VCUT level set method for topology optimization of functionally graded cellular structures

This paper presents a variable cutting (VCUT) level set based topology optimization method to design functionally graded cellular structures (FGCS). A variable and continuous cutting function by interpolating with a set of height variables is proposed to generate functionally graded cellular structures, which offers a novel tool to optimize the macroscopic graded pattern. Due to the continuity of the cutting function, perfect geometric connections between adjacent cells are guaranteed without imposing extra constraints in the optimization. In addition, a solid covering skin can be easily attached to the FGCS by means of the variable cutting function. Three FGCS design problems, including graded density control, compliance minimization and layered cellular structure design, are presented to demonstrate the effectiveness and applicability of the proposed method. The optimized 2D and 3D macroscopic FGCS designs exhibit well-performing structural layout with fully connected micro-scale geometries. (C) 2019 Elsevier B.V. All rights reserved.