On the interaction of uni-directional and bi-directional buckling of a plate supported by an elastic foundation

TL;DR

This paper investigates the complex post-buckling behavior of a supported rectangular plate under in-plane load, revealing pattern transitions and localized responses influenced by nonlinear elastic foundations, with implications across scales.

Contribution

It introduces a detailed analysis of pattern transitions and localized buckling responses in plates supported by nonlinear elastic foundations, expanding understanding of post-buckling phenomena.

Findings

Transition from stripe to spot patterns and back

Existence of localized buckling responses

Relevance to micro- and nano-scale deformations

Abstract

A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become unstable. Here the post-buckling of such a structure is investigated and several important phenomena are identified, including the transition of patterns from stripes to spots and back again. The interaction between these forms is of importance for understanding the possible post-buckling behaviours of this structural system. In addition, both periodic and some localized responses are found to exist as the dimensions of the plate are increased and this becomes relevant when the characteristic wavelengths of the buckle pattern are small compared to the size of the plate. Potential application of the model range from macroscopic industrial manufacturing of structural elements to the understanding of micro- and nano-scale deformations in materials.