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This and the next slide are from:
Dominik Schillinger, Vissarion Papadopoulos, Manfred Bischoff and Manolis Papadrakakis,
“Buckling analysis of imperfect I-section beam-columns with stochastic shell finite elements”, Computational Mechanics, Vol. 46, No. 3, 2010, pp. 495-510, doi: 10.1007/s00466-010-0488-y
ABSTRACT: Buckling loads of thin-walled I-section beam-columns exhibit a wide stochastic scattering due to the uncertainty of imperfections. The present paper proposes a finite element based methodology for the stochastic buckling simulation of I-sections, which uses random fields to accurately describe the fluctuating size and spatial correlation of imperfections. The stochastic buckling behaviour is evaluated by crude Monte-Carlo simulation, based on a large number of I-section samples, which are generated by spectral representation and subsequently analyzed by non-linear shell finite elements. The application to an example I-section beam-column demonstrates that the simulated buckling response is in good agreement with experiments and follows key concepts of imperfection triggered buckling. The derivation of the buckling load variability and the stochastic interaction curve for combined compression and major axis bending as well as stochastic sensitivity studies for thickness and geometric imperfections illustrate potential benefits of the proposed methodology in buckling related research and applications.
From the website:
Dominik Schillinger writes on the Stochastic Buckling Analysis of Imperfect Structures:
"Buckling loads of thin-walled structures exhibit a wide stochastic scattering due to the uncertainty of imperfections. I worked on finite element based methodologies for the stochastic buckling simulation of I-sections, which employ random fields to accurately describe the fluctuating size and spatial correlation of imperfections. In particular, I developed specialized methods that calibrate random field based imperfection models with series of imperfection measurements."
"The basic simulation process: (1) Measure random imperfections in a series of structural members; (2) Calibrate a suitable power spectrum; (3) Simulate random imperfections; (4) Determine corresponding buckling loads with nonlinear finite elements; (5) Extract stochastic information, e.g. by crude Monte-Carlo."
"The example shows an I-beam with a stochastic geometric imperfection profile that is modeled by the superposition of several 1D random fields."
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