Shape and Generalized Topology Optimization of Curved Grid Stiffeners Through the Level Set-Based Density Method

A shape and generalized topology optimization method based on the level set-based density method is proposed to design the curved grid stiffeners. The overall layout of the stiffeners is described by combining many single stiffeners, and each single stiffener is described by a level set function parameterized by using the compactly supported radial basis functions (CS-RBFs). The curvilinear path of each stiffener is described by the zero iso-contour of each level set function, and the width of each stiffener is described by applying an interval projection to each level set function. The combination operation that is similar to the Boolean operation "union" is achieved by using the p-norm method. The expansion coefficients of CS-RBFs are taken as part of the design variables of the optimization, and they are responsible for changing the shape of curved stiffeners. A topology design variable is assigned to each single stiffener, and it is responsible for changing the existence of single stiffeners. The proposed method is validated through several numerical examples, and the results demonstrate that the shape and topology of stiffeners can be effectively changed during the optimization.