摘要
基于弹性有限变形理论和电弹性体偏场理论,对半无限压电体及其表面电极层间存在穿透脱层的屈曲问题进行了分析.采用平面应变模型,在脱层远处作用有平行于脱层的应变载荷.使用Fourier积分变换,应用脱层界面的连续条件和电极表面的边界条件将问题归为第2类Cauchy型奇异积分方程组.利用Gauss-Chebyshev积分公式将奇异积分方程组变为齐次线性代数方程组,以确定临界应变载荷.通过数值算例,给出了底层为PZT-4材料、电极为金属Pt在不同的脱层长厚比时的临界应变载荷和屈曲形状,分析了压电体的压电、介电效应对屈曲载荷的影响.另外给出了脱层屈曲时,脱层尖端奇异性振荡因子随不同脱层长厚比的关系曲线.
The paper investigated the electrode delamination buckling of the layered system containing a through-the-width delamination between the metallic electrode and the half-space piezoelectric substrate based on the finite deformation theory of elasticity and the biasing field theory of the electroelastic body. The layered system in the plane strain problem is subjected to the compressive strain-load parallel to the free surface. Mean- while, the theoretical model is reduced to the second kind Cauchy-type singular integral equations by means of the Fourier integral transform, the boundary conditions and the interfacial continuous conditions. The singular integral equations are solved numerically by utilizing Gauss-Chebyshev integral formulae. As an example, the layered system of the metallic electrode Pt and piezoelectric substrate PZT-4 is considered. Numerical results for the critical strains of buckling and the corresponding delamination buckling shapes are prosented for, respectively, various ratios of the delamination length to thickness and the effect of electromechanical coupling in the piezoelectric substrate. The curves of the singular oscillating factors in the delamination tip with respect to the ratios of delamination length to thickness are also given.
出处
《力学学报》
EI
CSCD
北大核心
2009年第4期489-502,共14页
Chinese Journal of Theoretical and Applied Mechanics
基金
教育部博士点基金资助项目(20050247004)~~
关键词
电极脱层
屈曲
Fourier积分变换
奇异积分方程
临界应变载荷
electrode delamination, buckling, Fourier integral transform, singular integral functions, critical strains
