Large Deflections of Structures With Small Elastic Strains (Nonlinear, Rotations)
Im, Seyoung
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https://hdl.handle.net/2142/71682
Description
Title
Large Deflections of Structures With Small Elastic Strains (Nonlinear, Rotations)
Author(s)
Im, Seyoung
Issue Date
1985
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
Abstract
A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending of a beam by end loads and by its own weight, and to the bending of a long rectangular plate and of a circular plate by uniform pressure. The theory provides solutions for geometries between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff's theory for rods and the von Karman equations for plates, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior. For the plate problems considered the von Karman equations are found to provide accurate results for thin plates for which deflections are not small.
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