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

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.