Logo Max-Planck-Institute for Mathematics in the Sciences, Go to Homepage

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
61/2013

On the general homogenization and Γ-closure for the equations of von Kármán plate from 3D nonlinear elasticity

Igor Velčić

Abstract

Starting from 3D elasticity equations we derive the model of the homogenized von K\'arm\'an plate by means of Γ-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic. We also prove the locality of Γ-closure i.e. that every energy density obtained in this way by mixing n different materials is at almost every point of domain limit of some sequence of the energy densities obtained by periodic homogenization.

Contact the author per mail Download full preprint 514 KB
Received:
26.06.13
Published:
01.07.13
MSC Codes:
35B2, 74Q15, 74K20
Keywords:
elasticity, dimension reduction, homogenization, von K\'arm\'an plate model

Related publications

inJournal
2017 Repository Open Access
Igor Vel?i?

On the general homogenization of von Kármán plate equations from three-dimensional nonlinear elasticity

In: Analysis and applications, 15 (2017) 1, pp. 1-49
BibTex DOI: 10.1142/S0219530515500244 ArXiv: 1306.0287