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Closed‐form analysis of a higher‐order composite box beam theory
Author(s) -
Kroker Andreas M.,
Becker Wilfried
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910080
Subject(s) - cantilever , beam (structure) , kinematics , timoshenko beam theory , structural engineering , discretization , finite element method , stiffness , bending moment , stiffness matrix , displacement (psychology) , shell (structure) , transverse plane , plane (geometry) , mathematics , mathematical analysis , geometry , physics , materials science , engineering , classical mechanics , composite material , psychology , psychotherapist
A higher‐order theory is developed for composite box beams with rectangular, closed cross‐sections. Each cross‐section is therefore divided into two flanges and webs. Displacement representations are chosen for each part separately. The in‐plane kinematics is 2nd order for the flanges and even 3rd order for the webs. The kinematics of the four parts is interconnected with the help of geometric coupling. All in‐plane stress components can be obtained directly by using a reduced stiffness matrix for each single layer. The layups of the laminates for the flanges and webs are independent from each other. Only a symmetric layup with balanced angles is necessary. The determined differential equation system of 2nd order including four independent functions can be solved completely in a closed‐form analytical manner. As an actual example a cantilever beam under combined bending moment and transverse force is considered. The results obtained by this new theory are compared with the results of a FEM‐model with a very fine shell element discretization. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)