Topology optimization design of graded infills for 3D curved volume by a conformal sweeping method

• Published in: Computer methods in applied mechanics and engineering Vol. 412; p. 116009
• Main Authors: Zhou, Ying, Gao, Liang, Li, Hao
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2023
• Subjects: Conformal mapping; Graded infill; Swept volume; Topology optimization; Topology optimization; Swept volume; Graded infill; Conformal mapping
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2023.116009

Swept volumes are widely existed in various significant engineering applications. However, an effective design method for the lightweight swept volume with porous infills is lacking. This paper develops a novel topology optimization method for the design of curved volumes filled with spatially-varying microstructures. The infill optimization formulation for the curved swept volume is established to concurrently optimize both the microstructural geometry and the macroscopic distribution of the graded infills, aiming at minimizing the structural compliance subject to a global volume constraint. A conformal sweeping approach is developed to map the curved volume into a regular parameterization​ cube along the sweeping trajectory. In this fashion, the graded infills defined in a regular unit cell can be first filled into this cubic parameterization space, and then reversely mapped into the original volume to conformally match the curved geometry. A numerical homogenization method for parallelepiped microstructures is introduced to evaluate several sampling microstructures. The local level sets approach is used to create a family of connectable microstructures, while a polynomial interpolation is employed to rapidly interpolate the graded property of the generated microstructures based on the properties of sampling microstructures. Two different sweeping volume types are investigated. Several examples with respect to the infill optimization design of curved swept volumes are provided to illustrate the characteristics of the proposed method. [Display omitted] •A systematic optimization method is presented for graded infill within swept volumes.•A conformal parameterization approach is developed for swept volumes.•Geometries between curved volumes and infill microstructures are well matched.•Infill design by two different sweeping types are investigated.•The presented method is general and suitable for different infill types.