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Finite Deformation of Slender Beams
Author(s) -
Reismann H.
Publication year - 2001
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 - 10.1002/1521-4001(200107)81:7<481::aid-zamm481>3.0.co;2-1
Subject(s) - cantilever , torsion (gastropod) , beam (structure) , boundary value problem , oblique case , conjugate beam method , deformation (meteorology) , timoshenko beam theory , structural engineering , physics , mechanics , mathematics , mathematical analysis , bending stiffness , engineering , medicine , linguistics , philosophy , surgery , meteorology
The present investigation considers the problem of finite deformation of slender, elastic beams with constant cross‐section. The pertinent non‐linear equations characterizing the deformation of the beam are derived using a variational principle which also yields the associated natural and imposed boundary conditions. The mathematical model of the beam accounts for the (coupled) flexure, torsion, and extension (contraction) of the beam but it neglects deformations due to shear. Two example problems are presented, each considering the deformation of a cantilever beam subjected to oblique (unsymmetrical) loading. Example 1 treats the case of an end loaded beam, whereas Example 2 treats the same beam subjected to a uniformly distributed load. In both examples results are compared to the equivalent cases treated within the framework of (conventional) linear theory.