On the nonlinear mechanics of discrete networks
type: Item
instance of: scholarly article
title: On the nonlinear mechanics of discrete networks
zbMATH Open document ID: 0879.73045
published in: Archive of Applied Mechanics
publication date: 1998-01-29T00:00:00Z
review text: A formulation of the equilibrium problem for nonlinear elastic networks is presented. Explicit necessary and sufficient conditions for minimum-energy configurations are derived. These are used to generate a relaxed formulation of the theory in which fibre slackening is accounted for automatically. For the relaxed problem, minimum-energy and uniqueness theorems are proved and used as the basis of a numerical method in which equilibrium configurations are recovered asymptotically in the long-time limit of an artificial dynamical problem. Several illustrative examples are discussed.
Mathematics Subject Classification ID: 74K99
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 1038598
zbMATH Keywords: convexity
zbMATH Keywords: long-time limit of artificial dynamical problem
zbMATH Keywords: equilibrium problem
zbMATH Keywords: nonlinear elastic networks
zbMATH Keywords: necessary and sufficient conditions for minimum-energy configurations
zbMATH Keywords: fibre slackening
zbMATH Keywords: uniqueness
author: Ali Asghar Atai
author: David J. Steigmann
MaRDI profile type: Publication
full work available at URL: s004190050119
OpenAlex ID: W2073490690
DOI: 10.1007/S004190050119
description: scientific article; zbMATH DE number 1038598