Abstract
This new method for deriving the equations of an effective average model involves constructing exact expressions for the displacement and stress fields for the periodic medium. The limit of an infinite number of periods is then taken, wish an infinite decrease in the length of the periods. Equations satisfied by the displacement and stress fields after this limit is taken are found. Since these equations are independent of the source, they are treated as the equations of an effective average model.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 195, pp. 82–102, 1991.
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Molotkov, L.A. New method for deriving equations of an effective average model of periodic media. J Math Sci 62, 3103–3117 (1992). https://doi.org/10.1007/BF01095684
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DOI: https://doi.org/10.1007/BF01095684