功能梯度压电夹层板条中的反平面裂纹问题

本文研究了夹在两个均匀压电材料半空间中功能梯度压电板条内的反平面裂纹问题。假设功能梯度压电夹层板条的材料参数沿厚度方向连续变化，并考虑裂纹面上电绝缘型和电渗透型两种边界条件。利用Fourier变换，首先将混合边值问题转化为对偶积分方程，即而归结为求解第二类Fredholm积分方程。通过数值计算，求得了功能梯度压电夹层板条内反平面裂纹的应力强度因子、电位移强度因子和能量释放率，分析了材料物性参数梯度、几何尺寸和载荷条件对它们的影响。

Anti-plane shear crack in a functionally gradient piezoelectric layer bonded to dissimilar half spaces

In this paper the problem of a crack located in a functionally graded piezoelectric interlayer between two dissimilar homogeneous piezoelectric half planes and subjected to an anti-plane mechanical loading and an in-plane electric loading is considered. The material properties of the interlayer, such as the elastic stiffness, piezoelectric constant and dielectric constant, are assumed to vary continuously along the thickness of the interlayer, and the crack surface condition is assumed to be impermeable or permeable. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into a Fredholm integral equation of the second kind. Numerical calculations are carried out, and the stress and electric field intensity factors and the energy release rate are shown graphically for piezoelectric ceramics.