渐进多尺度展开方法的精度和物理意义

多尺度渐进展开方法(MsAEM)是分析周期复合材料结构力学行为的代表性方法,可以通过加权残量等方法实现,作者曾针对MsAEM的精度和力学含义进行研究。本文对作者的工作进行了总结,进一步明确了一维周期结构的单元阶次、摄动阶次和精确解的关系,揭示了不同阶次虚拟载荷和影响函数的物理意义,从物理角度强调了二阶展开项是不可缺少的,并对未来工作进行了展望。

Accuracy and physical interpretation of multiscale asymptotic expansion method

The multiscale asymptotic expansion method (MsAEM) can be implemented by using weighted residual method etc.The authors have studied the accuracy and physical interpretation of MsAEM for years.This paper reviewed the authors'' previous works,further demonstrated the relationships of element order and perturbation order with exact solution for one-dimensional periodical structures;revealed the physical interpretations of different orders of influence functions and self-balanced quasi loads;and emphasized that the second order of expansion is essential for the accuracy of MsAEM from the physical perspective.It also presented an outlook of future work.