Derivation of homogenized Euler-Lagrange equations for von Karman rod

2016/07/06 by M. Bukal, Bukal, M., M. Pawelczyk +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1607.01813

arxiv created 2016/10/11 · arxiv updated 2016/10/12

Abstract

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 Kármán scaling. Assuming stationarity condition 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 Kármán rod model. The analogous result holds true for the von Kármán plate model.

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