电弹性耦合偏微分方程组带型裂纹问题

Strip Crack Problem for Electroelastic Coupled Partial Differential Equations

摘要: 根据压电体中扩展的介质裂纹模型，本文讨论了压电带型机电荷载下的Griffith裂纹问题，在裂纹边界条件假设下，得到一组耦合偏微分方程组。运用傅立叶变换，将电弹性耦合偏微分方程组问题转化为求解第二类Fredholm类积分方程组。采用Lobatto-Chebyshev配置法，得到了非线性代数方程，并对其进行数值求解。通过数值计算分析了不同边界条件下断裂参量的变化规律并和已有实验结果进行了比较。

Abstract: Based on the extended dielectric crack model in piezoelectric materials, this study examines the Griffith crack problem in piezoelectric strip structures under electromechanical loading. By assuming specific crack boundary conditions, a system of coupled partial differential equations governing the electroelastic field is formulated. Applying Fourier transforms to convert the coupled partial differential equations into a system of the second kind Fredholm integral equations. The Lobatto-Chebyshev collocation method is used to form a nonlinear system of algebraic equations, which is solved by proposing an algorithm. Numerical results are carried out to show the variations of the fracture parameters of concern on the physical properties of the dielectric inside the crack under the two boundary conditions. the formats.