Axially Compressed Cylindrical Shell Containing Axisymmetric Random Imperfections:

Abstract

ABSTRACT This paper presents the comparison of reliability technique that employ Fourier series representations of random asymmetric imperfections in axially compressed cylindrical shell with evaluations prescribed by ASME Boiler and Pressure Vessel Code, Section VIII, Division 1 and 2. The ultimate goal of the reliability type technique is to predict the buckling load associated with the axially compressed cylindrical shell. Initial geometric imperfections have significant effect on the load carrying capacity of asymmetrical cylindrical shells. Fourier decomposition is used to interpret imperfections as structural features can be easily related to the different components of imperfections. The initial functional description of the imperfections consists of an axisymmetric portion and a deviant portion appearing as a double Fourier series. The representation of initial geometrical imperfections in the cylindrical shell requires the determination of appropriate Fourier coefficients. The mean vector and the variance-covariance matrix of Fourier coefficients are calculated from the simulated shell profiles. Multi-mode analysis are expanded to evaluate a large number of potential buckling modes for both predefined geometries and associated asymmetric imperfections as a function of position within a given cylindrical shell. 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 also be calculated. Keywords: Buckling; Asymmetric Imperfections; Fourier Series; Cylindrical Shell. NOMENCLATURE λ = Non-dimensional buckling load μ = Poisson"s ratio ξ i = Magnitude of imperfection as a fractional value of shell thickness θ = Non-dimensional number associated with the circumferential coordinates ξ = Non-dimensional number associated with the axial coordinates σ A (ξ) = Elements of Variance-covariance matrix C w0 (ξ 1 ,θ 1 ,ξ 2 ,θ 2 ) = Auto-covariance function k = Number of half waves in axial direction l = Number of full waves in circumferential direction P cl = Classical buckling load of a perfect shell P cr = Critical buckling load of a shell with imperfections Proceedings of IMECE2008 2008 ASME International Mechanical Engineering Congress and Exposition October 31-November 6, 2008, Boston, Massachusetts, USA Copyright©2008 by ASME 2 R = Radius of the shell E = Young"s Modulus L = Length of the shell t = Wall thickness of the shell D 0 = Outside diameter of the shell W n (ξ,θ) = Initial imperfection function IMECE2008-6879