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Geometrically non‐linear elastic model for a thin composite layer with wavy surfaces
Author(s) -
Kalamkarov A. L.,
Tornabene F.,
Pacheco P. M. C. L.,
Savi M. A.,
Saha G. C.
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700018
Subject(s) - homogenization (climate) , asymptotic homogenization , composite number , linear elasticity , stiffness , moduli , mathematical analysis , mathematics , homogeneous , asymptotic expansion , limiting , composite material , materials science , geometry , finite element method , physics , thermodynamics , mechanical engineering , biodiversity , ecology , quantum mechanics , combinatorics , engineering , biology
The geometrically non‐linear elastic thin composite layer model is developed through the application of the modified asymptotic homogenization method. The set of local unit cell problems and the analytical formulae for the effective stiffness moduli of the non‐linear homogenized plate accounting the higher order terms of the asymptotic expansions are derived. They make it possible to gain useful insight into the manner in which the geometrical and mechanical properties of the individual constituents affect the elastic properties of the composite layer with wavy surfaces. It is shown that in the limiting case of a homogeneous layer of constant thickness the derived asymptotic homogenization model converges to the geometrically non‐linear mean‐flexure plate theory. And the obtained expressions for the mid‐surface strains converge to von Kármán's formulae. The derived non‐linear homogenization model is illustrated by an example of a laminated plate.