细观周期性结构复合材料热固耦合双尺度渐进均匀化分析方法及有限单元法实现

推进技术 ›› 2016, Vol. 37 ›› Issue (1): 18-24.

细观周期性结构复合材料热固耦合双尺度渐进均匀化分析方法及有限单元法实现

巩龙东,申秀丽

北京航空航天大学能源与动力工程学院，北京 100191,北京航空航天大学能源与动力工程学院，北京 100191

发布日期:2021-08-15
作者简介:巩龙东，男，博士生，研究领域为SiCf/SiC复合材料在航空发动机热端部件中的应用。

Thermal-Elastic Two-Scale Asymptotic Analysis Method

School of Energy and Power Engineering，Beijing University of Aeronautics and Astronautics，Beijing 100191，China and School of Energy and Power Engineering，Beijing University of Aeronautics and Astronautics，Beijing 100191，China

Published:2021-08-15

摘要/Abstract

摘要： 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。

关键词: 复合材料；热固耦合；双尺度；均匀化

Abstract: Focused on micro periodic composites，the elastic matrix and the coefficient of thermal conductivity matrix were merged and the formal asymptotic expansion of displacements and temperature，as tensor of space，was obtained by small parameter from the steady state thermal-elastic coupling equation，using perturbation and homogenization theory. The thermal-elastic two-scale asymptotic analysis method was established，which generalized the compound material mechanics analysis from a single physical field to thermal-elastic coupling field and could be applied to perform two-scale mechanics analysis of composites structure with thermal and mechanics loads. The finite element form was established utilizing variational principle according to partial differential equation established and the program software was developed using VC++6.0. The macro equivalent parameters of unidirectional fiber reinforced composites，whose fiber volume content was from 20% to 80%，as a sample to prove the accuracy of the method，were studied. When the fiber volume content was below 65%，the date calculated is consistent with experimental result. The calculation precision will be further improved with the composites mesoscopic structure model being more accurate.

Key words: Composites；Thermal-elastic coupling；Two-scale；Homogenization1

巩龙东,申秀丽. 细观周期性结构复合材料热固耦合双尺度渐进均匀化分析方法及有限单元法实现[J]. 推进技术, 2016, 37(1): 18-24.

GONG Long-dong,SHEN Xiu-li. Thermal-Elastic Two-Scale Asymptotic Analysis Method[J]. Journal of Propulsion Technology, 2016, 37(1): 18-24.

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