Keywords: non-linear shell finite element, stability analysis, random imperfections, non-Gaussian stochastic fields, translation fields, spectral representation.

The analysis and design of imperfection sensitive shells had always an appeal to structural engineers and constitute the subject of extensive research. The main issue when dealing with this problem is the big discrepancy between theory and experiment as well as the large scatter in the measured buckling loads. It was soon realized that the problem could only be addressed through modelling taking into account the randomness of the imperfect geometries [1]. In the present paper, the effect of combined geometric, material and thickness variations on the buckling load of thin isotropic imperfect cylindrical shells is re-evaluated, with respect to previous work [2,3], taking into account additional sensitivities due to various non-Gaussian assumptions. To this purpose, a non-Gaussian spatial variability of the Young's modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric imperfections. The Young's modulus and the shell thickness are described by two-dimensional uni-variate uncorrelated homogeneous non-Gaussian stochastic fields using the spectral representation method in conjunction with the translation field theory [4].

The numerical examples presented in this work focus on the relative influence of the non-Gaussian assumption (a lognormal and a beta distribution are used) on the variability of the buckling load, which is calculated by means of the Monte Carlo simulation method. For the determination of the limit load of the shell, a stochastic formulation of the geometrically nonlinear elastoplastic facet triangular shell element TRIC based on the midpoint method, is implemented. A shallow hinged isotropic cylindrical panel with a point load at the middle of its top surface is selected as a test example. As a result of the analysis, the first two statistical moments of the buckling load seem to be independent from the marginal probability density function of the input parameters (Young's modulus and thickness). However, the shape of the buckling load distribution is different in each case. In addition, the lowest buckling load is found to be substantially reduced with respect to the buckling load of the perfect shell. Useful conclusions are finally derived concerning the effect of the spectral characteristics of the geometric, material and thickness imperfections on the buckling behaviour of the shell structure.

1

C.A. Schenk, G.I. Schuëller, "Buckling Analysis of Cylindrical Shells with Random Geometric Imperfections", Int. J. of Non-Linear Mechanics, 38(7), 1119-1132, 2003. doi:10.1016/S0020-7462(02)00057-4

2

V. Papadopoulos, M. Papadrakakis, "The Effect of Material and Thickness Variability on the Buckling Load of Shells with Random Initial Imperfections", Computer Methods in Applied Mechanics and Engineering, 194(12-16), 1405-1426, 2005. doi:10.1016/j.cma.2004.01.043

3

G. Stefanou, M. Papadrakakis, "Stochastic Finite Element Analysis of Shells with Combined Random Material and Geometric Properties", Computer Methods in Applied Mechanics and Engineering, 193(1-2), 139-160, 2004. doi:10.1016/j.cma.2003.10.001

4

M. Grigoriu, "Simulation of Stationary Non-Gaussian Translation Processes", J. of Engineering Mechanics (ASCE), 124(2), 121-126, 1998. doi:10.1061/(ASCE)0733-9399(1998)124:2(121)

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