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压电切口张开角和深度对其尖端力电损伤场的影响 总被引:2,自引:1,他引:1
基于三维各向异性压电损伤本构理论,导出了广义平面应力问题的损伤本构方程,并据此分析了压电薄板板边V形切口尖端附近的力电损伤,研究了切口张开角和深度对切口尖端力电损伤的影响规律.结果发现:和张开角对切口尖端损伤的影响相比,深度的影响更为明显;在张开角对切口尖端力损伤的影响规律方面,压电材料与一般弹塑性材料存在明显差异,原因在于压电切口尖端力电载荷比会随着深度的改变发生很大变化;不同深度下张开角与切口尖端力、电损伤关系曲线随着张开角的增大由发散逐渐会聚,不同张开角下深度与切口尖端力、电损伤关系曲线随着切口加深由会聚逐渐发散,并且电损伤曲线表现得更为明显. 相似文献
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层状压电陶瓷致动器中力电耦合场奇异性的数值分析 总被引:2,自引:0,他引:2
首先推导了不同压电材料界面裂纹尖端处的扇形区域内包含基本方程、裂纹面D-P边界条件和交界面处边界条件的弱形式。通过假设力电耦合位移场(位移和电势)与到裂纹尖端距离的(λ 1)次方成正比,可以得到一个分析压电材料裂纹尖端处力电耦合场奇异性的特殊的一维有限元列式。该一维有限元列式只需对扇形区域在角度方向上离散,最后的总体方程为一个关于λ的二次特征根方程。探讨了层状压电陶瓷致动器中可能出现奇异力电耦合场的部位的裂纹面边界条件及交界面处边界条件,进而将该一维有限元法进行推广,用于研究了这些部位的力电耦合场的奇异性。通过数值算例与相应的精确解的比较表明该方法是正确的,而且仅用很少单元就可以得到非常精确的结果。 相似文献
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建立了含裂纹损伤的曲梁压电能量俘获系统在强迫振动下的动力学模型. 基于Prescott型压电曲梁力电耦合振动方程的解析解和裂纹截面处的连续性条件, 求解了含裂纹损伤的压电曲梁的格林函数. 根据线性叠加原理, 对含裂纹的力电耦合模型的系统方程解耦, 得到强迫振动下含裂纹损伤的曲梁压电俘能器的输出电压. 在得到模型的强迫振动解析解后, 提出逆方法检测结构中的裂纹损伤, 这一检测方法适用于处于振动状态下的结构. 在数值计算中, 令裂纹深度为零, 通过对比本文的解析解与现有文献中的解析解, 验证了本文解的有效性. 分别分析了含裂纹损伤的压电曲梁的电压响应与裂纹深度、裂纹位置、材料的几何参数以及阻尼之间的关系. 研究结果表明: 裂纹的存在对曲梁式压电俘能器的影响比直梁式更加复杂; 裂纹出现时, 损伤曲梁在健康曲梁的一阶频率值处一定会出现波动并被激励出二阶频率, 此时的二阶频率是开路中健康压电曲梁的一阶频率值; 通过对电压响应的检测可以确定的损伤裂纹的深度和在结构中出现的位置范围; 利用振动问题的解来检测压电曲梁的健康状况是可行且准确的. 相似文献
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平面问题中弹性压电材料的本构关系及应用 总被引:6,自引:0,他引:6
本文在三维压电材料本构方程的基础上,推导出二维压电材料的机电耦合方程系统,并分析了受轴向力,弯矩作用时的位移和电势分布情况。 相似文献
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压电材料裂纹顶端条状电饱和区模型的力学分析 总被引:3,自引:0,他引:3
在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析.完整地考虑了各向异性力电耦合效应.建立了电饱和区尺寸与外加电场的依赖关系.证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加.当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响 相似文献
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在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析.完整地考虑了各向异性力电耦合效应.建立了电饱和区尺寸与外加电场的依赖关系.证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加.当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响. 相似文献
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Both the mechanical and the electrical damages are introduced to study fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are proposed by using the damage theory combined with the well-known piezoelectric fracture experiments of Park and Sun [Fracture criteria of piezoelectric ceramics, J. Am. Ceram. Soc. 78 (1995) 1475-1480]. One is based on a critical state of the mechanical damage and the other on a critical value of a proper linear combination of both the mechanical and the electrical damage variables. It is found that the fracture load predicted, which takes the mechanical damage into account only (mode 1), has greater deviation than predicted result by considering a proper linear combination of the mechanical and the electrical damages (mode 2). And the fracture criterion corresponding to mode 2 presented is shown to be superior to mode 1. It is also demonstrated that the mechanical damage has greater effect on fracture than the electrical damage. 相似文献
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WangBaolin HanJiecai DuShanyi 《Acta Mechanica Solida Sinica》2004,17(4):290-296
The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is consi… 相似文献
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Introduction Brittlenessmightresultinmicro_crackordamageinthepiezoelectricmediasubjectedto variousexternalmechanicalandelectricalloads.Thesedefectswilldevelopgraduallyand eventuallyemergeintomacrocracksandevenleadtothefailureofpiezoelectricdevices. Therefore,itisimportantthatthefracturemechanismofpiezoelectricceramicsisinvestigatedin detailfirstsothatthereliabilitypredictionandlifetimeestimationofpiezoelectricdevicescanbe made.Ithasbeenconfirmedthatthereexistsanunexplaineddiscrepancybetweensom… 相似文献
