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Higher‐order beam model with eigenstrains: theory and illustrations
Author(s) -
Corre Grégoire,
Lebée Arthur,
Sab Karam,
Ferradi Mohammed Khalil,
Cespedes Xavier
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700180
Subject(s) - beam (structure) , cantilever , kinematics , degrees of freedom (physics and chemistry) , order (exchange) , box girder , mathematics , structural engineering , mathematical analysis , physics , classical mechanics , engineering , girder , finance , quantum mechanics , economics
A higher‐order beam model based on the asymptotic expansion method was suggested by Ferradi et al.[11][M. K. Ferradi, 2016] Introducing new degrees of freedom specific to the applied loads into the kinematics of the beam, this model yields fast and accurate results. The present paper focuses on the extension of this model to the case of arbitrary eigenstrains expressed in a separate form between the longitudinal coordinate and the in‐section coordinates. The asymptotic expansion procedure is recalled and the derivation of a higher‐order beam model performed. The beam model is interpolated with NURBS. The case of a bridge deck heated on a localized area is studied. A second case study of a prestressed cantilever beam is then investigated. The results of the higher‐order beam model are compared to a 3D solution in each example. The performances of the beam model appears to be accurate and very time‐efficient.