Second-order two-scale computational method for damped dynamic thermo-mechanical problems of quasi-periodic composite materials

In this paper, a novel second-order two-scale (SOTS) analysis method and related numerical algorithm are developed for damped dynamic thermo-mechanical problems of quasi-periodic composite materials. The formal SOTS solutions for these problems are constructed by the multiscale asymptotic analysis. Then we theoretically explain the importance of the SOTS solutions by the error analysis in the pointwise sense. Furthermore, the convergence result with an explicit rate for the SOTS solutions is obtained in the integral sense. In addition, a SOTS numerical algorithm is proposed to solve these problems effectively. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.