平面应力状态下复合材料弹性等效性质分析

利用Hill条件和扰动场理论，建立了平面应力状态下复合材料有效矛盾度的平移性质的普适微分方程，所得方程与复合材料微结构形状和分布无关，通过有限元方法实现了具有3种不同二维微结构分布的复合材料的优化设计，从数值的角度计算了复合材料和多孔介质的有效模量，计算结果与理论关系相符。

Investigation of the Elastic Effective Compliance for Planar Composites

Based on the Hill's condition and field fluctuation approach, a set of universal differential equations are derived for the shift property of the effective compliances of planar composites in plane stress state. The derived equations are independent of the distribution and the shape of the microstructures. Three types of microstructures are investigated by the numerical method, 2 D composites and voided materials are examined, the results of numerical calculations agree well with the theoretical prediction.