Deformation and stability of an elastica constrained by curved surfaces

• Deformation maps of the pressed elastica are constructed with shooting method.
• The stability of the elastica is determined via a vibration method.
• No secondary buckling will occur when the top wall is concave.
• When the top wall is convex, no line contact on the top wall is possible.

In this paper we study 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 with shooting method. The stability of various deformation patterns is determined via a vibration method. The theoretical predictions on the deformation evolution when the top wall presses downward quasi-statically are verified experimentally. In the case of plane top wall, the external pressing force reduces to zero as soon as the free fold of a previous deformation touches the top wall. In the case when the top wall is not a plane, this is not necessarily 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.