【作者】 马海龙；

【导师】 李星；

【作者基本信息】 宁夏大学 ， 应用数学， 2004， 硕士

【摘要】 本文共分五部分： 第一部分简要介绍功能梯度压电材料中动态裂纹问题的发展历史、研究现状、电弹性动态控制方程及本文研究的主要内容。 第二部分研究无限大功能梯度压电材料中反平面Yoffe型运动裂纹问题。 第三部分研究半无限大功能梯度压电材料中反平面Yoffe型运动裂纹问题。 第四部分研究功能梯度压电带型材料中反平面Yoffe型运动裂纹问题。 第五部分对全文进行了简要的总结并且提出了一些今后感兴趣的工作。 中间三部分内容都是在三维弹性理论和压电理论的基础上，首先导出了材料系数在横观各向同性平面内梯度分布的压电体的状态方程，进而对材料系数按各部分所提出的规律分布的压电体中的反平面Yoffe型运动裂纹问题进行了求解；首先使用Fourier变换，然后求解对偶积分方程，分别给出了无限大、半无限大及带型压电体中应力、电势、电场强度及电位移的解析表达式；通过使用Matlab语言分别求出了各部分裂纹尖端动应力强度因子、电位移强度因子及电场强度因子的大小及相应的数值结果，最后均分析了不同的非均匀材料系数、几何因素及裂纹运动速度对它们的影响。 本文结果可以用来指导功能梯度压电材料的设计和各种压电元件的性能预报。更多还原

【Abstract】 This thesis constitute of five parts.In the first part, the historical development and the basic equations of functionally graded piezoelectric materials are briefly introduced.The second part focus on the anti-plane moving Yoffe-crack problem in an infinite plane of functionally graded piezoelectric materials.The third part is about the anti-plane moving Yoffe-crack problem in a half plane of functionally graded piezoelectric materials.The fourth part lays emphasis upon anti-plane moving Yoffe-crack problem in a strip of functionally graded piezoelectric materials.The last part sums the thesis briefly and put forward to the furthermore research in the near future.Based on the three-dimensional theory of piezoelectric elasticity, the governing equations are deduced for the functionally graded piezoelectric materials, and the anti-plane fracture problems for piezoelectric medium are solved for three cases. We get the displacement, stress, electric potential and electric displacement around the crack in an infinite plane of functionally graded piezoelectric materials, a half plane of functionally graded piezoelectric materials and a strip of functionally graded piezoelectric materials by Fourier Transforms, respectively. Numerical results of the dynamic stress intensity factor, electric displacement intensity factor and electric field intensity factor near the crack tip are obtained by the way of MATLAB. Finally, the influences of different nonhomogene-ous material properties, geometrical size and the moving velocity of .the crack (v/c) on dynamic stress intensity factor, electric displacement intensity factor and electric field intensity factor are revealed.The results of this thesis may guide the design of functionally graded piezoelectric materials and forecast the function of piezoelectric medium.更多还原