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Communication Dans Un Congrès Année : 2017

Exponential approximation and enriched FEM for rods and Timoshenko beams

Résumé

This study proposes a new enriched finite element method to handle vibrations of rods (traction-compression) and beams (bending) with varying cross-sections. In time-harmonic domain, closed-form analytical solutions for Timoshenko beams exist only for exponential cross-sections, and we therefore focus on finite elements enriched with such solutions. More precisely, for a given beam or rod with varying section, we use the enrichment corresponding to an optimal approximation by an exponential-by-parts beam or rod. The best approximation is established using an energetic criterion. Thereafter, the proposed method is presented for a rod whose section is approximated by a unique exponential profile, and extensions are then briefly discussed.
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Dates et versions

hal-01835865 , version 1 (11-07-2018)

Identifiants

  • HAL Id : hal-01835865 , version 1

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Rémi Cornaggia, Eric Darrigrand, Loïc Le Marrec, Fabrice Mahé. Exponential approximation and enriched FEM for rods and Timoshenko beams. 8e Biennale Française des Mathématiques Appliquées et Industrielles (SMAI 2017), Jun 2017, Ronce-les-Bains, France. ⟨hal-01835865⟩
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