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含圆孤裂纹系的压电材料反平面应变问题 总被引:5,自引:0,他引:5
应用复变函数解析延展原理,并通过求解Riemann-Hilbert问题,得到了含圆弧裂纹压电材料反平面应变问题的一般解,对单个圆弧裂纹的情形,给出了封闭形式的复函数解和场强度因子,结果表明,当无限远处或裂纹表面同时受机械载荷(应力τ^∞或Tz)和电载荷(电位移D^∞或电荷q)联合作用时,应力强度因子仅与机械载荷有关,而电位移动强度因子仅与电载荷有关。 相似文献
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压电材料反平面应变状态的椭圆夹杂及界面裂纹问题 总被引:11,自引:0,他引:11
本文采用共法求解了压电材料反平面变形的椭圆夹杂及界面裂纹问题,前者的解答表明当远场外力均匀分布对夹杂内的应力场及电位移场是常量,后者解答表明在界面裂纹的裂尖处,应力及电位移都具有γ^-1/2的奇异性。 相似文献
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本文首次将不同弹性材料界面共圆弧裂纹版平面问题,化为解析函数边值问题,获得了一般解答,由此求出了几种典型情况的精确解,算出了应力强度因子。当两种材料相同时,本文结果与文[S]完全吻合。 相似文献
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压电材料反平面应变状态的任意形状夹杂问题 总被引:4,自引:0,他引:4
应用复函数的Faber级数展开方法,分析了含任意形状夹杂的压电材料反平面应变问题,给出了问题的复势函数解。利用这个解,具体讨论了椭圆形夹杂及其极限(几何方面与物理方面)问题。并给出了三角形、正方形夹杂的近似结果。其特例结果与早期工作一致 相似文献
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研究压电材料双周期裂纹反平面剪切与平面电场作用的问题.运用复变函数方法,获得了该问题严格的闭合解,并由此给出了裂纹尖端应力强度因子和电位移强度因子的精确公式.数值算例显示了裂纹分布特征对材料断裂行为的重要影响.叠间小裂纹能够对主裂纹的应力和电位移场起着屏蔽作用,相反行间小裂纹却起着放大作用,至于钻石形分布裂纹的影响规律则更为复杂.对于某些特殊情形给予了解答并导出一系列有意义的结果。 相似文献
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压电材料中心裂纹问题 总被引:6,自引:3,他引:3
以电位移法向分量及电势连通过裂纹面为边界条件,对均匀电材料的裂纹问题及两种不同压材料界面裂纹问题进行了系统分析,得到了含中心裂纹无限大体封闭形的全场解。证实了裂纹引起的非均匀扰动场只信赖于外加场而外加电场无关。 相似文献
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圆形界面裂纹反平面问题的基本奇异解 总被引:4,自引:0,他引:4
本文研究反平面集中力作用下,不同弹性材料的圆形界面上有多条裂纹的问题。运用复变函数的解析延拓技术与奇性主部分析方法,首次获得该问题的一般解答,求出了几种典型情况的封闭解;算出了应力强度因子,并由此导出一系列特殊结果,其中几个与已有文献完全吻合。 相似文献
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利用积分变换技术,得到不同压电介质界面上的平面运动裂纹问题的分析解。结果表明应力及电位移强度因子均与界面裂纹扩展速度及材料参数相关,这不同于均匀压电介质中运动裂纹的结论,当两种压电介质完全相同时,本文结果将退化为均匀压电介质中反平面运动裂纹问题的解。 相似文献
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Analysis of Two Collinear Cracks in a Piezoelectric Layer Bonded to Two Half Spaces Subjected to Anti-plane Shear 总被引:1,自引:0,他引:1
In this paper, the behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by a new method for the impermeable crack face conditions. The cracks are parallel to the interfaces in the mid-plane of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks. 相似文献
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The generalized two-dimensional problem of a dielectric rigid line inclusion, at the interface between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh theory. The problem was reduced to a Hilbert problem, and then closed-form expressions were obtained, respectively, for the complex potentials in piezoelectric media, the electric field inside the inclusion and the tip fields near the inclusion. It is shown that in the media, all field variables near the inclusion-tip show square root singularity and oscillatory singularity, the intensity of which is dependent on the material constants and the strains at infinity. In addition, it is found that the electric field inside the inclusion is singular and oscillatory too, when approaching the inclusion-tips from inside the inclusion. 相似文献
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In this paper, we report on an experimental study of spontaneous, mixed-mode, crack propagation in weakly bonded similar and
dissimilar materials. A unique experimental configuration is proposed to induce spontaneous crack growth events along the
interfaces. The cracks nucleate from tiny circular holes and are triggered by an exploding wire. They subsequently propagate
under the action of a constant, far-field load. Dynamic photoelasticity in conjunction with high speed photography is used
to capture the real-time isochromatics associated with crack propagation. In the case of identical materials, crack propagation
is anti-symmetric with respect to the crack nucleation point while strong asymmetry is observed for the case of dissimilar
materials. In both cases, cracks propagate at constant velocity from the initiation point. The time histories of dynamic stress
intensity factors and of energy release rates of the propagating cracks along the bonded similar materials are also reported. 相似文献
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Alessandra Borrelli Cornelius O. Horgan M. Cristina Patria 《Journal of Elasticity》2001,64(2-3):217-236
This paper is concerned with further investigation of the effect of mechanical/electrical coupling on the decay of Saint-Venant end effects in linear piezoelectricity. Saint-Venant's principle and related results for elasticity theory have received considerable attention in the literature but relatively little is known about analogous issues in piezoelectricity. The current rapidly developing smart structures technology provides motivation for the investigation of such problems. The decay of Saint-Venant end effects is investigated in the context of anti-plane shear deformations for linear homogeneous piezoelectric solids. For a rather general class of anisotropic piezoelectric materials, the governing partial differential equations of equilibrium are a coupled system of second-order partial differential equations for the mechanical displacement u and electric potential ?. The traction boundary-value problem with prescribed surface charge can be formulated as an oblique derivative boundary-value problem for this elliptic system. Energy-decay estimates using differential inequality methods are used to study the axial decay of solutions on a semi-infinite strip subjected to non-zero boundary conditions only at the near end. This analysis is carried out for a rather general class of materials (the tetragonal ${\bar 4}$ crystal class). The boundary-value problem involves a full coupling of mechanical and electrical effects. There are four independent material constants appearing in the problem. An explicit estimated decay rate (a lower bound for the actual decay rate) is obtained in terms of two dimensionless piezoelectric parameters d 0,r, the first of which provides a measure of the degree of piezoelectric coupling. The estimated decay rate is shown to be monotone decreasing with increasing values of the coupling parameter d 0. In the limit as d 0→0, we recover the exact decay rate for the purely mechanical case. Thus, for the tetragonal ${\bar 4}$ class of materials, piezoelectric end effects are predicted to penetrate further into the strip than their elastic counterparts, confirming recent results obtained in other contexts in linear piezoelectricity. 相似文献
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研究含双周期分布的圆形刚性夹杂在无穷远受纵向剪切的弹性平面问题,遵循复合材料中各夹杂相互影响的重要条件。采用复变函数方法。构造相应模型的复应力函数。通过坐标变换,同时满足夹杂边界位移条件,再利用围线积分将求争方程组化为线性代数方程组。导出了圆形刚性夹杂双周期分布的界面应力解析表达式。算例给出了界面应力最大值与夹杂间距的变化规律。求出了刚性夹杂的合理间距问题,本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。 相似文献