Two-scale buckling topology optimization for grid-stiffened cylindrical shells

Stiffened shells are widely used in aerospace structures such as launch vehicles and aircraft wings. This paper presents a novel two-scale topology optimization method to design the innovative grid-stiffened pattern for maximizing the critical buckling load of thin-walled cylindrical shells. On the micro-scale, the asymptotic homogenization method is employed to calculate the general stiffness coefficients of the cell. On the macro-scale, the maximum critical buckling load is set as the objective to drive the topology optimization on the micro-scale. Besides, the repeated eigenvalues are considered both in the sensitivity analysis of buckling loads and the optimization solver with a sub-problem based on the Method of Moving Asymptotes (MMA). Through the optimization, we can obtain the optimal configuration of the grid-stiffened cell. In this paper, an illustrative example of the grid-stiffened cylindrical shell for maximizing the critical buckling load is carried out to validate the effectiveness of the proposed optimization method. In comparison to the optimal orthogrid shell, the critical buckling load with the optimal pattern obtained by the proposed optimization method have a dramatically increase of 21.7%. It can be concluded that the proposed method has huge potential to design the configuration of the grid-stiffened cell of cylindrical shells.