University of Illinois Urbana-Champaign

Energy method for certain second order effect with application to torsion of elastic bars under tension

Shield, Richard T.

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https://hdl.handle.net/2142/112169

Description

Title
Energy method for certain second order effect with application to torsion of elastic bars under tension
Author(s)
Shield, Richard T.
Issue Date
1979-05
Keyword(s)
  • Elastic Bars
  • Torsion
Abstract
When a mechanical system has a potential energy, it is a simple matter to show that if the generalized force corresponding to a coordinate p is known to first order in p for a range of the other coordinates of the system, then the other generalized forces can be found immediately to second order in p , without requiring a second-order analysis of the system. By this method the second-order change in the axial force when a finitely extended elastic cylinder is twisted is found from the first order value of the twisting moment. Numerical results for a realistic form of the strain energy function for an incompressible material suggest that the second-order expression for the axial force is very accurate for a wide range of twist for circular cylinders of rubber-like materials extended 100% or more.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 433
  • 1979-6003
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112169
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.