功能梯度压电材料反平面裂纹问题

基于三维弹性理论和压电理论，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，进而对材料系数指数函数规律分布的半无限大压电体中的反平面裂纹问题进行了求解，利用Fourier变换给出了半无限大压电体中位移，应力，电势及电位移的解析表达式，并求得了裂纹尖端的应力强度因子和电位移强度因子，分析了不同的非均匀材料系数及几何尺寸对它们的影响。     

埋入压电元件的自诊断智能结构的理论分析与实验研究

将压电元件埋设于复合材料层板结构中，可实现结构应变分布的在线监测。本文提出一种采用压电应变传感器阵列和人工神经网络模型的自诊断方法，对局部埋入压电应变传感元件的平板结构进行了分析，采用神经网络模型根据压电传感器组的输出识别结构承载位置和大小，对该方法进行了数值模拟和实验验证。     

含压电层的功能梯度柱壳的自由振动分析

基于三维弹性理论，导出了带有压电层的圆柱形梯度壳的动力学方程以及相应的边界条件，用幂级数展开法得到了求解该圆柱形梯度壳自由振动的三维精确公式．通过实例模型求解了该壳体的自由振动的固有频率；分析了不同电学边界条件对壳体的振动频率的影响。结果可评估各种近似理论解和数值解的正确性。     

T-STRESS IN PIEZOELECTRIC SOLID

The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely isotropic piezoelectric solid for the plane problem was dealt with. The principle of superposition and the Plemelj formulation were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms are influenced by the elastic and electric constants.     

双周期裂纹压电材料反平面剪切问题断裂力学分析

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。     

The scattering of harmonic elastic anti-plane shear waves by two collinear cracks in the piezoelectric plate by using the non-local theory

In this paper, the dynamic interaction between two collinear cracks in a piezoelectric material plate under anti-plane shear waves is investigated by using the non-local theory for impermeable crack surface conditions. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. These equations are solved using the Schmidt method. This method is more reasonable and more appropriate. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The project supported by the Natural Science Foundation of Heilongjiang Province and the National Natural Science Foundation of China(10172030, 50232030)     

垂直磁压电材料界面三维裂纹的超奇异积分法

应用有限部积分概念和广义位移基本解，垂直于磁压电双材料界面三维复合型裂纹问题被转 化为求解一组以裂纹表面广义位移间断为未知函数的超奇异积分方程问题. 进而，通过主部 分析法精确地求得裂纹尖端光滑点附近的奇性应力场解析表达式. 然后，通过将裂纹表面 位移间断未知函数表达为位移间断基本密度函数与多项式之积，使用有限部积分法对超奇异 积分方程组建立了数值方法. 最后，通过典型算例计算，讨论了广义应力强度因子的变化规 律.     

Interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric material

The interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric medium is investigated. Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle. Based on the electroelastic fields derived, the stress and electric displacement intensity factors, the image force acting on the dislocation are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants. In the case where one of two phases is purely elastic, the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect, the position of the dislocation and the material properties on the interaction mechanism. The project supported by the Doctoral Foundation of Hebei Province (B2003113)     

线性分布荷载作用下梯度功能压电悬臂梁的解

采用逆解法求解了上表面受线性分布荷载作用的压电悬臂梁执行器，其中体积力$F_z$ 呈非线性分布. 首先确定了应力函数和电位移函数的多项式表达式，进而研究了该问题的 通解，以及体积力的不同分布对解答的影响. 常体积力和无体力情况下的解可以由上述 解直接得到. 本文为研究其它类型的压电梯度微观结构提供了一种可行的方法.     

压电传感器探测层合板分层的数值分析

用修正的准三维有限元法分析了受单轴拉伸表面覆盖有压电薄膜的复合材料层合板。文中首先讨论了压电薄膜层对层合板层间应力的影响，然后在存在分层裂纹的情况下，计算了压电层的电压分布。结果表明将压电薄膜作为传感器来进行分层探测是可行的。文中最后考虑了多种因素对传感灵敏度的影响。