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中文摘要：
本文利用复变函数方法，借助于Riemann—Schwarz延拓技术和保形映照方法，研究了渗透性边界条件下周期共线反平面裂纹问题，获得了解的表达式，得到了力学和电学强度因子。结果表明在裂纹尖端应力和电位移的奇异性都与远场作用的应力载荷和裂纹长度有关，其中应力的奇异性与材料无关，电位移的奇异性则与材料有关，电载荷对裂尖的奇异性没有影响。最后，运用数值算例，给出周期裂纹问的干涉效应和裂纹的尺度效应。
英文摘要：
In this paper, the anti-plane problems of the periodic collinear crack in an infinite piezoelectric material are investigated by using the complex variable method in the case of permeable boundary condition. By continuation technology and conformal mapping~ explicit solutions are obtained~ and the formulae for the stress intensity factors and electric displacement intensity factors are derived. We conclude that the singularity of stress and electric displacement is dependent on stress and length of crack, and the singularity of stress is independent of material constant, but contrary to the singularity of electric displacement. The electric loading has no effect on the field singularities. Finally, the interaction effects and scale effects of periodicity are illustrated by figures.
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