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1.
SCATTERING OF THE HARMONIC STRESS WAVE BY CRACKS IN FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS 总被引:1,自引:0,他引:1
Ma Li Nie Wu Wu Linzhi Zhou Zhengong 《Acta Mechanica Solida Sinica》2005,18(4):295-301
The present paper considers the scattering of the time harmonic stress wave by a single crack and two collinear cracks in functionally graded piezoelectric material (FGPM). It is assumed that the properties of the FGPM vary continuously as an exponential function. By using the Fourier transform and defining the jumps of displacements and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the influences of material properties on the dynamic stress and the electric displacement intensity factors. 相似文献
2.
DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL 总被引:2,自引:0,他引:2
IntroductionInrecentyears,greatattentionshavebeenpaidtotheresearchofFunctionallyGradedMaterials(FGM).Fromtheviewpointsofappliedmechanics,FGMarenon_homogeneoussolids.Thenon_homogeneityofFGMhasagreatinfluenceontheirmechanicalbehavior,especiallywhenthecomp… 相似文献
3.
The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks. 相似文献
4.
Jun Liang 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(6):443-464
The dynamic behavior of two parallel symmetric cracks in functionally graded piezoelectric/piezomagnetic materials subjected
to harmonic antiplane shear waves is investigated using the Schmidt method. The present problem can be solved using the Fourier
transform and the technique of dual integral equations, in which the unknown variables are jumps of displacements across the
crack surfaces, not dislocation density functions. To solve the dual integral equations, the jumps of displacements across
the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the electric, magnetic
flux, and dynamic stress fields near crack tips can be obtained. Numerical examples are provided to show the effect of the
functionally graded parameter, the distance between the two parallel cracks, and the circular frequency of the incident waves
upon the stress, electric displacement, and magnetic flux intensity factors at crack tips. 相似文献
5.
Pei-Wei Zhang Zhen-Gong Zhou Zeng-Tao Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(6):411-430
The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this
paper using the generalized Almansi’s theorem. To make the analysis tractable, it was assumed that the shear modulus varies
exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into
two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve
the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi
polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at
the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials;
however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties.
It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials. 相似文献
6.
In this paper, the interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material was investigated by using the generalized Almansi's theorem. In the analysis, the electric permittivity of the air inside the crack was considered. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the electric permittivity of the air inside the crack and the gradient parameter of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials. 相似文献
7.
在忽略界面裂尖端裂纹面相互叠入的条件下,对功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载响应问题进行了分析。利用傅立叶变换,将问题的求解转换为对以裂纹面上位移差为未知函数的对偶积分方程的求解。为了求解对偶积分方程,将裂纹面上的位移差函数展开为雅可毕多项式的级数形式。最终给出了裂纹长度、入射波频率和材料性质对应力强度的影响。结果表明,当界面材料不连续时,获得了具有普通1/2奇异性的近似解。 相似文献
8.
The behavior of two parallel non-symmetric cracks in piezoelectric materials subjected to the anti-plane shear loading was studied by the Schmidt method for the permeable crack electric boundary conditions. Through the Fourier transform, the present problem can be solved with two pairs of dual integral equations ip which the unknown variables are the jumps of displacements across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials. Finally, the relations between electric displacement intensity factors and stress intensity factors at crack tips can be obtained. Numerical examples are provided to show the effect of the distance between two cracks upon stress and electric displacement intensity factors at crack tips. Contrary to the impermeable crack surface condition solution, it is found that electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. At the same time, it can be found that the crack shielding effect is also present in the piezoelectric materials. 相似文献
9.
The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor. 相似文献
10.
The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack. 相似文献
11.
The dynamic stress intensity factors (DSIFs) of two 3D rectangular cracks in a transversely isotropic elastic material under an incident harmonic stress wave are investigated by generalized Almansi’s theorem and the Schmidt method in the present paper. Using 2D Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the DSIFs of the transversely isotropic elastic material. 相似文献
12.
In this paper, the basic solution of a mode-I crack in functionally graded piezoelectric materials was investigated by using
the generalized Almansi’s theorem. In the analysis, the electric permittivity of air inside the crack were considered. To
make the analysis tractable, it was assumed that the shear modulus, piezoelectric constants and dielectric constants vary
exponentially with coordinate parallel to the crack. The problem was formulated through Fourier transform into two pairs of
dual integral equations, in which the unknown variables are jumps of displacements across the crack surfaces. To solve the
dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi
polynomials. The solution of the present paper shows that the effects of the electric boundary conditions on the electric
displacement fields near the crack tips can not be ignored. Simultaneously, the solution of the present paper will revert
to a closed form one when the functionally graded parameter equals to zero. 相似文献
13.
In this paper, the behavior of an interface crack for a functionally graded strip sandwiched between two homogeneous layers
of finite thickness subjected to an uniform tension is resolved using a somewhat different approach, named the Schmidt method.
The Fourier transform technique is applied and a mixed boundary value problem is reduced to two pairs of dual integral equations
in which the unknown variables are the jumps of the displacements across the crack surface. To solve the dual integral equations,
the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite
different from those adopted in previous works. Numerical examples are provided to show the effects of the crack length, the
thickness of the material layer and the materials constants upon the stress intensity factor of the cracks. It can be obtained
that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation
method. As a special case, when the material properties are not continuous through the crack line, an approximate solution
of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near
the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities
of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials. 相似文献
14.
《European Journal of Mechanics - A/Solids》2006,25(5):793-807
In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in the piezoelectric materials subjected to a uniform tension loading. The permittivity of the air in the crack is considered. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the materials constants, the electric boundary conditions and the lattice parameter on the stress and the electric displacement fields near the crack tips. It can be obtained that the effects of the electric boundary conditions on the electric displacement fields are large. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips, thus allowing us to use the maximum stress as a fracture criterion. 相似文献
15.
In this paper, the behavior of a Griffith crack at the interface of a layer boned to a half plane subjected to a uniform tension is investigated by use of the Schmidt method under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible and also there is a sufficiently large component of mode-I loading so that the crack essentially remains open. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the thickness of the material layer and the materials constants upon the stress intensity factor of the crack. As a special case in our solution, we also give the solution of the ordinary crack in homogeneous materials. Contrary to the previous solution of the interface crack problem, it is found that the stress singularities of the present interface crack solution are similar with ones for the ordinary crack in homogeneous materials. 相似文献
16.
17.
The solutions of a 3-D rectangular limited-permeable crack or two 3-D rectangular limited-permeable cracks in piezoelectric
materials were given by using the generalized Almansi’s theorem and the Schmidt method. At the same time, the electric permittivity
of the air inside the rectangular crack was considered. The problem was formulated through Fourier transform as three pairs
of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve
the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi
polynomials. Finally, the effects of the electric permittivity of the air inside the rectangular crack,the shape of the rectangular
crack and the distance between two rectangular cracks on the stress and electric displacement intensity factors in piezoelectric
materials were analyzed. 相似文献
18.
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method.The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces.To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials.Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained.The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks.It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials. 相似文献
19.
The solutions of a 3-D rectangular permeable crack and two 3-D rectangular permeable cracks in a piezoelectric material were
investigated by using the generalized Almansi’s theorem and the Schmidt method. The problem was formulated through Fourier
transform into three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the
crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded
as a series of Jacobi polynomials. Finally, the effects of the shape of the rectangular crack and the distance between two
rectangular cracks on the stress and electric displacement intensity factors in a piezoelectric material were analyzed. These
results can be used for the strength and the coupling effect evaluation of cracked piezoelectric materials. 相似文献
20.
Pei-Wei Zhang Zhen-Gong Zhou Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(10):965-979
In this paper, the behavior of three parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic material plane
subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier
transform into three pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack
surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded
as a series of Jacobi polynomials. Finally, the relations among the electric displacement, the magnetic flux and the stress
fields near the crack tips can be obtained. The results show that the stress, the electric displacement and the magnetic flux
intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding
effect is present in piezoelectric/piezomagnetic materials. 相似文献