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A nonlinear theory for spinning anisotropic beams using restrained warping functionsA geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.
Document ID
Document Type
Conference Paper
Ie, C. A. (NASA Langley Research Center Hampton, VA, United States)
Kosmatka, J. B. (California Univ. La Jolla, United States)
Date Acquired
August 16, 2013
Publication Date
April 1, 1993
Subject Category
Report/Patent Number
AIAA PAPER 93-1303
Meeting Information
AIAA, ASME, ASCE, AHS, and ASC, Structures, Structural Dynamics and Materials Conference, 34th and AIAA and ASME, Adaptive Structures Forum(La Jolla, CA)
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