In structural engineering the usage of slender and thin-walled structures is essential to tackle weight-critical problems. It is well-known that many of these structures are stability sensitive and hence tend to buckle if subjected to a compressive loading. This work focuses on a stochastic approach to quantify the impact of geometrical imperfections, which are commonly recognized to be the most influential uncertainties in stability analysis. A Finite Element workflow is presented to retrieve a full statistical description of the critical buckling load of the structure by employing the Monte Carlo Method. It is implemented within the open-source software Kratos Multiphysics. Thereby, the so-called consistently linearized eigenvalue problem is evaluated to obtain the limit or bifurcation points on the structure's load displacement path. With the help of an iterative scheme the classical prebuckling analysis is extended to nonlinear problems. However, before the stability analysis is performed the nodal positions of the FEM mesh are manipulated to account for the to be quantified uncertainties. A geometry perturbation approach is derived from the random field theory, whereby the Karhunen-Loeve (KL) expansion enables the generation of discretized deviation fields. Moreover, a numerical integration scheme is adopted from Betz et al. and applied to solve the KL expansion for arbitrary shaped domains. Taking a closer look at actual engineering structures shows that real imperfections are correlated and spatially dependent. Therefore, an appropriate correlation function is linked to the KL expansion to render a random field that contains the desired characteristics. The correlation length $l_c$ is introduced as governing parameter and its impact on the shape of the final perturbations is extensively discussed. Due to the requirement of a fully populated and hence dense matrix correlating all nodes contained in the FEM model, the presented approach lacks of proper scalablity. To extend the standard implementation to models with larger complexity, the KL expansion is either evaluated in a reduced subspace or an artificially sparse correlation matrix is assembled. It is shown that the results of the given workflow enable the formulation of an accurate lower bound buckling model for the investigated structure. Moreover, additional statistical properties such as estimated expected value and standard deviation can be derived from the obtained load distributions. For validation purposes, the results are exemplary compared to a tried and tested empirical lower bound model.     «

In structural engineering the usage of slender and thin-walled structures is essential to tackle weight-critical problems. It is well-known that many of these structures are stability sensitive and hence tend to buckle if subjected to a compressive loading. This work focuses on a stochastic approach to quantify the impact of geometrical imperfections, which are commonly recognized to be the most influential uncertainties in stability analysis. A Finite Element workflow is presented to retrieve...     »