Sensitivity analysis for optimization design of non-uniform curved grid-stiffened composite (NCGC) structures

Conventional grid-stiffened composite structures are designed with straight and uniformly distributed stiffeners. In this paper, a new concept of non-uniform curved grid-stiffened composite structures (NCGCs) with curved non-uniformly distributed stiffeners is proposed, which can significantly boost the design space and flexibility for high efficient composite structures. Under the framework of homogenization-based global/local analysis, optimization design of NCGCs can be solved as material/sizing and shape optimization of local representative cell configurations (RCCs). In the presented contribution, efficient analytical sensitivities with respect to both the skin/stiffener material/sizing parameters and the RCC shape parameters are derived systemically. Sensitivities with respect to the RCC shape parameters are highlighted and derived based on linear membrane and bending transformations between physical and master domains by an affine mapping for the assumed parallelogram RCCs. Optimal material properties, sizes or curved stiffener layout can be efficiently obtained by using the proposed sensitivity calculation method. The accuracy is validated using numerical examples with analytical and finite difference solutions. Finally, a design study of a NCGC panel with linearly varying stiffener angles is presented to demonstrate the feasibility and efficiency of the proposed method.