中文摘要：

研究了双周期含涂层纤维增强复合材料在远场反平面载荷作用时的问题，利用Eshelby等效夹杂方法和Laurent级数展开技术，并结合双准周期Riemann边值问题理论，获得了其全场解析解，得到了应力场和有效模量表达式。与有限元结果的对照显示出本方法的效率和精度。考察了涂层参数对复合材料细观应力场和宏观有效性能的影响。当涂层刚度较大时，涂层内存在高的应力集中，且涂层刚度越大、涂层相对厚度越小，应力集中系数越大。纤维刚度对复合材料有效模量的影响也取决于涂层性能，非常软或非常硬的涂层都大大限制了纤维刚度对复合材料有效模量的贡献。

英文摘要：

The elastic properties of composite materials with a doubly periodic array of coated fibers under antiplane shear were studied. An analytical solution for the problem was presented by applying the Eshelby＇s equivalent inclusion method and Laurent＇s series expansion technique as well as combining the theory of the doubly quasi-periodic Riemann boundary value problem. The expressions for the stress field and effective modulus were obtained. The comparisons with the finite element method （FEM） show the efficiency and accuracy of the present method. The influence of the coating parameters on the stress concentration and the effective modulus of the composites was discussed. A very high stress concentration may occur in the coating, and the stifier and thinner the coating is, the higher the stress concentration. A very soft or very hard coating can shield the contribution of the fiber stirfhess to the effective modulus of composites.