Optimal design of non-uniform curved grid-stiffened shell with various stiffener patterns

This paper presents a non-uniform curved grid-stiffened shell design method aiming to enhance structural performance using various stiffener patterns, allowing simultaneous optimization of stiffener thickness and stiffener layout. Firstly, the grid-stiffened cell description function is defined using quadratic polynomial functions, comprising the orthogrid, the triangle grid, the rotated triangle grid, and the Kagome grid. Then, the non-uniform stiffener layout description function is established using the sawtooth function, while a filter function is employed to ensure the smooth and continuous of the stiffeners. Moreover, the analytical sensitivity is thoroughly derived, and the optimization problem is formulated. Finally, the effectiveness of the proposed method is demonstrated through three representative optimization examples: the cantilever beam, the special-shaped plate, and the S-shape shell. The study concludes that the proposed method can optimize arbitrary flat plates by embedding the design domain into the background domain. Additionally, the proposed method can be extended to perform stiffener design on complex surfaces by establishing projection relationship between the flat surface and the curved surface. Optimization results indicate that the non-uniform curved grid-stiffened shell design exhibits superior structural performance compared to the uniform grid-stiffened shell design.