Multi-scale design methods for topology optimization in the context of extremal stiffness

Groen, J. P. (Guest lecturer)

Activity: Talks and presentationsGuest lectures, external teaching and course activities at other universities


We present a highly efficient method to obtain large-scale, near-optimal designs that are based on optimal multi-scale topologies in the context of extremal stiffness. To do so we make use of a class of multi-scale materials that can reach the theoretical bounds on strain energy. The theory of homogenization-based topology optimization using this class of composite materials is well-developed, and can therefore be used to find an overall optimal material distribution at low computational cost. A downside of these optimal multi-scale designs is that features exist at several length-scales limiting the manufacturability.

The key contribution of this work is to interpret these optimal multi-scale designs on a single length-scale (de-homogenization) while still being close to what is theoretically possible. First of all, a method to interpret these optimal multi-scale microstructures on a single-scale is presented. By doing so a simple class of microstructures can be achieved that is outperforming microstructures obtained by standard topology optimization for multiple anisotropic loading conditions. Afterwards, a method to de-homogenize spatially varying multi-scale designs is presented. By doing so high-resolution designs, near-optimal designs can be achieved on a standard PC. Furthermore, we present a method to have explicit control of the minimum feature size ensuring manufacturability. Compared to standard density-based topology optimization we achieve a reduction in computational cost by almost 2 orders of magnitude for 2D examples, and at least three orders of magnitude in the case of 3D, paving the way for giga-scale designs on a standard PC.

Co-authors: Florian Stutz, Erik Träff, Jun Wu, Yiqiang Wang, Andreas Bærentzen, Niels Aage and Ole Sigmund.
Period25 Oct 2019
Held atComputer Science and Artificial Intelligence Laboratory, MIT, United States, Massachusetts
Degree of RecognitionInternational


  • Topology Optimization