Homogenization-based topology optimization for multiple loading cases

Groen, J. P. (Speaker), Stutz, F. C. (Other), Sigmund, O. (Other), Erik Träff (Other), Jun Wu (Other)

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The objective of this work is to present a method to obtain high-resolution, manufacturable designs based on efficient homogenization-based topology optimization for multiple loading cases. The focus of this work is on compliance minimization of linear-elasticity problems, for which it is known that the optimal solution is in the space of layered materials, specifically in the space of rank-3 laminates for plane problems s.t. multiple loads [1].

Recently, an efficient method has been proposed that can be used to obtain high-resolution manufacturable structures for plane problems with a single loading case [2]. However, for engineering practice more complicated loading situations are required. A key problem however, is that there are multiple laminates that can achieve the same optimal properties when multiple loadings are considered. Hence, when topology optimization is performed for multiple loading cases a large (possibly infinite) number of solutions can attain the optimal energy. Besides an optimal shape we thus require something extra, i.e. a parameterization that can be interpreted efficiently on a single scale.

A novel method to obtain such a smooth and manufacturable parameterization will be presented. Comparisons with traditional high-resolution or multi-scale topology optimization methods will not only emphasize the near-optimality of the obtained designs, but also show a significant reduction in computational cost.

[1] Avellaneda M. Optimal bounds and microgeometries for elastic two-phase composites. SIAM Journal on Applied Mathematics 1987; 47(6):1216–1228, doi:10.1137/0147082.
[2] J.P. Groen and O. Sigmund. Homogenization-based topology optimization for high-resolution manufacturable micro-structures. International Journal of Numerical Methods in Engineering 2018(online, 2017); 113(8):1148–1163, doi: 10.1002/nme.5575

Period20 May 2019
Event title13th World Congress of Structural and Multidisciplinary Optimization: null
Event typeConference
Conference number13
LocationBeijing, China
Degree of RecognitionInternational


  • Topology Optimization
  • Homogenization