Keywords: reliability analysis, random fields, stochastic finite elements, robustness analysis, response surfaces, moving least squares.

Any mechanical or civil engineering structure possesses some natural randomness in its properties which fluctuates over space: deviations from the design geometry, surface roughness, scatter of material properties and distributed loads are few examples. When such random fluctuations shall be taken into account in an optimization, robustness or reliability analysis, they are modelled as random fields. A random field normally comprises a great number of random variables. The high dimension most often inhibits accurate reliability analyses based on Monte Carlo methods. Former methods to reduce the space of random variables may be not suitable for certain kinds of problem, as in the present case of stability analysis of a geometrically imperfect shell.

The present paper proposes a method to identify the most relevant random variables, such that both reqirements are met: to model the random field accurately and to consider those variables which have greatest influence on the structural response which will be considered in the subsequent reliability analysis.

This method uses tools from robustness analysis. Based on a Monte Carlo simulation, robustness analysis identifies statistical dependencies between any input and output quantities in the observed system. It comprises tools such as quadratic correlations and coefficients of determination, among others. It helps to identify the most relevant random variables in the sense explained above and thus to reduce the random space drastically.

For computation of reliability, an adaptive response surface method is introduced, which utilizes improved moving least squares approximations. It is very flexible and able to model even highly nonlinear limit state functions and such with multiple beta points. Additional support points are considered in an automatic adaptive scheme in order to get local refinements of the model in important regions. The surrogate model is very fast to evaluate compared to a limit state evaluation by finite element analyses. This allows for an accurate reliability calculation by advanced Monte Carlo methods.

As an example, the stability of a cylindrical shell structure with random imperfections is studied. Imperfections are discretized by using the stochastic finite element method. The conventional and the proposed new way to reduce the random space are compared by means of the resulting failure probability. The reduced random field model is analysed by the adaptive response surface method in combination with adaptive sampling. Accuracy and efficiency are compared with directional sampling with direct evaluation of the structure.

It is demonstrated that first, the used methodology is accurate and second, the efficiency is so good that analyses of real examples of reliability assessment involving random fields become feasible. The probabilistic and structural analysis tasks are performed with the optiSLang, SoS and SLang software packages.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £120 +P&P)