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|Title:||Variational Principles in Finite Elasticity With Applications|
|Author(s):||Lee, Sang Jin|
|Department / Program:||Theoretical and Applied Mechanics|
|Discipline:||Theoretical and Applied Mechanics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980.
|Date Available in IDEALS:||2014-12-14|
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Dissertations and Theses - Theoretical and Applied Mechanics (TAM)
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois