세미나

Recent developments in multi-scale and non-linear topology optimization problems

By Ole Sigmund, Villum Investigator, Dept. of Mechanical Engineering, Technical University of Denmark

Topology optimization was introduced as a multi-scale approach in the seminal paper by Bendsøe and Kikuchi from 1988.

However, simpler isotropic density interpolation schemes soon substituted the original homogenization-based approach.

With advances in additive manufacturing technologies that may realize complex lattice and infill structures, needs for efficient multiscale topology optimization approaches have been revived.

The first part of the talk will give an overview of latest advances in so-called de-homogenization techniques that generate highly optimized lattice structures from homogenization-based topology optimization results, also taking local and global buckling instabilities into account.

The obtained results will be compared and discussed in relation to alternative, but much more expensive “one-scale” topology optimization problems run on super computers.

The second part of the talk will give an overview of latest developments within single and multi-material topology optimization approaches for generating pre-scribed non-linear force-displacement relations. 

By appropriate definition of goal and response functions, it is demonstrated that one can tailor very complex response curves almost at will. 

On-going studies include formulations that allow internal member contact through so-called third medium approaches.