Isogeometric analysis-based buckling optimization framework for grid-stiffened shells using asymptotic homogenization method and Rayleigh-Ritz method

The grid-stiffened shell is a promising aerospace structure configuration with high load-carrying capacity. However, it is challenging to fully exploit its optimal load-carrying efficiency. In this paper, an isogeometric analysis-based optimization framework in which the size and layout of stiffeners can be optimized simultaneously is provided to maximize the buckling load of the grid-stiffened shell. Firstly, the grid-stiffened cell is established by the beam-shell coupling model. The high-order continuous isogeometric degenerated shell elements and Timoshenko beam elements are used to simulate the skin and the stiffener, respectively. Owing to the high-order continuous property of isogeometric degenerated shell elements, the sensitivity required for the gradient-based optimization solver can be obtained analytically. Then, the equivalent stiffness coefficients of the grid-stiffened cell are obtained by the asymptotic homogenization method, and the buckling analysis efficiency of the equivalent model is improved by the Rayleigh-Ritz method. Typical illustrative examples are carried out to verify the effectiveness and efficiency of the proposed framework, and the effects of initial stiffener layouts and stiffener heights on the optimization results are discussed in detail. The optimization results indicate that the proposed framework can obtain novel grid-stiffened shells, which significantly outperforms traditional orthogonal grid-stiffened shells in terms of load-carrying capacity.