The aim of contribution is twofold. First, the new asymptotic modelling method for the analysis of functionally graded multilayered two-phase composites (FGM) is for- mulated. Second, there is proposed an independent (n on asymptotic) modelling procedure which makes it possible to satisfy boundary conditions related to the asymptotic model. For the sake of simplicity considerations are restricted to problems described by scalar elliptic 2-nd order equations, e.g. to the stationary heat conduction problems, but the proposed modelling method can be also applied to investigations of many other problems in thermo- mechanics of microlayered FGM.

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