Non-parametric Structural Reliability Analysis using Random Fields and Robustness Evaluation

In reliability and robustness analysis, imperfections of a mechanical or structural system, such as material properties or geometrical deviations, are modelled as random fields in order to account for their fluctuations over space. A random field normally comprises a huge number of random variables. The present paper proposes a method to reduce the random variables set. This reduction is performed on the basis on a robustness analysis. In this way, numerical difficulties can be avoided and the efficiency of the subsequent reliability analysis is enhanced. As an example, the reliability of a cylindricral shell structure with random imperfections is studied. Within this example, the imperfections are discretized by Stochastic Finite Element methods. it is demonstrated, how robustness analysis is employed in order to identify the most relevant random variables. The probability of failure is computed by Monte Carlo simulation involving Latin Hypercube sampling. The failure criterion is derived from a comparison of the linear buckling loads of the perfect and the imperfect structures. This so-called non-parametric structural reliability analysis is a new method to estimate the safety and reliability of finite element structures in such cases where a CAD-based parametrization is not possible or not meaningful. The probabilistic and structural analysis tasks are performed with the optiSLang, SoS and SLang software packages.