Robust structural optimization using gauss-type quadrature formula

Sanghoon Lee, Ki G. Seo, Shikui Chen, Wei Chen

Research output: Contribution to journalArticlepeer-review


In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.

Original languageEnglish (US)
Pages (from-to)745-752
Number of pages8
JournalTransactions of the Korean Society of Mechanical Engineers, A
Issue number8
StatePublished - Aug 1 2009


  • Gaussian quadrature
  • Robust design
  • Sensitivity analysis
  • Tatistical moments

ASJC Scopus subject areas

  • Mechanical Engineering


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