Deformation and Stability of an Elastica Constrained by Curved Surfaces
Date Issued
2011
Date
2011
Author(s)
Hung, Shao-Yu
Abstract
In this paper we consider the deformation and stability of a clamped-clamped elastica resting on a bottom plane and pressed by a top wall laterally. Three types of top walls are considered; they are concave, convex, and plane surfaces. Deformation maps of the pressed elastica are first constructed. The stability of various deformation patterns is determined via a vibration method. The theoretical predictions on the deformation evolution when the top wall presses quasi-statically are verified experimentally. In the case of plane top wall, the external pressing force reduces to zero whenever the free fold of a previous deformation starts to touch the wall. In the case when the top wall is not a plane, this is in general no longer true. The multiplicity of line-contact deformations in the case of plane top wall is destroyed when the top wall is curved. No secondary buckling will occur when the top wall is concave. Instead, line contact on the sides of the bottom plane will develop. In the case when the top wall is convex, no line contact on the top wall is possible.
Subjects
Elastica
Deformation
Stability
Curved Surface
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