Topology optimization of microstructures using FFT-based homogenization method

Junji Kato

Nagoya University

With the growing interest in additive manufacturing utilizing topology optimization, it has recently become possible to fabricate optimized porous and lattice structures at the micro-scale (or meso-scale) level. For topology optimization at such small scales, a homogenization method based on the finite element method is generally used. However, in the optimal design of 3D microstructures considering material nonlinearity, the computational cost and memory usage increase dramatically, requiring treatments such as considerably coarsening the element mesh of the microstructures. As a result, a truly optimal topology of microstructure cannot be obtained.

Therefore, we propose a new multiscale topology optimization method using a homogenization method based on Fourier Fast Transform (FFT). Here, we address the problem of finding the optimal topology of a microstructure consisting of two different elastoplastic materials in order to maximize the energy absorption of the entire macrostructure.

It is shown that the proposed method can significantly reduce the computational cost and memory usage, with results that are almost identical to those of conventional homogenization methods based on finite element methods.

Short Bio:

  • February 2010: Received Doctor of Engineering (Dr.-Ing.) from Institute for Structural Mechanics, University of Stuttgart, Germany (Supervisor: Professor Ekkehard Ramm)
  • June 2010: Assistant Professor in the Department of Civil Engineering at Tohoku University, Japan
  • April 2012: Assistant Professor in the International Research Institute of Disaster Science (IRIDeS) at the Tohoku University
  • January 2015: Associate Professor in the Department of Civil Engineering at Tohoku University
  • April 2018-current: A Full Professor in the Department of Civil Engineering at Nagoya University, Japan
  • My research interests include topology optimization and optimal design of microstructures considering nonlinear mechanical behavior and its application to additive manufacturing.
  • I am also a board member of JSCES since 2018, a GC member of IACM since 2023, and an EC member of ISSMO since 2024.