Stochastic analysis of imperfection sensitive unstiffened composite cylinders using realistic imperfection models

Abstract The important role of imperfections on decreasing the buckling load of structural cylinders has been investigated by scientists and engineers for the past century, yet there is currently no method that is able to stochastically replicate the full range of realistic imperfections for a full account of possible buckling loads. This drawback impairs optimised design as designers are restrained to using an outdated and conservative design philosophy which dates from 1968. Modern manufacturing methods and materials such as composites require new, optimised design measures to take full advantage of their efficiencies. Stochastic analyses can optimise and improve the reliability of such cylinders through accurate prediction of the range of conceivable buckling loads by realistic simulation and sensitivity analyses. A stochastic procedure which realistically models imperfection sensitive composite shells is investigated in this paper. Monte-Carlo simulations of axially compressed cylinders with the full range of imperfection types are performed to show that the stochastic methods described here are able to accurately capture the scatter in the buckling load introduced from the imperfections. The results from a sensitivity analysis indicate that loading imperfections play the largest role in reducing the buckling load knockdown factors of the shell.

[1]  Mark W. Hilburger,et al.  Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells , 2000 .

[2]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Stochastic Processes by Spectral Representation , 2007 .

[3]  Matteo Broggi,et al.  Efficient modeling of imperfections for buckling analysis of composite cylindrical shells , 2011 .

[4]  Raimund Rolfes,et al.  Sensitivities to Geometrical and Loading Imperfections on Buckling of Composite Cylindrical Shells , 2002 .

[5]  Dominik Schillinger,et al.  The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes , 2013 .

[6]  Th. A. Winterstetter,et al.  Stability of circular cylindrical steel shells under combined loading , 2002 .

[7]  Richard Degenhardt,et al.  The influence of imperfections on the buckling behavior of unstiffened CFRP-cylinders , 2008 .

[8]  James H. Starnes,et al.  Future directions and challenges in shell stability analysis , 1997 .

[9]  Forrest J. Masters,et al.  Non-Gaussian simulation of local material properties based on a moving-window technique , 2003 .

[10]  Manolis Papadrakakis,et al.  EVOLUTIONARY POWER SPECTRUM ESTIMATION OF STRONGLY NARROW-BAND RANDOM FIELDS , 2009 .

[11]  Richard Vynne Southwell,et al.  On the General Theory of Elastic Stability , 1914 .

[12]  Theodore V. Galambos,et al.  Guide to stability design criteria for metal structures , 1998 .

[13]  W. T. Koiter THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[14]  Johann Arbocz,et al.  The effect of general imperfections on the buckling of cylindrical shells , 1968 .

[15]  J. H. Starnes,et al.  Buckling behavior of compression-loaded composite cylindrical shells with reinforced cutouts , 2005 .

[16]  W. Root,et al.  An introduction to the theory of random signals and noise , 1958 .

[17]  Theodore von Karman,et al.  The buckling of thin cylindrical shells under axial compression , 2003 .

[18]  J. Arbocz,et al.  The Imperfection Data Bank, a Mean to Obtain Realistic Buckling Loads , 1982 .

[19]  Raimund Rolfes,et al.  PROBABILISTIC DESIGN OF AXIALLY COMPRESSED COMPOSITE CYLINDERS WITH GEOMETRIC AND LOADING IMPERFECTIONS , 2010 .

[20]  R. C. Tennyson,et al.  Buckling of laminated composite cylinders: a review , 1975 .

[21]  Mark W. Hilburger,et al.  Toward a Probabilistic Preliminary Design Criterion for Buckling Critical Composite Shells , 2003 .

[22]  Endre Dulácska,et al.  Buckling of Shells for Engineers , 1984 .

[23]  Dominik Schillinger,et al.  The Method of Separation: A Novel Approach for Accurate Estimation of Evolutionary Power Spectra , 2011 .

[24]  Richard O. Duda,et al.  Use of the Hough transformation to detect lines and curves in pictures , 1972, CACM.

[25]  David Bushnell,et al.  Buckling of Shells-Pitfall for Designers , 1981 .

[26]  Rolf Zimmermann,et al.  Geometric imperfections and lower-bound methods used to calculate knock-down factors for axially compressed composite cylindrical shells , 2014 .

[27]  Richard Degenhardt,et al.  Investigations on imperfection sensitivity and deduction of improved knock-down factors for unstiffened CFRP cylindrical shells , 2010 .

[28]  Carlo Poggi,et al.  Stochastic imperfection modelling in shell buckling studies , 1995 .

[29]  Johann Arbocz,et al.  ANILISA - Computational module for Koiter's imperfection sensitivity theory , 1989 .

[30]  Richard Degenhardt New robust design guideline for Imperfection sensitive composite launcher Structures , 2011 .

[31]  Pol D. Spanos,et al.  Spectral Stochastic Finite-Element Formulation for Reliability Analysis , 1991 .

[32]  Raimund Rolfes,et al.  Robust design of composite cylindrical shells under axial compression — Simulation and validation , 2008 .

[33]  Jendi Kepple,et al.  Improved stochastic methods for modelling imperfections for buckling analysis of composite cylindrical shells , 2015 .

[34]  Dominik Schillinger,et al.  Accurate estimation of evolutionary power spectra for strongly narrow-band random fields , 2010 .

[35]  Johann Arbocz,et al.  Collapse of axially compressed cylindrical shells with random imperfections , 1995 .

[36]  Matteo Broggi,et al.  RELIABILITY ASSESSMENT OF AXIALLY COMPRESSED COMPOSITE CYLINDRICAL SHELLS WITH RANDOM IMPERFECTIONS , 2011 .

[37]  J. Arbocz,et al.  The initial imperfection data bank at the Delft University of Technology: Part I , 1979 .

[38]  Johann Arbocz,et al.  The effect of imperfect boundary conditions on the collapse behavior of anisotropic shells , 2000 .

[39]  Rolf Zimmermann,et al.  Experiments on buckling of CFRP cylindrical shells under non-uniform axial load. , 1994 .

[40]  J. P. Peterson,et al.  Buckling of thin-walled circular cylinders, NASA SPACE VEHICLE DESIGN CRITERIA (Structures) , 1965 .

[41]  Mark W. Hilburger,et al.  Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures , 2003 .

[42]  W. Flügge,et al.  Die Stabilität der Kreiszylinderschale , 1932 .

[43]  Richard Degenhardt,et al.  Exploring the constancy of the global buckling load after a critical geometric imperfection level in thin-walled cylindrical shells for less conservative knock-down factors , 2013 .