%0 Journal Article
%T A model reduction technique for beam analysis with the asymptotic expansion method
%+ Laboratoire Navier (navier umr 8205)
%+ Strains
%A Ferradi, Mohammed Khalil
%A Lebée, Arthur
%A Fliscounakis, Agnès
%A Cespedes, Xavier
%A Sab, Karam
%< avec comité de lecture
%@ 0045-7949
%J Computers & Structures
%I Elsevier
%V 172
%P 11 - 28
%8 2016-08
%D 2016
%R 10.1016/j.compstruc.2016.05.013
%K Higher order 3D beam element
%K Transverse deformation
%K Warping
%K Model reduction
%K Asymptotic analysis
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph]Journal articles
%X In this paper, we apply the asymptotic expansion method to the mechanical problem of beam equilibrium, aiming to derive a new beam model. The asymptotic procedure will lead to a series of mechanical problems at different order, solved successively. For each order, new transverse (in-plane) deformation and warping (out of plane) deformation modes are determined, in function of the applied loads and the limits conditions of the problem. The presented method can be seen as a more simple and efficient alternative to beam model reduction techniques such as POD or PGD methods. At the end of the asymptotic expansion procedure, an enriched kinematic describing the displacement of the beam is obtained, and will be used for the formulation of an exact beam element by solving analytically the arising new equilibrium equations. A surprising result of this work, is that even for concentrated forces (Dirac delta function), we obtain a very good representation of the beam’s deformation with only few additional degrees of freedom.
%G English
%L hal-01691129
%U https://enpc.hal.science/hal-01691129
%~ ENPC
%~ CNRS
%~ UR-NAVIER
%~ PARISTECH
%~ IFSTTAR
%~ UNIV-EIFFEL
%~ IFSTTAR-UNIVEIFFEL