Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity
- 1 July 1994
- journal article
- Published by SAGE Publications in Asymptotic Analysis
- Vol. 9 (1) , 61-100
- https://doi.org/10.3233/asy-1994-9105
Abstract
We consider families of variational problems Fε over domains Ωε whose extension in one or more directions is small compared to the extension in the other directions, and goes to zero while ε tends to zero. We study then the “variational” convergence of the functionals Fε to a new functional defined on a domain A in a lower dimensional space, where those “dimensions” that were small in Ωε disappear. A general framework is presented in the first part of the paper and an application to the elastic rod and the elastic plate is given in the second part.This publication has 0 references indexed in Scilit: