拼接梯度压电材料中多裂纹的响应问题

研究了拼接梯度压电材料中多裂纹的响应问题,考虑关于y轴对称的材料结构,多个裂纹分布在x轴上.运用傅里叶变换技术并结合边界条件将混合边值问题转化为第一类奇异积分方程.引入位错函数,并且通过高斯-切比雪夫方法对积分方程进行求解,得出切应力和电位移的解析表达式以及裂纹端的强度因子表达式.最后借助MATLAB进行数值算例分析,给出裂纹端强度因子受裂纹间距、裂纹几何尺寸、梯度参数以及材料带宽比的影响情况.

Response of multiple cracks in stitched graded piezoelectric materials

In this paper, the anti-plane problem of multi-cracks in tiled gradient piezoelectric materials discussed. Considering the material structure with respect to axial symmetry, there are n cracks distributed along the x-axis. The mixed boundary value problem is transformed into the first kind of singular integral equation by using the Fourier transform technique and the boundary condition, and the dislocation function is introduced, and the integral equation is solved by the Gauss-Chebyshev method, the analytical expressions of shear stress and electric displacement and the strength factor of crack tip are obtained. Finally, numerical examples are given by Matlab to show the influence of crack spacing, crack geometric size, gradient parameters and material width ratio on the strength factor at the crack tip.