that is solved numerically. Numerical results of two collinear cracks in a functionally graded material strip are obtained to show the influence of material inhomogeneity and crack position on crack tip field intensities. 相似文献
5.
Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure
In this paper, the interface cracking between a functionally graded material (FGM) and an elastic substrate is analyzed under
antiplane shear loads. Two crack configurations are considered, namely a FGM bonded to an elastic substrate containing a single
crack and a periodic array of interface cracks, respectively. Standard integral-transform techniques are employed to reduce
the single crack problem to the solution of an integral equation with a Cauchy-type singular kernel. However, for the periodic
cracks problem, application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem
for a typical strip to triple series equations, then to a singular integral equation with a Hilbert-type singular kernel.
The resulting singular integral equation is solved numerically. The results for the cases of single crack and periodic cracks
are presented and compared. Effects of crack spacing, material properties and FGM nonhomogeneity on stress intensity factors
are investigated in detail. 相似文献
6.
The paper deals with a 2-dimensional problem of an anisotropic elastic strip having an infinite row of Griffith cracks. By using integral equation approach, the problem is treated analytically. The stress intensity factor, the critical pressure and the energy required to open the crack are studied for two cases—(a) when the edges of the strip are in contact with smooth and rigid planes and (b) when the edges of the strip are free of tractions. Numerical results for the aforementioned quantities are obtained for both the cases for a specific anisotropic material and a comparison is made with the corresponding results for a strip made of an isotropic material. 相似文献
7.
《Engineering Analysis with Boundary Elements》2005,29(5):466-476
Using the fundamental solutions and the Somigliana identity of piezoelectric medium, the boundary integral equations are obtained for a conductive planar crack of arbitrary shape in three-dimensional transversely isotropic piezoelectric medium. The singular behaviors near the crack edge are studied by boundary integral equation approach, and the intensity factors are derived in terms of the displacement discontinuity and the electric displacement boundary value sum near the crack edge on crack faces. The boundary integral equations for two dimensional crack problems are deduced as a special case of infinite strip planar crack. Based on the analogy of the obtained boundary integral equations and those for cracks in conventional isotropic elastic material and for contact problem of half-space under the action of a rigid punch, an analysis method is proposed. As an example, the solution to conductive Griffith crack is derived. 相似文献
8.
Doo-Sung Lee 《Acta Mechanica》2004,169(1-4):101-110
Summary. The elastostatic plane problem of an infinite strip having a circular hole and containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of triply coupled integral equations. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. Quantities of physical interest are displayed in graphical forms. 相似文献
9.
In this paper, the Fourier integral transform–singular integral equation method is presented for the problem of a periodic array of cracks in a functionally graded piezoelectric strip bonded to a different functionally graded piezoelectric material. The properties of two materials, such as elastic modulus, piezoelectric constant and dielectric constant, are assumed in exponential forms and vary along the crack direction. The crack surface condition is assumed to be electrically impermeable or permeable. The mixed boundary value problem is reduced to a singular integral equation over crack by applying the Fourier transform and the singular integral equation is solved numerically by using the Lobatto–Chebyshev integration technique. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived. The effects of the loading parameter λ, material constants and the geometry parameters on the stress intensity factor, the energy release ratio and the energy density factor are studied. 相似文献
10.
Ranjit S. Dhaliwal 《International Journal of Engineering Science》1973,11(5):489-500
We consider the problem of determining the stress intensity factors and the crack energy in an infinitely long elastic strip containing two coplanar Griffith cracks. We assume that the strip is bonded to semi-infinite elastic planes on either side and that the cracks are opened by constant internal pressure. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations withcosine kernel and a weight function. These equations are solved using Finite Hilbert transform techniques. Analytical expressions upto the order off δ?10 where 2δ denotes the thickness of the strip and δ is much greater than 1 are derived for the stress intensity factors and the crack energy. 相似文献
11.
Summary The problem of an anti-plane shear crack embedded in a magnetoelectroelastic strip is investigated. The crack is assumed to
be normal to the strip edges. By using the finite Fourier transform, the associated mixed boundary-value problem is reduced
to triple series equations, then to singular integral equations. Solving the resulting equations analytically, the field intensity
factors and energy release rates at the crack tips can be determined in explicit form. The influences of applied electric
and magnetic loadings on the normalized energy release rate and mechanical strain energy release rate are presented graphically.
Obtained results reveal that applied electric and magnetic loadings affect crack growth, depending on their directions and
adopted fracture criteria. The derived solution is applicable to other cases including two collinear cracks distributed symmetrically
in a magnetoelectroelastic strip, and a periodic array of collinear cracks in a magnetoelectroelastic plane. 相似文献
12.
