Simultaneous sizing, layout and topology optimization for buckling and postbuckling of stiffened panels

This thesis aims to develop a computational scheme for simultaneous sizing, layout and topology optimization for buckling and postbuckling of stiffened panels. Many efforts have been made using structural optimization techniques to improve the buckling and postbuckling behaviours of stiffened panels, focusing on sizing and layout optimization. Stiffener internal topologies have however, received little attention for optimization. This reduces the design space that can be searched, and consequently limits the potential improvement in structural performance. In this thesis, a level-set-based topology optimization parameterization is developed, enabling the simultaneous optimization of the thicknesses of the skin and stiffeners, and stiffener layout and internal topologies. The simultaneous sizing, layout and topology optimization for buckling of panels stiffened with straight stiffeners is investigated for the first time. Numerical investigations demonstrate the effectiveness of the proposed method. The benefit of simultaneously conducting sizing, layout and topology optimization for the design of stiffened panels is also demonstrated. Since stiffness is commonly considered in the topology optimization field, the difference between buckling-driven and stiffness-driven designs is investigated and discussed. Besides buckling, stress is another critical failure criterion of stiffened panels. The proposed method is extended to stiffened panel design under both stress and buckling constraints. The simultaneous sizing, layout and topology optimization for postbuckling of panels with straight stiffeners is investigated for the first time. The proposed method is extended to postbuckling optimization. The out-of-plane skin deformation and the load-carrying capability are considered to access the postbuckling behaviours of stiffened panels. Compared with buckling optimization, postbuckling optimization can provide a design with more promising postbuckling behaviours of interest. The design of panels with curved stiffeners is investigated. The level-set-based method is extended to simultaneously optimize both stiffener curves and internal topologies. Numerical investigations demonstrate and validate the proposed method for simultaneous layout and topology optimization of curved stiffened panels. Compared with panels with straight stiffeners, curved stiffened panels have the potential to result in lighter weight designs