Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume 19, Issue 8, Pages 900-924Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286513493107
Keywords
Generalized Beam Theory; thin-walled beams; cross-section analysis; dynamic approach; extensional modes; shear modes
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Funding
- Italian Ministry of Education, Universities and Research (MIUR), through the PRIN [2010MBJK5B]
- Australian Research Council [DP1096454]
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A simple and efficient complete dynamic approach' is proposed, and named GBT-D, to evaluate a suitable basis of modes for the elastic analysis of thin-walled members in the framework of Generalized Beam Theory (GBT). The basis includes conventional and non-conventional modes, the latter accounting for transverse extension and membrane shear strain of the plate elements forming the cross-section, which identically vanish in the former set. The method relies on the solution of two distinct eigenvalue problems, governing the in-plane and the out-of-plane free oscillations of a segment of a thin-walled beam. Both the eigenvalue problems, differential in origin, and defined on a one-dimensional spatial domain, are transformed into an algebraic problem by means of a discretization carried out at the cross-section middle line. Numerical examples are then presented to outline the ease of use of the proposed method considering a single plate, an open cross-section and a partially closed one. Member analyses are also performed for the simplest boundary conditions, to validate the accuracy of the proposed GBT-D approach against finite element method results and analytical solutions, highlighting the importance in including the non-conventional modes.
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