Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity

Article type: Research Article

Authors: Anzellotti, G.^{; ;} | Baldo, S. | Percivale, D.

Affiliations: Dipartimento di Matematica, Università degli Studi di Trento, 38050 Povo (Trento), Italy | Dipartimento di Matematica del Politecnico, Torino, Italy

Note: [] Correspondence to: G. Anzellotti, Dipartimento di Matematica, Università degli Studi di Trento, 38050 Povo (Trento), Italy

Note: [] This research is part of the project “EURHomogenization”, contract SC1-Cf91-0732 of the project “SCIENCE” of the Commission of the European Communities.

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.

DOI: 10.3233/ASY-1994-9105

Journal: Asymptotic Analysis, vol. 9, no. 1, pp. 61-100, 1994