Topology optimization for stiffened panels, from linear buckling to postbuckling

This study introduces topology optimization for postbuckling of stiffened panels. A level-set-based topology optimization parameterization, which has been successfully applied to linear buckling optimization, is extended to postbuckling optimization of stiffened panels. The thicknesses of the skin and stiffeners, as well as the stiffener layout and internal topologies can be simultaneously optimized. Stiffened panels under force loading are considered for optimization. The Newton-Raphson scheme with load control is used for postbuckling analysis, where a small imperfection in the form of the first linear buckling mode is imposed on the finite element model. The out-of-plane skin deformation and load-carrying capability are considered to assess the postbuckling behaviors of stiffened panels. Two optimization formulations, respectively considering these two postbuckling metrics are studied. Sensitivity information is shown, and a gradient-based optimizer is used to solve the optimization problems. A numerical example is used to demonstrate the application of the proposed method to postbuckling optimization of stiffened panels and highlight differences from linear buckling optimization.