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

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
Period7 Nov 2019
Held atStony Brook University, United States
Degree of RecognitionInternational