Abstract
A problem of elasticity theory in static statement on thin periodic box and rod frames whose geometry depends on two small parameters ɛ and h(ɛ) related to each other determining the cell of periodicity and thickness of the components (plates or rods, respectively) is studied. The homogenization of this problem is obtained in the most difficult case where \(\mathop {\lim }\limits_{\varepsilon \to 0} h(\varepsilon )/\varepsilon = \theta > 0\).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 12, Partial Differential Equations, 2004.
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Pastukhova, S.E. Homogenization of Problems of Elasticity Theory on Periodic Box and Rod Frames of Critical Thickness. J Math Sci 130, 4954–5004 (2005). https://doi.org/10.1007/s10958-005-0392-8
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DOI: https://doi.org/10.1007/s10958-005-0392-8