曲线坐标下多孔材料模型特征值问题的二阶双尺度分析与计算

Second order two scale calculation for eigenvalue problem of porous material model in curvilinear coordinates

摘要:

本文研究了一般曲线坐标系中具有拟周期孔洞结构的椭圆特征值问题. 通过坐标变换，本文在具有周期结构的曲线坐标系中重建了特征值方程. 然后利用二阶双尺度渐近展开方法给出了曲线坐标下特征值和对应特征函数的二阶双尺度渐近展开表达式. 并给出了相应的有限元计算方法，数值实验表明，二阶双尺度方法在解决复杂结构多孔材料模型特征值问题的有效性.

Abstract:

A second-order two-scale (SOTS) analysis method is developed for eigenvalue problems with quasi-periodic porous domain in curvilinear coordinates. Firstly, the eigenvalue equation is reformulated in the curvilinear coordinate system with periodic structure by using appropriate coordinate transformation. Secondly, the SOTS approximate solutions of the eigenvalues and corresponding eigenfunctions in curvilinear coordinates are constructed by the SOTS asymptotic expansion method and the corresponding finite element algorithms. The numerical experiments show that SOTS with its finite element algorithms has high computational accuracy and the algorithm in coordinate transformation is effective.