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nonlinear beam kinematics by decomposition of the rotation tensorA simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.
Document ID
Document Type
Reprint (Version printed in journal)
Danielson, D. A.
(Naval Postgraduate School Monterey, CA United States)
Hodges, D. H.
(Army Aviation Systems Command Moffett Field, CA United States)
Date Acquired
August 19, 2013
Publication Date
June 1, 1987
Publication Information
Publication: Journal of Applied Mechanics
Volume: 109
Subject Category
Structural Mechanics
Report/Patent Number
Meeting Information
Applied Mechanics, Biomechanics, and Fluids Engineering(Cincinnati, OH)
Distribution Limits
Work of the US Gov. Public Use Permitted.