The Analysis Of Structural Reliability Using Response Surface Methods

Reliability theory is widely adopted to analyze the practical engineering which theuncertainties are considered. Because of heavy demand of FEM calculations, traditionalstructural reliability analysis methods are difficult to be applied to practical engineering. Theimproved response surface method (RSM) is proposed and used to analyze the reliability of astiffened composite panel in this thesis researches. The main contents and conclusions in thisthesis are listed as following:1) Discussion of classical RSM and high dimensional model representation (HDMR)The paper discusses the advantage and disadvantage of classical RSM and HDMR. It isconvenient to use classical RSM in reliability analysis as the classical RSM adopts quadraticpolynomial, but classical RSM cannot ensure the accuracy of approximation in global. Theadvantage of HDMR is to convert exponential increasing function into polynomial function,but the Runge phenomenon arises when the degree of polynomial function is higher than7.2）Improved HDMRTo overcome the shortcomings of classical HDMR, The paper adopts Aitken rapiditeration, Aitken interpolation and Gauss-Hermite quadrature points to improve HDMR.Aitken interpolation resolves high order interpolation to multiple linear interpolation to avoidthe Runge phenomenon of classical HDMR. The numerical examples illustrated that theimproved HDMR has high accuracy and efficiency in the analysis of reliability.3） The application of improved HDMRThe paper analyzes the reliability of a stiffened composite panel using the improvedHDMR and introduces correlation coefficient R2to verify the accuracy of improved HDMR.As there is a large number of variables (118in total), the paper firstly reduces the number ofvariables according to the non-dimensional sensitivities and then analysis static strengthreliability and buckling reliability of a stiffened composite panel. The results illustrated thatthe improved HDMR has obvious advantage over classical RSM.