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Robust Structural Optimization Using Gauss-type Quadrature Formula

가우스구적법을 이용한 구조물의 강건최적설계

  • Lee, Sang-Hoon ;
  • Seo, Ki-Seog ;
  • Chen, Shikui (Northwestern University, Dept. of Mechanical Eng.) ;
  • Chen, Wei (Northwestern University, Dept. of Mechanical Eng.)
  • 이상훈 (한국원자력연구원) ;
  • 서기석 (한국원자력연구원, 핵주기시스템공학기술개발부) ;
  • ;
  • Published : 2009.08.01

Abstract

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.

Keywords

Robust Design;Gaussian Quadrature;Statistical Moments;Sensitivity Analysis

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