13.
The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometries and degrees of surface reinforcement. 相似文献
14.
《International Journal of Engineering Science》2006,44(11-12):807-818
The problem of two periodic edge cracks in an elastic infinite strip located symmetrically along the free boundaries under thermal shock is investigated. It is assumed that the infinite strip is initially at constant temperature. Suddenly the surfaces containing the edge cracks are quenched by a ramp function temperature change. Very high tensile transient thermal stresses arise near the cooled surface resulting in severe damage. The degree of the severity for a subcritical crack growth mode is measured by determining the stresses intensity factors. The thermoelastic problem is treated as uncoupled quasi-static. The superposition technique is used to solve the problem. The thermal stresses obtained from the uncracked strip with opposite sign are utilized as the only external loads to formulate the perturbation problem. By expressing the displacement components in terms of finite and infinite Fourier transforms, a hypersingular integral equation is derived with the crack surface displacement as the unknown function. Numerical results for stress intensity factors are carried out and presented as a function of time, cooling rate, crack length, and periodic crack spacing. 相似文献
15.
This paper considers the elastostatic plane problem of a finite strip. One end of the strip is perfectly bonded to a rigid support while the other is under the action of a uniform tensile load. Solution for the finite strip is obtained by considering an infinite strip containing a transverse rigid inclusion at the middle and two symmetrically located transverse cracks. The distance between the two cracks is equal to twice the length of the finite strip. In the limiting case when the rigid inclusion and the cracks approach the sides of the infinite strip, the region between one crack and the rigid inclusion becomes equivalent to the finite strip. Formulation of the problem is reduced to a system of three singular integral equations using the Fourier transforms. Numerical results for stresses and stress intensity factors are given in graphical form. 相似文献
16.
G.G. Adams 《International Journal of Engineering Science》1980,18(3):455-462
The problem considers an arbitrary number of colinear and unequal size Griffith cracks opened by a non-uniform internal pressure in an infinite elastic strip. The cracks are located halfway between and parallel to the surfaces of the 2-dimensional medium. By appropriate integral transformations the mixed boundary value problem is reduced to singular integral equations. The stress intensity factors, crack openings and crack energies are then determined for many different cases. 相似文献
17.
In an earlier paper [6] we have studied the case of interaction of shear waves with a crack centrally situated in an infinite elastic strip; we, in this paper, extend the study to the case of two coplanar Griffith cracks. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic — elastic material. This method resolves the problem into an integral equation. It has been observed that shear waves with frequencies less than a parameter depending on the width of the wave guide can only propagate. The integral equation is solved numerically for a range of values of wave frequency, width of strip and the inter-crack distance. These solutions are used to calculate the dynamic stress intensity factor. The results are shown graphically. 相似文献
18.
《International Journal of Engineering Science》1987,25(2):213-226
This paper is concerned with the plane strain problem of an elastic incompressible layer bonded to a rigid foundation. An upward tensile force is applied to the top surface of the layer through a rigid strip of finite thickness. The layer contains either a finite central crack or two semiinfinite external cracks. The analysis leads to a system of singular integral equations. These integral equations are solved numerically and the interface stress distributions, stress intensity factors at the crack tips and at the corners of the rigid strip, probable cleavage angle for the finite crack and strain energy release rate are calculated for various geometries. 相似文献
19.
《International Journal of Engineering Science》1987,25(7):807-820
This paper is concerned with the plane strain problem of an elastic incompressible layer bonded to a rigid foundation. An upward tensile force is applied to the top surface of the layer through a rigid strip of finite thickness. The layer contains either a finite central crack or two semi-infinite external cracks. The analysis leads to a system of singular integral equations. These integral equations are solved numerically and the interface stress distributions, stress intensity factors at the crack tips and at the corners of the rigid strip, probable cleavage angle for the finite crack and strain energy release rate are calculated for various geometries. 相似文献
20.
N.I. Ioakimidis 《Engineering Fracture Mechanics》1982,16(6):821-826
An elementary method for obtaining upper bounds for the stress intensity factors along the boundaries of interacting coplanar cracks inside an infinite isotropic elastic medium is presented. This method is based on the singular integral equation of the aforementioned elasticity problem and on the solutions of this equation for each particular crack problem, assumed known. The method is applied to the simple problem of interaction of two circular cracks, as well as to the similar problem of two cracks having the shape of a straight strip. The present results constitute a generalization of the corresponding method for crack problems in two-dimensional elasticity and can easily be further generalized to apply to more complicated crack problems in three-dimensional elasticity. 相似文献