Axially Compressed Cylindrical Shell Containing Axisymmetric Random Imperfections: Fourier Series Techniques and ASME Section VIII Division 2 Rules

This paper presents the comparison of reliability technique that employ Fourier series representations of random axisymmetric imperfections in axially compressed cylindrical shells with evaluations prescribed by ASME Section VIII, Division 2. The ultimate goal of the reliability type technique is to predict the buckling load associated with the axially compressed cylindrical shell. The representation of initial geometrical imperfections in the cylindrical shell requires the determination of appropriate Fourier coefficients. The buckling of cylindrical shells in any type of loading is sensitive to the form and amplitude of geometric imperfections present in the structure. Initial geometric imperfections have significant effect on the load carrying capacity of axisymmetrical cylindrical shells. Many deterministic and probabilistic techniques are there to predict shell behavior during buckling. Fourier decomposition is used to interpret imperfections as structural features can be easily related to the different components of imperfections. The mean vector and the variance-covariance matrix of Fourier coefficients are calculated from the simulated shell profiles. Recommendations for further use of Fourier coefficients through simulation by Monte Carlo Method are laid down. Large number of shells thus created can be used to calculate buckling stress for each shell. The probability of the ultimate buckling stress exceeding a predefined threshold stress can be calculated.