Generalised Beam Theory (GBT) for stiffened sections

Abstract

This paper presents an extension to the Generalised Beam Theory (GBT) approach to describe the response of prismatic thin-walled members stiffened by means of generic plate arrangements at different cross-sections along their length. The conventional deformation modes to be included in the GBT formulation are obtained as the dynamic modes of a planar frame, which represents the cross-section. Two numerical procedures are implemented to account for the presence of the stiffeners. One approach identifies different sets of deformation modes for the unstiffened and stiffened sections, which are then combined for the member analysis. The second procedure relies on the use of constraint equations at the stiffened locations to be included in the member analysis. For the cross-sectional analysis, a new mixed finite element is presented which incorporates the inextensibility condition usually adopted in the framework of the classical GBT, therefore simplifying the steps required for the evaluation of the conventional deformation modes. The proposed technique is applicable to open, closed and partially-closed stiffened sections. Two numerical examples are provided to highlight the ease of use of the method of analysis considering open and partially-closed sections, and their results are validated against those obtained with the commercial finite element software Abaqus.