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

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 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. Contatto: simona.perotto@polimi.it

Ole Sigmund is a world leading researcher within topology optimization. Ole Sigmund is a Professor and Villum Investigator at the Department of Mechanical Engineering, Technical University of Denmark (DTU). He obtained his Ph.D.-degree in 1994 and Habilitation in 2001 and has held research positions at University of Essen and Princeton University. He is a member of the Danish Academy of Technical Sciences and the Royal Academy of Science and Letters and is the former President (2011-15, now EC member) of ISSMO (International Society of Structural and Multidisciplinary Optimization) and former Chairman of DCAMM (Danish Center for Applied Mathematics and Mechanics, 2004-2010). Together with Noboru Kikuchi and Martin Bendsøe, Ole Sigmund is one of the founders and present main contributors to the development of topology optimization methods in academia and industry. His +300 scientifc papers have received ~50000 citations in Google Scholar and an H-index of 85.