Two-Scale Analysis Of One Class Of Thermoelastic Coupling Problem With General Items In Small Periodic Structure

Because of the multi-scale and multi-physical coupling of composite materials in their local structures, some new composites play the irreplaceable roles in the development of new materials and design. In mathematics, physics and computational mechanics, the effective properties of composites are main research fields, and in these researches, the analysis for effectiveness of materials in multiple physical fields is the important research direction.In this paper, by means of the two-scale method, the two-scale asymptotic analysis of one class of thermal coupling partial differential boundary value problem with general terms in periodic domain is given. The analysis is organized as following four parts.In Chapter 1, some related background of materials and their research methods, some fundamental knowledge in mathematics and recent known results are introduced.In Chapter 2, the two-scale asymptotic expansions of one class of coupling thermoelastic problem with general items in small periodic domain are given. The corresponding two-scale asymptotic expansions, homogenization constants and the homogenization equations are presented.And the existence and uniqueness of cell solutions and homogenization solutions are analyzed.In Chapter 3, based on the asymptotic expression of Chapter 2, we constructed the two-scale approximate solution for boundary value problems, and the asymptotic error estimates are presented.In Chapter 4, conclusions and some suggestions are given.