Two-order And Two-scale Asymptotic Analysis For The Quasi-periodic Structures Of Composite Materials

The two-order and two-scale analysis for the quasi-periodic structures of com-posite materials by means of two-scale method is discussed. The two class equa-tions are discussed.The first class is elliptic boundary value problem of quasi-periodicity;The second class is coupled thermoelastic equations in quasi-periodicstructures.In Chapter 1, the relational background of composite with quasi-periodic con-figuration is introduced firstly,then some known results,the background and the fun-damental knowledge of these classes of equations are presented.In Chapter 2, the two-scale analysis of the elliptic boundary value problem inquasi-periodic structure is given.The two-scale asymptotic expansions,the homoge-nization equations and the asymptotic errors are presented.One new effective numeri-cal method is obtained for elliptic problem in quasi-periodic structure.On the one hand,this method reduces the difficulty of computation, on the other hand,it improves theaccuracy of the error fromε21 toεin entirely quasi-periodic structure.In Chapter 3, the two-scale asymptotic expressions for the solutions of the dis-placement and the increment of temperature in the structure with quasi-periodic con-figuration under coupled thermoelasticity are presented .The two-scale asymptotic ex-pression for the solution of the displacement for quasi-periodic structure under cou-pled thermoelasticity can be divided into two parts:the first part is composed of thehomogenization solution u0(x) defined on global ? and a series of small scale so-lutions Nα1(ξ),Nα1α2(ξ) ,which depended on each component of materials and theirdistribution inside the basic configuration Q;The second part is formed by the ho-mogenization solutionθ0(x) defined on global ? and a series of small scale solutionsM0(ξ),Mα1(ξ),which are related to the thermal properties of different componentsand their distribution inside the basic configuration Q.The two-scale asymptotic behavior for quasi-periodic structures of compositesmaterials with two parameters and two scales is discussed.Up to now,these questionsare analyzed by the homogenization method in many articles.In order to improve theaccuracy of computation, some special problems of the quasi-periodic structures of composite materials by two-scale method. The results have some practical value andsignificance in new materials development and utilization of the process.