Reliability of axially compressed cylindrical shells with random axisymmetric imperfections

Abstract

The paper is concerned with the effect of random axisymmetric imperfections on the buckling of circular cylindrical shells under axial compression. The initial imperfections are considered as random functions of the axial coordinate. This is done by expanding them in terms of the buckling modes of the associated perfect structure, and then treating the Fourier coefficients as random variables.Initially the probabilistic properties of the initial imperfections of cylindrical shells, produced by the same manufacturing process, are studied. In contrast to earlier works the probabilistic properties (the mean function and the autocorrelation function or the spectral density) are not assumed. The mean vector and the variance-covariance matrix of the Fourier coefficients are calculated from experimental measurements of the shell profiles.Next the Monte Carlo Method is applied. The Fourier coefficients of the initial imperfection representations are simulated by a special numerical procedure. Thus large number of shells is “created”. For each shell a deterministic analysis of buckling stress evaluation is carried out. Finally, the reliability function representing the probability (i.e. fraction of an ensemble) of the buckling stress exceeding the specified stress is calculated. The reliability function permits to evaluate the design stress for the whole ensemble of shells produced by a given manufacturing process, defined as the stress level for which the desired reliability is achieved. The paper represents an extension of the approach given in Ref. [1] to shell structures.