Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Sorbonne Université, Campus Pierre et Marie Curie
Paris, Francetel: +33 1 44 27 72 61
e-mail: sebastien.neukirch (-atat-) upmc.fr
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Jiayu Wang, Stéphanie Deboeuf, Arnaud Antkowiak, and Sébastien Neukirch
Constrained Euler buckling: The von Kármán approximation
International Journal of Solids and Structures, 313 (2025) pp-113279
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 K\'arm\'an) small deflection approximation. We list the different equilibrium states and their domain of validity in terms of the imposed horizontal Delta 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 sqrt(Delta)/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 behaviour.
DOI: 10.1016/j.ijsolstr.2025.113279
pre-print version and data: hal-04839683
journal version: PDF