On the convergence of the energy, stress tensors, and eigenvalues in homogenization problems of elasticity. (English) Zbl 0572.73059

In the framework of homogenization problems the authors study the convergence of the energy integrals, stress tensors and eigenvalue for elastic problems. The domain with smooth boundary belongs to a class of perforated domains. The medium is supposed nonhomogeneous and porous elastic with a periodic structure of period \(\epsilon\) which tends to zero. Starting from the estimates of the solutions in the norm \(L^ 2\) and, using correctors, in \(H^ 1\), the convergence of energy integrals is valuated. Moreover, using correctors, an estimate is furnished for the difference between the stress tensors of the problems with \(\epsilon >0\) and \(\epsilon =0\). Some inequality is also obtained for the frequencies of free vibrations.
Reviewer: M.Codegone


74H45 Vibrations in dynamical problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
35J25 Boundary value problems for second-order elliptic equations
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