scholarly journals Equilibrium states of nonlinearly elastic rods

1968 ◽  
Vol 23 (2) ◽  
pp. 459-470 ◽  
Author(s):  
Stuart S Antman
Keyword(s):  
Equilibrium States ◽  
Elastic Rods ◽  
Nonlinearly Elastic

Corrections and Additions: Global Behavior of Buckled States of Nonlinearly Elastic Rods

SIAM Review ◽  
1980 ◽  
Vol 22 (2) ◽  
pp. 186-187 ◽  
Author(s):  
Stuart S. Antman ◽  
Gerald Rosenfeld
Keyword(s):  
Global Behavior ◽  
Elastic Rods ◽  
Nonlinearly Elastic

5.—Qualitative Aspects of the Spatial Deformation of Non-linearly Elastic Rods.

1975 ◽  
Vol 73 ◽  
pp. 85-105 ◽  
Author(s):  
Stuart S. Antman ◽  
Kathleen B. Jordan
Keyword(s):  
Boundary Value Problem ◽  
Geometric Structure ◽  
Constitutive Relations ◽  
Equilibrium States ◽  
Linear Functions ◽  
Order System ◽  
Elastic Rods ◽  
Qualitative Behaviour ◽  
Spatial Deformation ◽  
Planar Equilibrium

In this article we examine the qualitative behaviour of non-planar equilibrium states ofnon-linearly elastic rods subject to terminal loads. In our geometrically exact theory, a rod is endowed with enough geometric structure for it to undergo flexure, torsion, axial extension, and shear. The constitutive equations give appropriate stress resultants and couples as non-linear functions of appropriate strains. These constitutive relations must meet minimal conditions ensuring that they be physically reasonable. It turns out that the equilibrium states of such a rod are governed by a boundary value problem for a quasilinear fifteenth-order system of ordinary differential equations.

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