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On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
Author(s) -
Oleinik O. A.,
Shamaev A. S.,
Yosifian G. A.
Publication year - 1985
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.19850650106
Subject(s) - homogenization (climate) , eigenvalues and eigenvectors , elasticity (physics) , mathematical analysis , vibration , mathematics , boundary value problem , homogeneous , convergence (economics) , physics , acoustics , thermodynamics , biodiversity , ecology , quantum mechanics , biology , combinatorics , economics , economic growth
In this paper we study the convergence of energy integrals, stress tensors and frequencies of free vibrations for non‐homogeneous and porous elastic bodies with a periodic structure of period ε as ε → 0. The results are based on the estimates for solutions of the boundary value problem of the elasticity system with rapidly oscillating periodic coefficients, obtained in [4], [11].