A geometry projection method for shape optimization

J. Norato, R. Haber, D. Tortorelli, M. P. Bendsøe

Research output: Contribution to journalArticlepeer-review


We present a new method for shape optimization that uses an analytical description of the varying design geometry as the control in the optimization problem. A straightforward filtering technique projects the design geometry onto a fictitious analysis domain to support simplified response and sensitivity analysis. However, the analytical geometry model is referenced directly for all, purely geometric calculations. The method thus combines the advantages of direct geometry representations with the simplified analysis procedures that are possible with fictitious domain analysis methods, such as the material distribution methods commonly used in topology optimization. The projected geometry measure converges to the indicator function of the analytical geometry model in the limit of numerical mesh refinement. Consequently, optimal designs obtained with the new method converge to solutions of well-defined continuum optimization problems in the limit of mesh refinement. This property is confirmed in example computations for minimum compliance design of an elastic structure subject to a volume constraint and for minimum volume design subject to a maximum stress constraint.

Original languageEnglish (US)
Pages (from-to)2289-2312
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Issue number14
StatePublished - Aug 14 2004


  • Fictitious Domain
  • Geometry Projection
  • Shape Optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


Dive into the research topics of 'A geometry projection method for shape optimization'. Together they form a unique fingerprint.

Cite this