A variational approach to the Cosserat-like continuum
type: Item
instance of: scholarly article
title: A variational approach to the Cosserat-like continuum
zbMATH Open document ID: 0780.73009
DOI: 10.1016/0020-7225(93)90025-P
author: J. Saczuk
published in: International Journal of Engineering Science
publication date: 1994-01-30T00:00:00Z
review text: The exposition is intended to show an equivalent variational approach to formulation of the virtual work principle for the Cosserat-like continuum. Stationarity conditions for an action integral lead to the Euler-Lagrange equations identified with the balance equations for stresses and couple-stresses within micropolar and micromorphic continua. Vector fields as independent variables are taken so as to satisfy the known Stokes' decomposition. Based on the standard variational arguments, for a given Lagrangian function and an assumed one-parameter family of transformations of both the independent and dependent variables, the fundamental variational formula identified with the virtual work principle of the Cosserat-like continuum is obtained.
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
zbMATH DE Number: 465217
zbMATH Keywords: transversality conditions
zbMATH Keywords: \(r\)-parameter Lie group
zbMATH Keywords: virtual work principle
zbMATH Keywords: Euler-Lagrange equations
zbMATH Keywords: balance equations
zbMATH Keywords: micropolar and micromorphic continua
zbMATH Keywords: Stokes' decomposition
MaRDI profile type: Publication
cites work: Introduction to vectors and tensors. Vol. 1: Linear and multilinear algebra. Vol. 2: Vector and tensor analysis
cites work: Q5590281
cites work: Aspects of variational arguments in the theory of elasticity: fact and folklore
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full work available at URL: 0020-7225(93)90025-p
OpenAlex ID: W2021567030
description: scientific article; zbMATH DE number 465217