A complete dynamic approach to the Generalized Beam Theory cross-section analysis including extension and shear modes. (November 2014)

• Record Type: Journal Article
• Authors: Piccardo, Giuseppe; Ranzi, Gianluca; Luongo, Angelo
• Is Part Of: Mathematics and mechanics of solids. Volume 19:Number 8(2014:Nov.)
• Page Start: 900
• Page End: 924
• Publication Date: 2014-11
• Subjects: Generalized Beam Theory -- thin-walled beams -- cross-section analysis -- dynamic approach -- extensional modes -- shear modes; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286513493107
• Languages: English
• ISSNs: 1081-2865

Abstract

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.