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针对周期性结构复合材料,根据稳态热固耦合平衡方程,将弹性矩阵和导热系数矩阵进行合并,将位移和温度作为空间场量同时进行小参数渐进展开,利用摄动理论和均匀化理论,推导并建立了周期性结构复合材料稳态热固耦合双尺度渐进均匀化分析方法。将复合材料力学分析从单一物理场推广到热固耦合场,为实现复合材料构件的热固耦合多尺度力学分析建立了基础。根据建立的偏微分方程式,利用变分原理推导得到其有限单元形式,用VC++6.0开发了热固耦合双尺度渐进均匀化分析程序。为验证该方法预测复合材料宏观等效性能的准确性,对纤维体积含量从20%到80%的单向纤维增强复合材料宏观等效参数进行了计算。当纤维体积含量低于65%时,得到的计算值与实验值吻合良好。更加真实地还原复合材料细观结构模型,计算精度将进一步提高。
For periodic structural composites, the elastic matrix and the thermal conductivity matrix are combined according to the steady-state thermomechanical coupling equilibrium equation, and the displacement and temperature are simultaneously expanded as the small parameters as well as the perturbation theory and the homogenization theory. The steady-state thermo-mechanical coupled two-scale progressive homogenization method for periodic structural composites was derived and established. The mechanical analysis of composite materials is extended from a single physical field to the thermomechanical coupling field, which establishes the foundation for the multi-scale mechanics analysis of thermo-mechanical coupling of composite materials. According to the established partial differential equation, the finite element form is deduced by using the variational principle. The thermosensitive coupling two-scale progressive homogenization analysis program was developed by VC ++ 6.0. To verify the accuracy of this method in predicting macroscopic equivalent properties of composites, macroscopic equivalent parameters of unidirectional fiber-reinforced composites with fiber volume contents from 20% to 80% were calculated. When the fiber volume content is less than 65%, the calculated value is in good agreement with the experimental data. Decreasing the mesostructure model of composite more realistically, the calculation precision will be further improved.