Level set based robust shape and topology optimization under random field uncertainties

Shikui Chen, Wei Chen*, Sanghoon Lee

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

231 Scopus citations


A robust shape and topology optimization (RSTO) approach with consideration of random field uncertainty in loading and material properties is developed in this work. The proposed approach integrates the state-of-the-art level set methods for shape and topology optimization and the latest research development in design under uncertainty. To characterize the high-dimensional random-field uncertainty with a reduced set of random variables, the Karhunen-Loeve expansion is employed. The univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is then employed for calculating statistical moments of the design response. The combination of the above techniques greatly reduces the computational cost in evaluating the statistical moments and enables a semi-analytical approach that evaluates the shape sensitivity of the statistical moments using shape sensitivity at each quadrature node. The applications of our approach to structure and compliant mechanism designs show that the proposed RSTO method can lead to designs with completely different topologies and superior robustness.

Original languageEnglish (US)
Pages (from-to)507-524
Number of pages18
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Apr 2010


  • Dimension reduction
  • Level set methods
  • Random field
  • Robust design
  • Shape optimization
  • Topology optimization
  • Uncertainty

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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