Mathematical analysis and homogenization of the torsion problem
type: Item
instance of: scholarly article
title: Mathematical analysis and homogenization of the torsion problem
zbMATH Open document ID: 1171.35316
DOI: 10.1155/2008/637035
author: D. Lukkassen
author: A. Meidell
author: Peter Wall
published in: Journal of Function Spaces and Applications
publication date: 2008-08-12T00:00:00Z
review text: This paper starting from the standard equations of elastic equilibrium, presents the limitations of the classical formulation of the torsion problem of bars consisting of different materials. The classical theory requires that the surface separating the different materials are sufficiently smooth. Weak and variational formulations of the torsion problem defined on Sobolev spaces enable the authors to relax this requirement and is suitable for obtaining bounds on the torsional rigidity and analyzing the limit torsional behavior of composite materials when the characteristic length of the microstructures (e.g. the diameter of the fibers) tends to zero. The analysis is based on the homogenization method in both the periodic and stochastic setting. The theoretical results are explained with numerical computations.
reviewed by: Marco Codegone
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 74Q05
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 5310050
zbMATH Keywords: Homogenization
zbMATH Keywords: Effective properties
zbMATH Keywords: torsion stiffness
zbMATH Keywords: limit torsional behavior
zbMATH Keywords: periodic and stochastic setting
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2008/637035
OpenAlex ID: W2159467618
description: scientific article; zbMATH DE number 5310050