Second-order two-scale analysis method for dynamic thermo-mechanical problems of composite structures with cylindrical periodicity

In this paper, a novel second-order two-scale (SOTS) analysis method and corresponding numerical algorithm is developed for dynamic thermo-mechanical problems of composite structures with cylindrical periodicity. The formal SOTS solutions are successfully constructed by the multiscale asymptotic analysis. Then we theoretically explain the necessity of developing the SOTS solutions by the error analysis in the pointwise sense. Futhermore, the convergence result with an explicit rate for the SOTS solutions is obtained. In addition, a SOTS numerical algorithm is presented to effectively solve these multiscale problems. Finally, some numerical examples verify the feasibility and validity of the SOTS numerical algorithm we proposed. This study offers a unified multiscale framework that enables the simulation and analysis of thermo-mechanical coupled behavior of composite structures with cylindrical periodicity.