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应用复变函数解析延展原理,并通过求解Riemann-Hilbert问题,得到了含圆弧裂纹压电材料反平面应变问题的一般解;对单个圆弧裂纹的情形,给出了封闭形式的复函数解和场强度因子。结果表明:当无限远处或裂纹表面同时受机械载荷(应力τ~∞或T_z)和电载荷(电位移D~∞或电荷q)联合作用时,应力强度因子仅与机械载荷有关,而电位移强度因子仅与电载荷有关。
The extended principle is solved by the complex function, and the general solution to the anti-plane strain problem of the circular arc cracked piezoelectric material is obtained by solving the Riemann-Hilbert problem. For the case of a single arc crack, the closed form complex function solution And field strength factor. The results show that the stress intensity factor is only related to the mechanical load when both the mechanical load (stress τ ~ ∞ or T_z) and the electrical load (electrical displacement D ~ ∞ or charge q) are combined at infinity or at the crack surface simultaneously. Displacement strength factor is only related to electric load.