Stochastic FEM Based Stability Analysis of I-Sections With Random Imperfections

The buckling behavior of thin-walled I-sections is very sensitive to imperfections. The experi-mental buckling load of an imperfect I-beam is drastically reduced as compared to the theoretical ultimate strength of the perfect member. Additionally, the fluctuating size and appearance of imperfections result in a wide scattering in experimental buckling loads of nominally equal mem-bers. So far, only little experience exists in modelling imperfection triggered buckling in I-sections from a stochastic point of view. The present study is targeted at simulating the buckling variability of an example series of 6 slender I-beams combining advanced methods of nonlinear structural finite elements and modern stochastic process theory. Closely based on experimental imperfection measurements, appropri-ate models for residual stresses, geometric and thickness imperfections are developed ranging from conventional deterministic approaches to non-homogeneous random fields. For the estima-tion of corresponding evolutionary power spectra, a wavelet based method for separable processes is established. Sampled by spectral representation, random imperfection data are finally intro-duced into a numerical finite element model. For stability analysis, a Fortran implementation of the triangular composite facet shell element TRIC with geometric and material nonlinearity is used. A large scale Monte Carlo simulation is then conducted to determine the response variability of a series of I-section samples with random imperfections under pure compression, pure major axis bending and varying combinations thereof. The results reproduce the stability behavior of experimental tests very well and offer insights into the role of imperfections in the buckling process of the examined I-beams. i