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Title:Variational principles in finite elasticity with applications
Author(s):Lee, S.J.; Shield, Richard T.
Subject(s):Complementary Energy Type
Elasticity
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.
Issue Date:1979-12
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 437
1979-6007
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112174
ISSN:0073-5264
Rights Information:Copyright 1979 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    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.

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