复合材料应力分析的均匀化方法

HOMOGENIZATION METHOD OF STRESS ANALYSIS OF COMPOSITE STRUCTURES

建立了基于均匀化理论的确定复合材料结构应力场的方法．其实质是用均质的宏观结构和非均质的具有周期性分布的细观结构描述原结构；将力学量表示成关于宏观坐标和细观坐标的函数，并用细观和宏观两种尺度之比为小参数展开，用摄动技术将原问题化为一细观均匀化问题和一宏观均匀化问题．这两个问题的解确定了包含等效位移和一阶近似位移的位移场，由此获得应力场．利用该方法给出了圆柱形孔隙材料和单向纤维复合材料在单向拉伸时的应力场以及空隙材料简支梁的局部应力场。

A homogenization method has been presented for deter min ing the stress distributions of composite structures. In this method, the composite structures are depicted by a homogeneous macrostructure and a heterogeneous microstructure. All quantities are expressed as functions of microscopic coordinates and macroscopic coordinates, and expanded into asymptotic series. Based on the perturbation method, the stress analysis problem leads to a microscopic homogenization problem and a macroscopic homogenization problem, from which the displacements included the effective displacement and the first order perturbation, are deter min ed. The stress fields are obtained by these displacements. Finally, the stress distributions of structures composed of circular cylindrical porous or/and unidirectional fiber reinforced composites are given. The resuits show that the method is reliable and effective.