Naslov
Derivation of a homogenized von-Karman plate theory from 3D nonlinear elasticity

Autori
Neukamm, Stefan ; Velčić, Igor

Izvornik
Mathematical models and methods in applied sciences (0218-2025) 23 (2013), 14; 2701-2748

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
elasticity; dimension reduction; homogenization; von-Karman plate theory; two-scale convergence

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA