Work

Constrained Euler buckling: The von Kármán approximation

Year: 2025

Type: article

Abstract: We consider the classical problem of the buckling of a planar elastica inside a rectangular cavity . We compute the equilibrium solutions analytically in the (von Kármán) small deflection approximation. We list the different equilibrium states and their domain of validity in terms of the imposed horizontal Δ and vertical H displacements. We compute the horizontal P and the vertical F applied forces and show how they increase and scale when the compaction ratio Δ / H is increased. Finally, we introduce an approximate response state, where the system adopts a periodic configuration with a noninteger number of repeated folds. This solution represents an average response of the structure and brings information on its global behavior.

Source: International Journal of Solids and Structures

DOI: 10.1016/j.ijsolstr.2025.113279

Authors: Jiayu Wang, Stéphanie Deboeuf, Arnaud Antkowiak, Sébastien Neukirch

Institutions: Centre National de la Recherche Scientifique, Sorbonne Université, Institut Jean Le Rond d'Alembert

Language: English

Topic: Structural Analysis and Optimization

Subfield: Civil and Structural Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: Centre National de la Recherche Scientifique, Sorbonne Université