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Large deformation and stability of a shear‐deformable beam with a variable length under a uniformly distributed force
Author(s) -
Humer Alexander
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110104
Subject(s) - beam (structure) , clamping , deformation (meteorology) , boundary value problem , mechanics , shear (geology) , shear force , conjugate beam method , transverse plane , physics , classical mechanics , geometry , mathematics , optics , materials science , structural engineering , mathematical analysis , engineering , mechanical engineering , bending stiffness , composite material , meteorology
A beam held by two spatially fixed supports, may slide relative to these as soon as external loads are imposed. In particular, the possibly large deformation of a shear‐deformable beam under a uniformly distributed, transverse force is investigated, which is clamped at its left side, while it may slide horizontally through another clamping device at its right side. Consequently, the material point of the beam that is currently located at the latter and the length of the portion of the reference configuration situated in between the two supports depend on the external forces and therefore are not known in advance. In order to obtain approximate solutions, a finite element scheme is utilized, in which a coordinate transformation is introduced, by which the difficulties of non‐material boundary conditions and the unknown length of the beam are circumvented elegantly. It turns out that no static equilibrium is found, if the external forces are increased beyond a critical value, since the beam would slide out infinitely in that case. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)