Topology optimization under uncertainty via non-intrusive polynomial chaos expansion

Vahid Keshavarzzadeh, Felipe Fernandez, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


This paper presents a systematic approach for topology optimization under uncertainty that integrates non-intrusive polynomial chaos expansion with design sensitivity analysis for reliability-based and robust topology optimization. Uncertainty is introduced in loading and in geometry to address the manufacturing variability. The manufacturing variability is modeled via a thresholding technique in which the threshold field is represented by a reduced dimensional random field. Response metrics such as compliance and volume are characterized as polynomial chaos expansions of the underlying uncertain parameters thus allowing accurate and efficient estimation of statistical moments, failure probabilities and their sensitivities. The number of simulations is reduced for linear structures under loading uncertainty by means of superposition. Efficiency of the non-intrusive polynomial chaos approach is highlighted by comparison with the Monte Carlo method in terms of the number of simulations. To demonstrate the effect of uncertainty, optimized designs that consider uncertainty are compared to those that do not. Comparisons of polynomial chaos expansion to existing analytical methods on a benchmark numerical example are also provided for reliability-based and worst case designs.

Original languageEnglish (US)
Pages (from-to)120-147
Number of pages28
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - May 1 2017


  • Manufacturing variability
  • Polynomial chaos expansion
  • Reliability based topology optimization
  • Robust topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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