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Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

By Rémi Cornaggia, Eric Darrigrand, Loïc Le Marrec and Fabrice Mahé

Abstract

International audienceThis work presents a new enriched finite element method dedicated to the vibrations of axially inhomogeneous Timo-shenko beams. This method relies on the "half-hat" partition of unity and on an enrichment by solutions of the Timo-shenko system corresponding to simple beams with a homogeneous or an exponentially-varying geometry. Moreover, the efficiency of the enrichment is considerably increased by introducing a new formulation based on a local rescaling of the Timoshenko problem. Validations using analytical solutions and comparisons with the classical high-order polynomial FEM, conduced for several inhomogeneous beams, show the efficiency of this approach in the time-harmonic domain. In particular low error levels are obtained over large ranges of frequencies using fixed coarse meshes. Possible extensions to the research of natural frequencies of beams and to simulations of transient wave propagation are highlighted

Topics: Vibrations, Enriched finite elements, Inhomogeneous Timoshenko beams, [PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Mechanics of the structures [physics.class-ph]
Publisher: 'Elsevier BV'
Year: 2020
DOI identifier: 10.1016/j.jsv.2020.115228
OAI identifier: oai:HAL:hal-02050532v2
Provided by: HAL AMU
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