Derivation of homogenized Euler Lagrange equations for von Karman rods

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Bukal, Mario¹  Pawelczyk, Matthaeus²  Velcic, Igor¹ 

[1] Univ Zagreb, Fac Elect Engn & Comp, Unska 3, Zagreb 10000, Croatia

[2] Tech Univ Dresden, Inst Geometrie, Fachrichtung Math, Zellerscher Weg 12-14, D-01069 Dresden, Germany

关键词: Elasticity;    Homogenization;    Dimension reduction;    Convergence of equilibria;   

DOI  :  10.1016/j.jde.2017.02.009

来源: Elsevier

【 摘 要 】

In this paper we study the effects of simultaneous homogenization and dimension reduction in the context of convergence of stationary points for thin nonhomogeneous rods under the assumption of the von Karman scaling. Assuming stationarity conditions for a sequence of deformations close to a rigid body motion, we prove that the corresponding sequences of scaled displacements and twist functions converge to a limit point, which is the stationary point of the homogenized von Karman rod model. The analogous result holds true for the von Karman plate model. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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