Abstract
In this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters.
Highlights
The problem of structural stability of mechanical systems [1], such as buckling of beam structures under axial compressive loading has attracted the attention of many researchers
In [27], Feng et al coupled random parameters and interval analysis for linear static analysis. If these approaches deal with the problem of mixed uncertainty, their cost remain in some cases high requiring numerous model evaluations
To go further in the analysis, the Sobol indices are directly extracted from the Polynomial Chaos Expansion (PCE) coefficients, they are given in Fig. 8 for both buckling loads, and the name of each variable is given at the top of each sub-figure
Summary
The problem of structural stability of mechanical systems [1], such as buckling of beam structures under axial compressive loading has attracted the attention of many researchers. The first step in engineering for the prediction of buckling is to consider idealized structures with mathematically exact geometries. Structures have imperfections due to the manufacturing process and cannot be considered as homogeneous or geometrically exact. The effect of material and geometric imperfections needs to be considered for a robust prediction of buckling and for the estimation of the main differences with the idealized buckling problem. Many researches carried out in the field of structural stability theory and practice for buckling of beams were focused
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