Multiscale Topology Optimization Applying FFT‐Based Homogenization

• Published in: International journal for numerical methods in engineering Vol. 126; no. 4
• Main Authors: Matsui, Masayoshi, Hoshiba, Hiroya, Nishiguchi, Koji, Ogura, Hiroki, Kato, Junji
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 28.02.2025; Wiley Subscription Services, Inc
• Subjects: Design optimization; Dimensional analysis; fast Fourier transform; Fast Fourier transformations; Finite element method; Fourier transforms; Homogenization; Macrostructure; Microstructure; microstructure design; multiscale analysis; Optimization; Topology optimization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.70009

ABSTRACT Advances in 3D‐printing technology have enabled the fabrication of periodic microstructures that exhibit characteristic mechanical performances. In response, multiscale topology optimization, which finds the optimal design of microstructure for the macrostructure geometry and performance requirements, has become a hot topic in the field of structural optimization. While the basic optimization framework based on the homogenization theory spanning macro and microscales is available, it is computationally expensive and not easily applicable in practical scenarios such as high‐resolution design for precision modeling and reliable design considering non‐linearities. To address this issue, we focus on a homogenization analysis using a fast Fourier transform as an alternative approach to conventional finite element analysis and develop an optimization method with fast computing speed and low memory requirements. In this paper, we define a simple stiffness maximization problem with linear elastic materials and conduct two and three‐dimensional optimization analyses to evaluate the validity and performance of the proposed method. We discuss the advantages of computational cost, the influence of the filtering process, and the appropriate setting of material contrast.