Conformal Modeling and Design of Thin-Walled Curved Lattice Structures With Multiple Gradient Parameters

Abstract

Abstract. In this work, a modeling and design method is proposed for the thin-walled curved lattice structure with multiple gradient parameters, including relative density, unit cell relative orientation, and unit cell size. For the thin-walled structure with a three-dimensional (3D) free-form surface, the relationship between the gradient parameters of the 3D free-form surface and the 2D parametric domain is established based on the conformal mapping method. Then, the signed distance function of the lattice unit cell is computed in the 2D parametric domain, and a Fourier transform-based method is used to obtain the 2D graded lattice structure according to gradient parameters. Then, the topology optimization for the compliance minimization is conducted in the 2D parametric domain, and the principal stress directions are calculated, which are used in the design of 2D graded lattice structures as a view to improve the stiffness performance. Based on the interpolation and offset algorithms, a 3D thin-walled structure with graded lattice is constructed from the 2D graded lattice structure. Finally, the effectiveness of the method is verified by several numerical examples and mechanical experiments, and the influences of gradient parameters on the stiffness performance of the thin-walled lattice structures are discussed.