Variational Principles in Finite Elasticity With Applications
Lee, Sang Jin
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https://hdl.handle.net/2142/68506
Description
Title
Variational Principles in Finite Elasticity With Applications
Author(s)
Lee, Sang Jin
Issue Date
1980
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
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 cylinders 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.
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