Homogenization of discrete thin structures

被引：4
|
作者：
Braides, Andrea [1 ]
D'Elia, Lorenza [2 ]
机构：
[1] SISSA, Via Bonomea 265, Trieste, Italy
[2] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, Vienna, Austria
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 231卷
基金：
奥地利科学基金会;
关键词：
Thin structures; Dimension reduction; Discrete-to-continuum; Lattice systems; Homogenization; CONTINUUM LIMITS; FILMS; ENERGIES; MODEL;
D O I：
10.1016/j.na.2022.112951
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider graphs parameterized on a portion X & SUB; Zd x {1,. .. , M}k of a cylindrical subset of the lattice Zd x Zk, and perform a discrete-to-continuum dimension-reduction process for energies defined on X of quadratic type. Our only assumptions are that X be connected as a graph and periodic in the first d-directions. We show that, upon scaling of the domain and of the energies by a small parameter & epsilon;, the scaled energies converge to a d-dimensional limit energy. The main technical points are a dimension-reducing coarse-graining process and a discrete version of the p-connectedness approach by Zhikov.& COPY; 2022 Elsevier Ltd. All rights reserved.
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页数：27
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