Geometrically nonlinear analysis of thin-walled beams based on the Generalized Beam Theory

The thesis addresses the geometrically nonlinear analysis of thin-walled beams by the Generalized Beam Theory ( GBT ). Starting from the recent literature, the linear theory is illustrated, along with some issues related to GBT finite element formulation. Potential benefits of using the GBT in design are exemplified with reference to the design of roofing systems. To assess the deterioration of member capacity due to cross-section distortion phenomena, the formulation of a geometrically nonlinear GBT is then pursued. The generalization of the GBT to the nonlinear context is performed by using the Implicit Corotational Method ( ICM ), devising a strategy to effectively apply the ICM when considering higher order deformation modes. Once, obtained, the nonlinear model has been implemented using a state-of-the-art mixed-stress finite element. The nonlinear finite element is then implemented starting from the linear GBT one. Extensive numerical results show the performance of the proposed approach in buckling and path-following analyses.