Optimization of structural topology in the high-porosity regime

Blaise Bourdin, Robert Kohn

Research output: Contribution to journalArticle

Abstract

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
Volume56
Issue number3
DOIs
StatePublished - Mar 2008

Fingerprint

Laminates
topology
Porosity
Topology
laminates
porosity
optimization
Quadratic programming
Shape optimization
quadratic programming
linear programming
Linear programming
Stiffness
continuity
stiffness
Microstructure
microstructure

Keywords

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

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

Optimization of structural topology in the high-porosity regime. / Bourdin, Blaise; Kohn, Robert.

In: Journal of the Mechanics and Physics of Solids, Vol. 56, No. 3, 03.2008, p. 1043-1064.

Research output: Contribution to journalArticle

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