Large deformations of Timoshenko and Euler beams under distributed load

A. Della Corte (1) , A. Battista (1, 2) , F. Dell'Isola (1, 3) , Pierre Seppecher (1, 4)

1 MEMOCS - International Research Center for the Mathematics & Mechanics of Complex Systems
2 ULR - La Rochelle Université
3 Dipartimento di Ingegneria Strutturale e Geotecnica [Rome]
4 IMATH - Institut de Mathématiques de Toulon - EA 2134

In this paper, the general equilibrium equations for a geometrically nonlinear version of the Timoshenko beam are derived from the energy functional. The particular case in which the shear and extensional stiffnesses are infinite, which correspond to the inextensible Euler beam model, is studied under a uniformly distributed load. All the global and local minimizers of the variational problem are characterized, and the relative monotonicity and regularity properties are established.

Mots clés: Nonlinear elasticity; Timoshenko beam; Euler beam; Stability of solutions of nonlinear ODEs

Domaines: Mécanique des matériaux [physics.class-ph]

A. Della Corte, A. Battista, F. Dell'Isola, Pierre Seppecher. Large deformations of Timoshenko and Euler beams under distributed load. Zeitschrift für Angewandte Mathematik und Physik, 2019, 70 (2), pp.52. ⟨10.1007/s00033-019-1098-y⟩. ⟨hal-02269403⟩