Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 66, Issue -, Pages 33-42Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijnonlinmec.2014.03.008
Keywords
Direct model; Fiber-model; Tubular beam; Ovalization; Identification of elastic constants
Categories
Funding
- Italian Ministry of University and Research (MIUR) [2010MBJK5B]
Ask authors/readers for more resources
A direct non-linear one-dimensional model of an elastic, thin-walled, planar beam is formulated. The model accounts for changes in shape of the cross-section, in particular the ovalization (or flattening) occurring in tubular beams. The deformation of the cross-section is described in the spirit of the Generalized Beam Theory, as a linear combination of known deformation modes and unknown amplitude functions, said to be distortions. Kinematics calls for introducing distortional and bi-distortional strains, in addition to the usual strain measures of rigid cross-section beams. The balance equations are derived through the Virtual Power Principle, in which distortional and bi-distortional stresses, as well as distortional forces, are defined as conjugate quantities of distortional strain-rates and velocities, respectively. A non-linear, fully coupled, hyperelastic law is assumed. All the distortional quantities and the constitutive law are identified, via energy equalities, from a three-dimensional fiber-model of thin-walled beam where, for simplicity, just a distortion mode is considered. The model is specialized to a Euler-Bernoulli tubular beam, in which only constitutive non-linearities are retained, while kinematics is linearized. The relevant non-linear equations are solved, via a perturbation method, for several static loadings and for large-amplitude free vibrations. The interaction occurring between global bending and cross-section distortion is analyzed. (C) 2014 Elsevier Ltd. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available