双周期圆截面纤维复合材料平面问题的解析法

结合双准周期Riemann边值问题理论与Eshelby等效夹杂原理，为双周期圆截面纤维复合材 料平面问题发展了一个实用有效的解析方法，获得了问题的全场级数解并与有限元结果进行 了比较. 该方法为非均匀材料的力学性质分析和复合材料等新材料的微结构设计提供了 一个有效的计算工具，也可用来评估有限元等数值与近似方法的精度.

An analytical method for the plane problem of doubly periodic circular cross-section fiber composite materials

Combining the theory of doubly periodic and doubly quasi-periodic Riemann boundary value problems and Eshelby's equivalent inclusion method, an analytical method for the plane problem of composite materials with a doubly periodic array of circular cross-section fibers is presented. The stresses expressions in series are obtained in the fibers and matrix and a comparison with the finite element calculations is done. The transverse tensile and shear moduli are predicted for a unidirectional fiber-reinforced composite with an doubly periodic array of circular fibers. It is found that for a composite with hard fibers and a soft matrix under a same fiber volume fraction, the effective moduli for a square array of fibers are larger than those for a hexagonal array of fibers. The present method provides an efficient tool for analyzing the mechanical properties of inhomogeneous materials and designing microstructures of composite materials, and can also be used to evaluate the precision of other numerical and approximate methods such as the finite element method.