A Level Set Based Density Method for Optimizing Structures with Curved Grid Stiffeners

A level set based density method is proposed for the optimization of structures with curved grid stiffeners. It combines the ideas of both the level set method and the three-field approach of the SIMP method to explicitly describe the fully-resolved details of stiffeners. The iso-contours of two basic level set functions are used to describe the curvilinear paths of two groups of stiffeners, and a cosine-transformation is respectively applied to the two basic level set functions so that the stiffeners are endowed with the information of width. Radial basis functions are used to parameterize the two basic level set functions. Thereafter, the two cosine-transformed level set functions are combined together by using a differentiable maximum function, and one obtains a pseudo density function. Finally, a threshold projection is applied to the pseudo density function, and one arrives at a physical density with a black–white pattern where the black stripes represent the stiffeners. The physical density is directly used for the finite element analysis. Several numerical examples prove that the proposed design optimization method is effective.