Derivation of a homogenized von-Karman plate theory from 3D nonlinear elasticity (CROSBI ID 201160)
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Podaci o odgovornosti
Neukamm, Stefan ; Velčić, Igor
engleski
Derivation of a homogenized von-Karman plate theory from 3D nonlinear elasticity
We rigorously derive a homogenized von-Kármán plate theory as a Γ-limit from nonlinear three-dimensional elasticity by combining homogenization and dimension reduction. Our starting point is an energy functional that describes a nonlinear elastic, three-dimensional plate with spatially periodic material properties. The functional features two small length scales: the period ε of the elastic composite material, and the thickness h of the slender plate. We study the behavior as ε and h simultaneously converge to zero in the von-Kármán scaling regime. The obtained limit is a homogenized von-Kármán plate model. Its effective material properties are determined by a relaxation formula that exposes a non-trivial coupling of the behavior of the out-of-plane displacement with the oscillatory behavior in the in-plane directions. In particular, the homogenized coefficients depend on the relative scaling between h and ε, and different values arise for h ≪ ε, ε ~ h and ε ≪ h.
elasticity; dimension reduction; homogenization; von-Karman plate theory; two-scale convergence
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Podaci o izdanju
23 (14)
2013.
2701-2748
objavljeno
0218-2025
10.1142/S0218202513500449