An unconstrained dynamic approach for the Generalised Beam Theory

Abstract

This paper presents a new approach for the cross-sectional analysis within the framework of the Generalised Beam Theory (GBT), and it is applicable to open, closed or partially closed cross-sections. This approach falls within a category of cross-sectional analysis available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses. The novelty of the proposed approach relies on the use of an unrestrained planar frame for the evaluation of the conventional and extension modes, therefore allowing the identification of both sets of modes from the solution of a planar eigenvalue problem, whose eigenmodes correspond to the sought conventional and extension modes. In the available dynamic GBT approach, the conventional modes are obtained from a planar dynamic analysis enforcing inextensibility to the members of the frame, and the extension modes are then evaluated from the conventional modes enforcing particular constraint conditions. Numerical examples are presented considering open unbranched, open branched and partially closed cross-sections to highlight the ease of use of the proposed approach and to discuss the contribution of the different modes to the structural response. The accuracy of the numerical results is validated against those calculated with a shell element model developed in Abaqus.