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The paper is devoted to development of the asymptotic averaging method for periodic structures being multilevel hierarchical ones. A determination method for effective elastic characteristics of composites with a multiscale hierarchical structure is suggested. Recurrent sequences of local and averaged problems of the elasticity theory are formulated over periodicity cells of different structural levels. The example of finite-element solving the number of local problems is given for the two-level structure model of a textile composite.

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