A MODEL FOR THE CORRELATION STRUCTURE OF THE RANDOM OUT-OF-FLATNESS IMPERFECTION OF THE PLATES

Abstract eng:
Structural reliability assessment requires accurate, realistic specifications of the stochastic properties of both the geometrical and mechanical uncertainties inherent in the system. For thin-walled structures, the most important factor determining the response variability is random deviation from the ideal shape: appropriate models of the configuration defects are therefore sought. For the plates of bridge and ship’s plating even today only very little information is available on the initial bowing in statistical terms, while theoretical approaches to the imperfection modelling appear quite arbitrary. The paper presents an analytical derivation of a second-moment stochastic model of the out-of-flatness imperfection of rectangular thin plates, closely fitting with the causal intervention of the manufacturing steps: (i) cutting from an indefinite, initially bent, sheet; (ii) best fitting at a specific member position; (iii) continuous welding to the boundary elements, with concomitant uneven heating and cooling. Via a mechanical-mathematical statement of the relations between the construction stages and the mid-surface warping, we reconstruct the analytical expression for the overall imperfection profile, which appears as the linear superposition of many contributions, that depend on a small number influencing factors. We use this representation to determine the first and second-order statistics of the non-homogeneous random field of the lack-of-flatness. In particular, we obtain the explicit format of the autocorrelation function, in terms of the stochastic properties of the “mother” sheet curvature tensor and of fastening and welding parameters. The achieved result is a deeper insight into the main features of the plate’s geometrical imperfection and a sort of correlation template, useful for evaluating other a priori assumed theoretical models.

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