压电复合材料的共线周期性裂纹平面问题的电弹性场分析

Electroelastic field analysis for the plane problem of piezoelectric composite material with collinear periodic cracks

利用复变函数知识、半逆解法及待定系数法,研究了压电复合材料的共线周期性裂纹问题,给出了在电不可渗透边界条件下的应力、电位移、应力强度因子、电位移强度因子和机械应变能释放率的解析解。当裂纹间距趋于无穷时,共线周期性裂纹退化为一条单裂纹,得到了压电复合材料一条单裂纹的结果。通过数值算例讨论了共线周期性裂纹的裂纹长度、裂纹间距和机电载荷对机械应变能释放率的影响规律。结果表明,机械应变能释放率随着共线周期性裂纹的裂纹长度、共线周期性裂纹的裂纹间距、机械载荷和正电场的增大而增大,随着负电场的增大而减小。

Using the complex-variable function knowledge,half-inverse method and undetermined coefficient method,the problem about piezoelectric composite material with collinear periodic cracks was investigated.The analytical solutions of the stress,electric displacement,the stress field intensity factor,electric displacement intensity factor and mechanical stain energy release rate were given explicitly with the assumption that the surface of the crack was electrically impermeable.When the distance of adjacent cracks tended to infinite,collinear periodic of cracks degenerated into a single crack,piezoelectric composite material with a single crack results was obtained.Numerical examples were given to discuss the influences of the length of the collinear periodic cracks,the distance of adjacent cracks of the collinear periodic cracks and the electromechanical loads on the mechanical stain energy release rate.The results show that mechanical stain energy release rate enhances as the length of collinear periodic cracks,the distance of adjacent collinear periodic cracks,mechanical loading,positive electric field increase,however,mechanical stain energy release rate reduces as the negative electric field increases.