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Diffraction of elastic waves in the plane multiply-connected region and dynamic stress concentration
盖秉政 《应用数学和力学(英文版)》1986,7(1):25-37
This paper deals with the problem of diffraction of elastic waves in the plane multiply-connected regions by the theory of complex functions. The complete function series which approach the solution of the problem and general expressions for boundary conditions are given.’ Then the problem is reduced to the solution to infinite series of algebraic equations and the solution can be directly obtained by using electronic computer. In particular, for the case of weak interaction, an asymptotic method is presented here, by which the problem ofp waves diffracted by a circular cavities is discussed in detail. Based on the solution of the diffracted wave field the general formulas for calculating dynamic stress concentration factor for a cavity of arbitrary shape in multiply-connected region are given. 相似文献
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Elastic wave scattering and dynamic stress concentrations in exponential graded materials with two elliptic holes 总被引:1,自引:0,他引:1
Based on the elastodynamics, employing complex functions and conformal mapping methods, and local coordinates, the scattering of elastic waves and dynamic stress concentrations in infinite exponential graded materials with two holes are investigated. A general solution of the problem and expression satisfying the given boundary conditions are derived. The problem can be reduced to the solution of an infinite system of algebraic equations. As an example, numerical results of dynamic stress concentration factors for two elliptic holes in exponential graded materials are presented, and the influence of incident wave number and holes spacing on dynamic stress distributions is analyzed. 相似文献
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SH波对双相介质界面附近圆形孔洞的散射 总被引:10,自引:1,他引:10
建立了求解平面SH波对双相介质界面附近圆形孔洞散射与动应力集中的一种分析方法.利用复变函数与多极坐标的方法构造了一个Green函数,它是在含有圆形孔洞的弹性半空间的水平面上任一点上作用时间谐和的出平面线源荷载的位移解.利用“契合”模型,并根据界面上位移连续性条件,建立了求解SH波对双相介质界面附近圆形孔洞散射的具有弱奇异性的第一类Fredholm型积分方程.给出了圆孔周边上动应力集中系数的表达式.作为算例,分析了在界面一侧或界面两侧附近具有圆形孔洞时SH波的散射,并讨论了入射波波数、不同的材料组合以及孔心至界面的距离对动应力集中的影响. 相似文献
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SH波作用下界面任意形状孔洞附近的动应力集中 总被引:1,自引:0,他引:1
采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数.最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响. 相似文献
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Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface 总被引:1,自引:0,他引:1
An analytical method is developed for scattering of SH-waves and dynamic stress concentration by an interacting interface crack and a circular cavity near bimaterial interface. A suitable Green‘s function is contructed, which is the fundamental solution of the displacement field for an elastic half space with a circular cavity impacted by an out-plane harmonic line source loading at the horizontal surface. First, the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and the other is a complete half space. Then the problem is solved according to the procedure of combination and by the Green‘s function method. The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, or with some forces to recover cracks by means of crack-division technique. A series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions as expressed in terms of the Green‘s function. Moreover, some expressions are given in this paper, such as dynamic stress intensity factor (DSIF) at the tip of the interface crack and dynamic stress concentration factor (DSCF) around the circular cavity edge. Numerical examples are provided to show the influences of the wave numbers, the geometrical location of the interface crack and the circular cavity, and parameter combinations of different media upon DSIF and DSCF. 相似文献
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本文提出一个计及轴销变形与接触区摩擦效应的弹性轴销模型,并采用弹性理论的复变函数解法,研究了正交各向异性无限大板的孔销接触问题.分析表明,板件的孔边应力分布与板件、轴销的材料性能密切相关,而且,摩擦系数的大小对应力分布也存在明显影响. 相似文献
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Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method (GCTM). The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor (DSCF) becomes singular when the inhomogeneity parameter of medium is close to zero. 相似文献
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Diffraction of an antiplane shear wave by two coplanar griffith cracks in an infinite elastic medium
The scattering of a time-harmonic antiplane shear wave by two parallel and coplanar Griffith cracks embedded in an infinite elastic medium is considered. The input wave normally impinges on the cracks. Fourier transformations are utilized to reduce the problem to two simultaneous integral equations which can be solved by the series expansion method. The dynamic stress intensity factors are numerically computed. 相似文献
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Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese. 相似文献
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The interaction of a general plane P wave and an elastic cylindrical inclusion of infinite length partially debonded from
its surrounding viscoelastic matrix of infinite extension is investigated. The debonded region is modeled as an arc-shaped
interface crack between inclusion and matrix with non-contacting faces. With wave functions expansion and singular integral
equation technique, the interaction problem is reduced to a set of simultaneous singular integral equations of crack dislocation
density function. By analysis of the fundamental solution of the singular integral equation, it is found that dynamic stress
field at the crack tip is oscillatory singular, which is related to the frequency of incident wave. The singular integral
equations are solved numerically, and the crack open displacement and dynamic stress intensity factor are evaluated for various
incident angles and frequencies.
