Fourier representation of geometrical imperfection for probabilistic buckling analysis

Abstract

This research studies the first part of the failure of a compression member structure due to buckling. This unstable equilibrium collapse, exposes brittle failure which occurs suddenly and therefore should be avoided wherever possible. Unavoidable geometric imperfections due to structural fabrication, will weaken the structure against buckling. The behavior of bar under compression will be closely examined by taking a set of geometric imperfection data synthesized from previously available from the measurement of conical shells. Therefore, the two-dimensional surface imperfection is converted into several one-dimensional imperfection with some probability properties. In order to obtain a comparison tool for different type of imperfections, Fourier analysis is used to convert the imperfection into coefficients of trigonometric function. By examining the coefficients, geometric imperfection patterns introduced by a certain fabrication process are able to be identified. The study successfully demonstrates the applicability of Fourier analysis in representing inherent geometric imperfections as an initial step for conducting probabilistic buckling analysis. Fourier analysis has shown its capability to simultaneously characterize imperfections in two crucial parameters - the magnitude and configuration of the imperfection.

Keywords

• buckling analysis
• fourier series
• geometric imperfection
• probabilistic