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Large deformations of 1D microstructured systems modeled as generalized Timoshenko beams

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Abstract

In the present paper we study a natural nonlinear generalization of Timoshenko beam model and show that it can describe the homogenized deformation energy of a 1D continuum with a simple microstructure. We prove the well posedness of the corresponding variational problem in the case of a generic end load, discuss some regularity issues and evaluate the critical load. Moreover, we generalize the model so as to include an additional rotational spring in the microstructure. Finally, some numerical simulations are presented and discussed.

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Authors and Affiliations

  1. Uiversité de La Rochelle, La Rochelle, France

    A. Battista

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

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

  3. University La Sapienza, Rome, Italy

    A. Della Corte & F. dell’Isola

  4. IMATH-Université de Toulon, Toulon, France

    P. Seppecher

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  1. A. Battista
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  2. A. Della Corte
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  3. F. dell’Isola
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  4. P. Seppecher
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Battista, A., Della Corte, A., dell’Isola, F. et al. Large deformations of 1D microstructured systems modeled as generalized Timoshenko beams. Z. Angew. Math. Phys. 69, 52 (2018). https://doi.org/10.1007/s00033-018-0946-5

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