Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
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Authors
Danielson, D.A.
Hodges, D.H.
Subjects
NONLINEARITY
BEAMS (SUPPORTS)
TENSORS
ROTATION
DEFORMATION
CURVED BEAMS
BENDING
TORSION
SPHERICAL COORDINATES
MAGNITUDE
DISPLACEMENT
DECOMPOSITION
CARTESIAN COORDINATES
NUMERICAL ANALYSIS
BEAMS (SUPPORTS)
TENSORS
ROTATION
DEFORMATION
CURVED BEAMS
BENDING
TORSION
SPHERICAL COORDINATES
MAGNITUDE
DISPLACEMENT
DECOMPOSITION
CARTESIAN COORDINATES
NUMERICAL ANALYSIS
Advisors
Date of Issue
1987-06
Date
Jun 01, 1987
Publisher
Language
Abstract
A 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.
Type
Article
Description
Applied Mechanics, Biomechanics, and Fluids Engineering; 14-17 Jun. 1987; Cincinnati, OH; United States
Series/Report No
Department
Organization
Ames Research Center
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Journal of Applied Mechanics; p. 258-262; Volume 109
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.