University of Illinois Urbana-Champaign

Variational principles in finite elasticity with applications

Lee, S.J.; Shield, Richard T.

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https://hdl.handle.net/2142/112174

Description

Title
Variational principles in finite elasticity with applications
Author(s)
  • Lee, S.J.
  • Shield, Richard T.
Issue Date
1979-12
Keyword(s)
  • Complementary Energy Type
  • Elasticity
Date of Ingest
2021-11-04T16:25:47Z
Abstract
A variational principle of the complementary energy type is derived. Trial functions for the actual deformation gradient are used in the formulation of the principle. Corresponding principles for elastic bodies subject to kinematical constraints such as incompressibility are formulated. The same approach can be used to obtain variational principles for infinitesimal deformations superposed on a known finite elastic deformation of an elastic body. For some deformations, the principle becomes an extremum principle and it can be used in conjunction with the principle of minimum potential energy to provide bounds on overall quantities of physical interest. The principles are applied to the problem of the all-around finite extension of a plane sheet with a circular hole and accurate estimates for the stress resultant at the outer edge for various extensions are obtained. The finite extension and torsion of an elastic cylinder is treated and bounds on the strain energy per unit length are obtained for elliptical cylinder of neo-Hookean material with axes in the ratios of 2:1 and 4:1. The bounds lead to reliable estimates for the twisting moment and the axial force.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 437
  • 1979-6007
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112174
Copyright and License Information
Copyright 1979 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.