Optimization of structural topology in the high-porosity regime

Blaise Bourdin, Robert V. Kohn

Research output: Contribution to journalArticlepeer-review


We propose a new approach to topology optimization, based on the use of "single-scale laminates" as structural components. The method is well-founded, because in the high porosity limit these structures achieve maximal stiffness and minimal weight. The method is useful, because the Hooke's law of a single-scale laminate has a simple, explicit formula which scales linearly with weight. And it is interesting, because the selection of relatively simple, manufacturable designs can be addressed using linear or quadratic programming. Our contributions are two-fold: (a) we establish the foundation of this approach, by defining single-scale laminates and giving self-contained proofs of their optimality in the high-porosity limit; and (b) we explore two numerical applications-minimizing weight with a constraint on the Hooke's law, and imposing continuity on a spatially varying microstructure.

Original languageEnglish (US)
Pages (from-to)1043-1064
Number of pages22
JournalJournal of the Mechanics and Physics of Solids
Issue number3
StatePublished - Mar 2008


  • Effective properties
  • Extremal microstructures
  • High-porosity limit
  • Homogenization
  • Optimal design

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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