The project supported by the National Natural Science Foundation of China (19872002) and Climbing Foundation of Northern Jiaotong
University 相似文献
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《International Journal of Solids and Structures》2007,44(22-23):7340-7356
This paper investigates transient stresses around a cylindrical crack in an infinite elastic medium subject to impact loads. Incoming stress waves resulting from the impact load impinge on the crack in a direction perpendicular to the crack axis. In the Laplace transform domain, by means of the Fourier transform technique, the mixed boundary value equations with respect to stresses and displacements were reduced to two sets of dual integral equations. To solve the equations, the differences in the crack surface displacements were expanded in a series of functions that are zero outside the crack. The boundary conditions for the crack were satisfied by means of the Schmidt method. Stress intensity factors were defined in the Laplace transform domain and were numerically inverted to physical space. Numerical calculations were carried out for the dynamic stress intensity factors corresponding to some typical shapes assumed for the cylindrical crack. 相似文献
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基于线性压电动力学理论,采用波函数展开法、保角映射以及复变函数,对含非圆孔洞无限大压电薄板弹性波的散射及动应力集中问题进行了分析,给出了其动弯矩集中系数(DMCF)的解析表达式。为说明问题,以PZT-4为例,讨论了外加电场、椭圆孔长短半轴比、椭圆孔倾角以及入射波频率对含圆孔和椭圆孔无限大压电薄板弹性波散射的影响,并分别给出了无限压电薄板开圆孔和椭圆孔动弯矩集中系数的数值结果。 相似文献
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R. Paskaramoorthy S. Bugarin R.G. Reid 《International Journal of Solids and Structures》2011,48(14-15):2255-2263
The fracture and fatigue properties of porous materials are strongly influenced by stress concentrations around the pores. In addition, failure of structural components initiates at locations of high stress concentration which is often caused by holes, inclusions or other discontinuities. In view of this, the stress concentration around a spheroidal cavity embedded in an elastic medium is studied under dynamic loading conditions. While solutions abound for static loads, only limited solutions exist for dynamic loads. The stress field around a spheroidal cavity is determined by using a hybrid methodology that combines the finite element technique with a spherical wave function expansion method. The stress concentrations within the matrix are found to be dependent on the frequency of excitation, aspect ratio of the cavity and the Poisson’s ratio of the matrix. The study reveals that dynamic stress concentrations can reach much higher values than those encountered under static loading. 相似文献
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V. V. Mikhas’kiv I. O. Butrak I. P. Laushnik 《Journal of Applied Mechanics and Technical Physics》2013,54(3):465-471
The propagation of harmonic elastic wave in an infinite three-dimensional matrix containing an interacting low-rigidity disk-shaped inclusion and a crack. The problem is reduced to a system of boundary integral equations for functions that characterize jumps of displacements on the inclusion and crack. The unknown functions are determined by numerical solution of the system of boundary integral equations. For the symmetric problem, graphs are given of the dynamic stress intensity factors in the vicinity of the circular inclusion and the crack on the wavenumber for different distances between them and different compliance parameters of the inclusion. 相似文献
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采用Green函数法研究界面上含圆孔边界径向有限长度裂纹的两半无限压电材料对SH波的散射和裂纹尖端动应力强度因子问题.首先构造出具有半圆型凹陷半空间的位移Green函数和电场Green函数,然后采用裂纹"切割"方法构造孔边裂纹,并根据契合思想和界面上的连接条件建立起求解问题的定解积分方程.最后作为算例,给出了孔边界面裂纹尖端动应力强度因子的计算结果图并进行了讨论. 相似文献