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

Neukamm, Stefan; Velčić, Igor
Derivation of a homogenized von-Karman plate theory from 3D nonlinear elasticity // Mathematical models and methods in applied sciences, 23 (2013), 14; 2701-2748 doi:10.1142/S0218202513500449 (međunarodna recenzija, članak, znanstveni)

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

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

Projekt / tema
037-0693014-2765 - Matematička analiza kompozitnih i tankih struktura (Zvonimir Tutek, )

Ustanove
Fakultet elektrotehnike i računarstva, Zagreb

Autor s matičnim brojem:
Igor Velčić, (267453)

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus