Uncertainty Quantification of Buckling Loads of Thin and Slender Structures Applying Linear and Nonlinear Analysis

Abstract

The evaluation of the buckling load is a crucial issue when designing different types of structures. It is well known that buckling loads of structures are highly sensitive to random deviations from a nominal design, which may involve uncertainty regarding structural properties, geometry or boundary conditions. Hence, quantifying the level of uncertainties associated with buckling loads is a task of paramount importance.

The buckling load can be approximated by means of a linearized approach (or linear buckling analysis), which involves the solution of an eigenvalue/eigenvector problem. While such an approach is quite convenient from a numerical viewpoint, it may offer limited insight due to its linearized nature. On the contrary, a full nonlinear buckling analysis (using, e.g. a Newton-Raphson scheme) may offer better prediction of the buckling load at the expense of higher numerical costs when compared to a linearized analysis. Considering these issues, this work aims at estimating the second-order statistics (mean and standard deviation) of buckling loads of structural systems which can be modeled as frames and whose imperfections are characterized by means of probabilistic models. The proposed approach is cast within the framework of control variates. This allows to exploit correlations existing between buckling loads predicted using linearized and nonlinear analysis. In fact, the more expensive analysis (that is, nonlinear approach) is run a few times only, while the cheaper analysis (that is, linearized approach) is run a considerable number of times. In this way, it is possible to estimate the statistics of the true buckling load, even when the linearized approach is involved in the analysis.