A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the proba...A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.展开更多
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the University Network of Excellence in Nuclear Engineering (UNENE) through an Industrial Research Chair program,"Risk-Based Life Cycle Management of Engineering Systems",at the University of Waterloo
文摘A novel numerical procedure, which realizes the stochastic analysis with dimensional reduction integration （DRI）, C-type Gram-Charlier （CGC） series, and finite element （FE） model, is proposed to assess the probability distribution of structural per- formance. From the relationship between the weighting function of orthogonal polynomial and probability density function （PDF） of random variable, the numerical integration formulas are derived for moment computation. Then, distribution of structural uncertainty response can be approximated by the CGC series with the calculated moments. Three engineering appli- cations for the distribution of, the maximum displacement of a ten-bar planer truss, natural frequency of an auto frame, and Von-Mises stress of a bending pipe, are employed to illustrate the computational efficiency and accuracy of the proposed methodology. As compared with plain Monte Carlo simulation （MCS）, the method can obtain the accurate distribution of structural performance. Especially at the tail region of cumulative distribution function （CDF）, results have shown the satisfy- ing estimators for small probabilities, say, Pc [104, 10-3]. That implies the method could be trusted for structural failure prob- ability prediction. As the computational efficiency is concerned, the procedure could save more than two orders of computational resources as compared with the direct numerical integration （NI） and MCS. Furthermore, realization of the procedure does not require computing the performance gradient or Hessian matrix with respect to random variables, or reshaping the finite element matrix as other stochastic finite element （SFE） codes. Therefore, it should be an efficient and reliable routine for uncertainty structural analysis.
