周期性复合材料等效传热系数预测的渐进均匀化新算法及其实现

A new algorithm of asymptotic homogenization method for predicting the effective thermal conductivity and its implementation of periodic composite materials

渐进均匀化方法具有严格的数学基础,预测周期性复合材料的等效热传导系数具有较高的计算精度。本文提出了基于渐进均匀化方法预测周期性复合材料等效热传导系数的新算法。相比原有的算法具有两个优点:它的实现与代表体元方法一样简单,新的算法以现有的有限元商业软件为黑箱,通过简单的几个分析步骤,即可以获得复合材料的等效热传导系数;可以利用商业软件提供的多种单元类型去离散同一个单胞,在处理复杂几何单胞结构时,可以节约大量的计算费用。通过几个典型的算例,验证了方法的有效性。该工作对于推广渐进均匀化方法在预测复合材料等效热传导系数的广泛应用具有积极作用。

Asymptotic homogenization（AH）method has rigorous mathematical foundation and can provide an accurate solution for the effective thermal conductivity（ETC）of periodic composite materials.A new implementation algorithm based AH method predicting the ETC of periodic composite materials was presented.Compared with the original implementation algorithm,the new implementation algorithm has two advantages：Its implementation as simple as representative volume element（RVE）method.The commercial finite element analysis（FEA）software as black box is used and the ETC of periodic composite materials through several simple steps can be obtained.The new implementation of AH can simultaneously use more than one element type to discretize a unit cell,which can save much computational cost in predicting the ETC of complex structure.This work is expected to greatly promote the widespread use of AH in predicting the ETC of periodic composite materials.