The Certain Generalized Stresses Method for the static finite element analysis of bar and beam trusses with variability

The main purpose of this paper is to present and evaluate the new Certain Generalized Stresses Method (CGSM) to take into account variability in finite element models for static applications. The method is dedicated to thin-walled structures and is presented here for bar and beam trusses. All physical properties may be uncertain. The method relies on the assumption that the generalized stresses are quite stable in presence of variability. This assumption is strictly satisfied for specific cases, when the structure is statically determinate or when the perturbation due to variability is uniform throughout the structure, so the CGSM is an exact method in these cases. The objective of this study is to assess the relevance of this assumption in a statistical sense, for the general case. The method only requires two finite element analyses. The displacement mean value, the standard deviation and the distribution of the displacement are obtained by a mixed CGSM+Monte Carlo approach. However, generally, the displacement mean value and the standard deviation can be obtained in an analytical way. In the examples presented, the variability of displacements is studied. The CGSM has been applied to statically determinate bar and beam structures and indeed exact results have been obtained for this class of examples. It has also been applied to statically indeterminate bar and beam trusses. Very precise results are obtained for the mean value, the standard deviation and the statistical distribution of the displacements. A detailed analysis of errors has been performed in order to justify the high quality level of the results obtained for these examples. The method is quite economical from a computational time point of view.