The two-scale finite element computation for thermoelastic problem in periodic perforated domain

The problems of composite structures containing small periodic perforated configurations are often encountered in the development of composite materials. These structures often consist of material with very fine micro-structures and vary sharply within a very small periodic domain. The traditional simulation of these structures involving multi-scale is very difficult because of the requirement for a tremendous amount of computer memory and CPU running time. The two-scale formal asymptotic expansions of the increment of temperature and the displacement for the structure with small periodic perforated configuration of composite material are given. The two-scale finite element algorithm is described and simple numerical results are evaluated by two-scale finite element computational method. The numerical results show that the basic configuration and the increment of temperature strongly affect local strains and local stresses inside basic cell. A new effective numerical method is presented for thermoelastic problem in a periodic perforated domain.