Reliability-based topology optimization of trusses with stochastic stiffness

Mehdi Jalalpour, James K. Guest, Takeru Igusa

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


A new method is proposed for reliability-based topology optimization of truss structures with random geometric imperfections and material variability. Such imperfections and variability, which may result from manufacturing processes, are assumed to be small in relation to the truss dimensions and mean material properties and normally distributed. Extensive numerical evidence suggests that the trusses, when optimized in terms of a displacement-based demand metric, are characterized by randomness in the stiffness that follow the Gumbel distribution. Based on this observation, it was possible to derive analytical expressions for the structural reliability, enabling the formulation of a computationally efficient single-loop reliability-based topology optimization algorithm. Response statistics are estimated using a second-order perturbation expansion of the stiffness matrix and design sensitivities are derived so that they can be directly used by gradient-based optimizers. Several examples illustrate the accuracy of the perturbation expressions and the applicability of the method for developing optimal designs that meet target reliabilities.

Original languageEnglish (US)
Pages (from-to)41-49
Number of pages9
JournalStructural Safety
StatePublished - Jul 2013
Externally publishedYes


  • Geometric imperfections
  • Manufacturing defects
  • Material uncertainties
  • Perturbations
  • Topology optimization

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Safety, Risk, Reliability and Quality


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