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A finite element model for composite beams undergoing large deflection with arbitrary cross‐sectional warping
Author(s) -
Stemple Alan D.,
Lee Sung W.
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280911
Subject(s) - image warping , finite element method , deflection (physics) , structural engineering , beam (structure) , mathematics , mathematical analysis , physics , engineering , classical mechanics , computer science , artificial intelligence
A finite element formulation has been developed to take into account the warping effect of composite beams undergoing large deflection or finite rotation. This formulation is to be used to model combined bending, torsional and extensional behaviour of composite helicopter rotor blades. The new approach can model thin to moderately thick walled composite beams with complicated cross‐sections, tapers and arbitrary planforms. The warping effects are incorporated by assuming warping displacements superimposed over cross‐sections normal to the beam axis in the deformed configuration of a shear flexible beam. The strain is assumed to vary linearly through the wall thickness. The fixed or total Lagrangian description is adopted in the present formulation and the Newton–Raphson method is used to solve the non‐linear equilibrium equation resulting from the finite element approximation. Numerical tests of example problems demonstrate the validity and effectiveness of the present approach.