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1.
《应用数学和力学(英文版)》2017,(2)
The dynamic behavior of a rectangular crack in a three-dimensional(3D)orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional(2D) Fourier transform is applied, and the mixedboundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves,and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite. 相似文献
2.
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
3.
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
4.
Dynamic behavior of unequal parallel permeable interface multi-cracks in a piezoelectric layer bonded to two piezoelectric materials half planes 总被引:2,自引:0,他引:2
Jian-Liang Sun Zhen-Gong Zhou Biao Wang 《European Journal of Mechanics - A/Solids》2004,23(6):993-1005
This study is concerned with the treatment of the dynamic behavior of interacting cracks in a piezoelectric layer bonded to two dissimilar piezoelectric half planes subjected to harmonic anti-plane shear waves. The permeable electric boundary condition is considered. By use of the Fourier transform technique, 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 two series of Jacobi polynomials. The electromechanical behavior of two pairs of unequal parallel cracks was determined. Numerical examples are provided to show the effects of the geometry of the cracks, the frequency of the incident waves and materials properties upon the dynamic stress intensity factors (DSIFs) and the electric displacement intensity factors. 相似文献
5.
Dynamic behavior of two unequal parallel permeable interface cracks in a piezoelectric layer bonded to two half piezoelectric materials planes 总被引:1,自引:1,他引:0
IntroductionDuetotheintrinsicelectro_mechanicalcouplingbehavior,piezoelectricmaterialsareveryusefulinelectronicdevices.However,mostpiezoelectricmaterialsarebrittlesuchasceramicsandcrystals.Therefore ,piezoelectricmaterialshaveatendencytodevelopcriticalcracksduringthemanufacturingandthepolingprocesses.So ,itisimportanttostudytheelectro_elasticinteractionandfracturebehaviorsofpiezoelectricmaterials.Theincreasingattentiontothestudyofcrackproblemsinpiezoelectricmaterialshasledtoalotofsignificantw… 相似文献
6.
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
7.
IntroductionThe vibration of the plate on the porous saturated building foundation is a complicateddynamic contact problem.Its consideration is very important in both earthquake and geo-technical engineering.Lots of research works have been done in recent… 相似文献
8.
横观各向同性材料的三维断裂力学问题 总被引:4,自引:0,他引:4
从三维横观各向同性材料弹性力学理论出发,
使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基
本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向
同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求
解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法,
精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场,
从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供
的能量释放率. 作为以上理论的实际应用,最后给出了一个圆形片状裂纹问题
的精确解例和一个正方形片状裂纹问题的数值解例.
对受轴对称法向均布载荷作用下圆形片状裂纹问题,
讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解,
此结果与现有理论解完全一致. 相似文献
9.
The dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed. 相似文献
10.
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
11.
The solution of a 3-D rectangular permeable crack in a piezoelectric/piezomagnetic composite material was 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 relations between the electric filed,the magnetic flux field and the stress field near the crack edges were obtained and the efects of the shape of the rectangular crack on the stress,the electric displacement and magnetic flux intensity factors in a piezoelectric/piezomagnetic composite material were analyzed. 相似文献
12.
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
13.
《European Journal of Mechanics - A/Solids》2007,26(2):325-336
Dynamic stress intensity factor for a Griffith crack in functionally graded orthotropic materials under time-harmonic loading is investigated in the present paper. By using the Fourier transform and defining the jumps of displacement 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 components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors of the functionally graded orthotropic materials with a Griffith crack. 相似文献
14.
IntroductionCompositematerialconsistingofapiezoelectricphaseandapiezomagneticphasehasdrawnsignificantinterestinrecentyears,duetotherapiddevelopmentinadaptivematerialsystems .Itshowsaremarkablylargemagnetoelectriccoefficient,thecouplingcoefficientbetweenst… 相似文献
15.
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
16.
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
17.
Zhen-Gong Zhou Pei-Wei Zhang Guoqiang Li 《European Journal of Mechanics - A/Solids》2009,28(4):728-737
In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into dual integral equations, in which the unknown variables are the 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 relation between the electric field and the stress field near the crack tips was obtained. The results show that the stress and the electric displacement intensity factors at the crack tips depend on the lengths and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric materials. 相似文献
18.
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
19.
20.
The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials. 相似文献