Deformations and Stability of an Elastica Subjected to a Point Constraint
Date Issued
2009
Date
2009
Author(s)
Ro, Wei-Chia
Abstract
This paper studies, both theoretically and experimentally, the deformation and stability of a buckled elastic strip (also known as an elastica) constrained by a space-fixed point in the middle. One end of the elastica is fully clamped, while the other end is allowed to slide without friction and clearance inside a rigid channel. The point constraint is located at a specified height above the clamping plane. The elastic strip buckles when the pushing force reaches the conventional buckling load. At this buckling load, the elastica jumps to a symmetric configuration in contact with the point constraint. As the pushing force increases, a symmetry-breaking bifurcation occurs and the elastica evolves to one of a pair of asymmetric deformations. As the pushing force continues to increase the asymmetric deformation experiences a second jump to a self-contact configuration. A vibration analysis of the constrained elastica based on an Eulerian description is described, and the stability of the calculated equilibrium configuration is determined. The experiment confirms the two jumps and the symmetry-breaking bifurcation predicted theoretically.
Subjects
elastica
point constraint
snap-through buckling
stability
symmetry-breaking
Type
thesis