Three-scale Asymptotic Analysis Of Coupling Thermoelastic Problem In Small Periodic Structure

With the application of composites in civil engineering, air transport and daily life, the research on the thermal properties and mechanical properties of composites is becoming more and more fruitful. In this paper, the performance of composite material with periodic perforated structure is analyzed by studying the effective performance. The problem of this kind of composite material can be described by some boundary value problems of partial differential equations with local oscillation coefficients. The multiscale asymptotic analysis of this kind of problem has a great influence on the prediction of the effective performance for these composites.Firstly, using three-scale method,by considering the connection among the micro,meso and macroscale structure and constructing fitting cell problems,the formal three-scale asymptotic expansions for coupling thermoelastic problem in periodic perforated structure is discussed.Secondly, based on the homogenization method and the multiscale method,the homogenization equation and coefficients of the problem are discussed.Finally, the asymptotic error and convergence of the three scale expansion are analyzed for the problem in perforated periodic structure.