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**On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen-Loève expansions.**
*(English)*
Zbl 1159.74351

Summary: For the accurate prediction of the collapse behaviour of thin cylindrical shells, it is accepted that geometrical and other imperfections in material properties and loading have to be accounted for in the simulation. There are different methods of incorporating imperfections, depending on the availability of accurate imperfection data. The current paper uses a spectral decomposition of geometrical uncertainty (Karhunen-Loève expansions). To specify the covariance of the required random field, two methods are used. First, available experimentally measured imperfection fields are used as input for a principal component analysis based on pattern recognition literature, thereby reducing the cost of the eigenanalysis. Second, the covariance function is specified analytically and the resulting Friedholm integral equation of the second kind is solved using a wavelet-Galerkin approach. Experimentally determined correlation lengths are used as input for the analytical covariance functions. The above procedure enables the generation of imperfection fields for applications where the geometry is slightly modified from the original measured geometry. For example, 100 shells are perturbed with the resulting random fields obtained from both methods, and the results in the form of temporal normal forces during buckling, as simulated using LS-DYNA\(^{\circledR}\), as well as the statistics of a Monte Carlo analysis of the 100 shells in each case are presented. Although numerically determined mean values of the limit load of the current and another numerical study differ from the experimental results due to the omission of imperfections other than geometrical, the coefficients of variation are shown to be in close agreement.

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\textit{K. J. Craig} and \textit{W. J. Roux}, Int. J. Numer. Methods Eng. 73, No. 12, 1715--1726 (2008; Zbl 1159.74351)

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