交错排列结构的多尺度渐近分析

Multiscale asymptotic analysis in staggered arrangement structure

针对一类交错排列结构上的具有快速振荡系数的椭圆问题进行了多尺度渐近分析.证明了多尺度渐近展开方法的相关基础定理和多尺度解的误差估计.数值算例验证了所提出的多尺度有限元算法的有效性.进一步地,讨论了不同交错排列方式对材料等效性能的影响.

The multiscale asymptotic behavior of a kind of elliptic problem with rapidly oscillating coefficients on structures with staggered arrangements made up of unit cell is analyzed. The corresponding fundamental theorems for the multiscale asymptotic expansion method are shown, and the multiscale error estimate is obtained. Numerical simulations are carried out to validate the proposed multiscale finite element method （FEM）. Moreover, the different staggered arrangements on the effect equivalent performance of the materials is discussed.