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Large deformations of Timoshenko and Euler beams under distributed load

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Abstract

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.

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Authors and Affiliations

  1. M&MoCS, Research Center, University of L’Aquila, L’Aquila, Italy

    A. Della Corte, A. Battista, F. dell’Isola & P. Seppecher

  2. Université de La Rochelle, La Rochelle, France

    A. Battista

  3. DISG, University La Sapienza, Rome, Italy

    F. dell’Isola

  4. IMATH, Université de Toulon, Toulon, France

    P. Seppecher

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  1. A. Della Corte
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  2. A. Battista
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  4. P. Seppecher
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Correspondence to A. Della Corte.

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Della Corte, A., Battista, A., dell’Isola, F. et al. Large deformations of Timoshenko and Euler beams under distributed load. Z. Angew. Math. Phys. 70, 52 (2019). https://doi.org/10.1007/s00033-019-1098-y

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