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徐耀玲, 蒋持平. 双周期圆截面纤维复合材料平面问题的解析法[J]. 力学学报, 2004, 36(5): 596-603. DOI: 10.6052/0459-1879-2004-5-2003-424
引用本文: 徐耀玲, 蒋持平. 双周期圆截面纤维复合材料平面问题的解析法[J]. 力学学报, 2004, 36(5): 596-603. DOI: 10.6052/0459-1879-2004-5-2003-424
An analytical method for the plane problem of doubly periodic circular cross-section fiber composite materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(5): 596-603. DOI: 10.6052/0459-1879-2004-5-2003-424
Citation: An analytical method for the plane problem of doubly periodic circular cross-section fiber composite materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(5): 596-603. DOI: 10.6052/0459-1879-2004-5-2003-424

双周期圆截面纤维复合材料平面问题的解析法

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

  • 摘要: 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.

     

    Abstract: Combining the theory of doubly periodic and doublyquasi-periodic Riemann boundary value problems and Eshelby's equivalentinclusion method, an analytical method for the plane problem of compositematerials with a doubly periodic array of circular cross-section fibers ispresented. The stresses expressions in series are obtained in the fibers andmatrix and a comparison with the finite element calculations is done. Thetransverse tensile and shear moduli are predicted for a unidirectionalfiber-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 asame fiber volume fraction, the effective moduli for a square array offibers are larger than those for a hexagonal array of fibers. The presentmethod provides an efficient tool for analyzing the mechanical properties ofinhomogeneous materials and designing microstructures of compositematerials, and can also be used to evaluate the precision of other numericaland approximate methods such as the finite element method.

     

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