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Wenjun Zeng Majid T. Manzari James D. Lee Yin-Lin Shen 《Mechanics Research Communications》2003,30(3):267-275
Rational design of smart sensors and actuators that consist of piezoelectric solids requires a thorough understanding of the constitutive behavior of this material under mechanical and electrical loading. Domain switching is the cause of significant nonlinearity in the constitutive behavior of piezoelectric solids, which may be enhanced in the presence of cracks. In this paper, the response of piezoelectric solids is formulated by coupling thermal, electrical, and mechanical effects. The corresponding finite element equations are derived and applied in the solution of the piezoelectric center crack problems. The effects of domain switching are evaluated on the near tip stress intensity factors. 相似文献
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分析了橡皮类薄膜缺口顶端的弹性场,借助于文[1]引入的本构关系得到了缺口顶端场的渐近方程.通过将缺日顶端场划分为收缩角区和扩张角区,得到了顶端场的解.该解表明,奇异特性与本构参数和缺口角度有关,这一结论得到了数值解的证实. 相似文献
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Stress-strain field near the notch tip of a rubber sheet 总被引:1,自引:0,他引:1
Analized in this paper is the elastostatic field near a notch tip in a rubber-like thin sheet. The asymptotic equations for
the notch tip field are derived based on the constitutive relation given by Ref. [1]. Near field solutions are obtained in
regions that decreases and increases in size as the notch tip is approached. Their singular character depends on the constitutive
parameters as well as the angle of notch that is evaluated numerically.
The project supported by the National Natural Science Foundation of China 相似文献
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《International Journal of Solids and Structures》2002,39(7):1743-1756
Using the integral transform and the Cauchy singular integral equation methods, the problem of an interface crack between two dissimilar piezoelectric layers under mechanical impacts is investigated under the permeable electrical boundary condition on the crack surface. The dynamic stress intensity factors (DSIFs) of both mode-I and II are determined. The effects of the crack configuration and the combinations of the constitutive parameters of the piezoelectric materials on the dynamic response are examined. The numerical calculation of the mode-I plane problem indicates that the DSIFs may be retarded or accelerated by specifying different combinations of material parameters. In addition, the parameters of the crack configuration, including the ratio of the crack length to the layer width and the ratio between the widths of two layers, exert a considerable influence on the DSIFs. The results seem useful for design of the piezoelectric structures and devices of high performance. 相似文献
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YangXinhua ChenChuanyao HuYuantai 《Acta Mechanica Solida Sinica》2003,16(2):147-154
The finite element formulation for analyzing static damage near a conducting crack in a thin piezoelectric plate is established from the virtual work principle of piezoelectricity. The damage fields under various mechanical and electrical loads are calculated carefully by using an effective iterative procedure. The numerical results show that all the damage fields around a crack tip are fan-shaped and the electric field applied has great influence on the mechanical damage,which is related to the piezoelectric properties. 相似文献