Buckling assessment of thin-walled plates with uncertain geometrical imperfections based on non-probabilistic field model

It is well-known that the buckling response of thin-walled structures is greatly affected by initial geometrical imperfections. In this study, the uncertainty in such geometrical imperfections is modelled by a non-probabilistic field model that is a reasonable and convenient alternative to the probabilistic random field representation of uncertainties with limited samples. After representing the bounded field uncertainty as a function of a reduced set of uncorrelated uncertain coefficients using the series expansion method, the buckling assessment problem of thin-walled plates is then constructed to minimize the critical buckling load under the non-probabilistic field description of imperfections and the volume constraint of plates. The optimization problem is solved effectively using a standard gradient-based algorithm with adjoint-variable sensitivity analysis. Numerical examples are given to demonstrate the validity and applicability of the proposed model for assessing both the critical buckling load and the worst imperfection pattern in thin-walled plates.