杨昌锦， 李尧臣^*

（  同济大学；  ）

摘要： 基于弹性有限变形理论和电弹性体的偏场理论，本文对有限厚度压电层及其上、下表面金属电极构成的三层结构内存在穿透脱层在纯弯曲载荷作用下电极局部脱层的屈曲问题进行了分析。采用平面应变模型，在脱层的远处作用有纯弯矩载荷。采用分层法，将整个有限厚度分成若干子层，对每一子层使用Fourier积分变换技术，结合脱层界面、子层间的连续条件和上、下电极表面的边界条件将此问题归为第二类Cauchy型奇异积分方程组。利用Gauss-Chebyshev积分公式将奇异积分方程组变为一组2N个齐次线性代数方程组，以确定临界应变载荷。在算例中，用Mathematica编程分析，给出了中间为PZT-4压电层，上、下电极为金属Pt的结构体系的电极局部脱层在不同脱层长厚比时的临界弯矩和脱层形状。并与有限元分析的结果进行了对比，两者吻合很好，说明了本文方法及求解过程是正确的。
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

Yang Changjin， Li Yaochen^*

（  Tongji University；  ）

Abstract： Based on the finite displacement theory of elasticity and the biasing field theory of the electro-elastic body, electrode delamination buckling of the layered system with finite thickness containing a through-the-width delamination between the metallic electrode and the piezoelectric layer is analyzed. In the plane strain problem, layered system subjected to the pure bending load is reduced to a system of homogeneous Cauchy-type singular integral equations of the second kind by means of the Fourier integral transform，boundary condition and interfacial continuous condition. The singular integral equations are solved numerically by utilizing Gauss-Chebyshev integral formulae. As an example, the finite sized layered system of the metallic electrode material Pt and piezoelectric material PZT-4 is considered. Numerical results for the critical buckling bending moments and corresponding delamination buckling shapes are presented for various ratios of the delamination length to thickness.

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