The effect of material and thickness variability on the buckling load of shells with random initial imperfections

Abstract

The effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper. For this purpose, the concept of an initial ‘imperfect’ structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as the thickness of the shell. The initial geometric imperfections are described as a two-dimensional uni-variate (2D-1V) stochastic field with statistical properties that are either based on an available data bank of measured initial imperfections or assumed, in cases where no experimental data is available. In order to describe the non-homogeneous characteristics of the initial imperfections, the spectral representation method is used in conjunction with an autoregressive moving average model with evolutionary power spectra based on a statistical analysis of the experimentally measured imperfections. In cases where no experimental results is available, the initial imperfections are assumed to be homogeneous and their impact on the buckling load is investigated on the basis of ‘worst’-case scenarios with respect to the correlation length parameters of the stochastic fields. The elastic modulus and the shell thickness are described as 2D-1V non-correlated homogeneous stochastic fields, while the stochastic stiffness matrix of the shell elements is formulated using the local average method. The Monte Carlo Simulation method is used to calculate the variability of the buckling load, while for the determination of the limit load of the shell, a stochastic formulation of the elastoplastic and geometrically non-linear TRIC facet triangular shell element is implemented.