有限厚压电层表面金属电极脱层的屈曲研究

INVESTIGATION ON THE BUCKLING OF DELAMINATION BETWEEN ELECTRODE AND PIEZOELECTRIC LAYER WITH FINITE THICKNESS

基于弹性有限变形理论和压电弹性体偏场理论,对上、下表面有金属电极的压电材料板内存在穿透脱层的屈曲问题进行了分析.采用平面应变模型,远处作用有均匀压应变载荷.用Fourier积分变换,界面连续条件和上、下电极表面的边界条件将问题归为第二类Cauchy型奇异积分方程组.利用Gauss-Chebyshev积分公式将该方程组变为一齐次线性代数方程组,以确定脱层屈曲载荷.算例给出了中间层为PZT-4,上、下电极为Pt的结构在不同脱层长厚比时的临界应变及相应屈曲形状.同时分析了压电层的机电耦合效应对临界应变的影响.

Based on the finite deformation theory of elasticity and the biasing field theory of piezoelec-tricity, delamination buckling between the metallic electrode and the piezoelectric layer of a sandwich plate subjected to a remote compressive loading is analyzed. The upper and lower surfaces are covered with metallic electrodes. The delamination is through the width of the plate. The problem is assumed to be plane strain. Fourier transform technique is employed to transform this problem into a set of homogeneous Cauchy-type singular integral equations of the second kind, which can be solved numerically through Gauss-Chebyshev integral formulae. As an example, a PZT-4 plate with platinum electrodes is considered. Numerical results for the critical strain of buckling and corresponding delaminate buckling configurations are presented for various ratios of the delamination length to the thickness of the electrode. The influences of the electromechanical coupling of the piezoelectric layer to the critical strains are also analyzed.