Simultaneous Size, Layout, and Topology Optimization of Stiffened Panels using CAD-based Parameterization

In this paper, an innovative design methodology is proposed to simultaneously optimize the size, layout, and number of stiffeners of a stiffened panel using a gradient-based optimizer. In the proposed method, CAD-based parameterization is used to parameterize the layout of the stiffeners. The location and orientation of each stiffener are controlled with only two layout variables. The geometric constraints to avoid overlapping and crossing of stiffeners are implicitly applied through the layout parameterization scheme, therefore no additional constraints on the grid point coordinates are required. Moreover, the CAD model is maintained throughout the optimization process, therefore the additional step of converting the optimal design back to CAD is eliminated. The layout changes are accommodated in the finite element mesh through the re-meshing technique. The number of stiffeners is controlled by allowing an optimizer to transform an existing stiffener into a ghost stiffener. Every stiffener is assigned a topology variable that can be optimized to a value of either 0 or 1 using a penalization constraint. In case the optimal value is 0 then the contribution of that stiffener in determining the mass and the stiffness of the panel is lost, and it is considered an inactive or ghost stiffener. The stiffener is considered fully active when the optimal value is 1. The sensitivities of grid point coordinates relative to layout variables are calculated analytically. The sensitivities of the structural responses relative to size, layout, and topology variables are achieved through Nastran. The effectiveness of the proposed methodology is evident from the obtained results.