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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Cornaggia_Darrigrand_Le-Marrec_Mahe_SAMAI_2017.pdf (159.18 Ko)
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