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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 knowledge of complex functions, semi-inverse solution and undetermined coefficient method, the problem of collinear periodic crack in piezoelectric composites was studied. The stress, electric displacement, stress intensity factor, electric displacement Analytic solution of strength factor and mechanical strain energy release rate. When the crack spacing tends to infinity, the collinear periodic cracks degenerate into a single crack, resulting in a single crack in the piezoelectric composite. Numerical examples are given to discuss the influence of crack length, crack spacing and electromechanical load on the mechanical strain energy release rate of collinear periodic cracks. The results show that the mechanical strain energy release rate increases with the crack length of the collinear periodic cracks, the crack spacing of the collinear periodic cracks, the mechanical load and the positive electric field, and decreases with the increase of the negative electric field.