中文摘要：

研究双周期带涂层纤维压电复合材料反平面问题。利用Eshelby等效夹杂原理引入特征应变和特征电场,并结合双准周期Riemann边值问题理论,获得了问题在反平面机械载荷和面内电载荷作用时的解析解。由本文解的特殊情形可以退化为已有结果。数值算例考察了复合材料内部应力和电场随复合材料各组分电弹参数的变化规律,研究了纤维排列方式和纤维体积分数对复合材料有效电弹系数的影响。带涂层纤维正六边形排列时的有效电弹系数与广义自洽方法的预测结果非常接近。结果对新型航空材料的设计和优化具有参考价值。

英文摘要：

The work addresses piezoelectric composites with doubly periodically distributed coated fiber under antiplane shear and inplane electrical field. By applying Eshelby＇s equivalent inclusion method, the eigenstrain and eigen-electrical-field concepts are introduced. Then combining the theory of doubly quasi-periodlc Riemann boundary value problem, an analytical solution to the problem is obtained. Some existing solutions can be obtained as special cases of the present solution. The variations of the stress and electrical field with piezoelectric parameters of the composites are investigated. The relations between the effective properties of the piezoelectric composites and the volume fraction of the fiber are discussed for the square and hexagonal coated fiber arrays. The effective piezoelectric coefficients for the hexagonal array of coated fibers are in agreement with the ones predicted by the generalized self-consistent method. The present solution is useful to estimate and optimize the performances of such piezoelectric heterogeneous materials.