Improved stochastic methods for modelling imperfections for buckling analysis of composite cylindrical shells

Abstract Imperfection sensitive CFRP cylindrical shells are used in a variety of civil and aerospace applications and feature a large scatter in buckling load levels induced from imperfections introduced from their manufacture. Currently, there are no complete methods that can realistically simulate cylinders with a full spectrum of imperfection types for a complete diagnosis of possible buckling loads. This forces shell designers to utilise an outdated, inefficient and conservative design philosophy that is unsuitable for modern manufacturing methods and materials. Stochastic analyses can optimise and improve the robust design and reliability of such cylinders through accurate prediction of the range of conceivable buckling loads by realistic simulation of structural imperfections. Such imperfections include initial shell-wall geometric, thickness and material imperfections and non-uniform applied end-loads. A procedure which aims to improve the stochastic modelling of thickness and material imperfections in imperfection sensitive composite cylindrical shells is proposed. Monte-Carlo simulations of axially compressed cylinders are performed to show that the stochastic methods described here are able to capture the scatter introduced from the imperfections. The results show that the axial buckling load of the specific cylinder analysed here can be reduced to 29.5 kN and increased to over 40 kN from a perfect load of 38.2 kN from material and thickness imperfections alone.

[1]  George Stefanou,et al.  Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields , 2007 .

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

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

[4]  Response variability of cylindrical shells with stochastic non-Gaussian material and geometric properties , 2011 .

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

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

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

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

[9]  Pol D. Spanos,et al.  Stochastic processes evolutionary spectrum estimation via harmonic wavelets , 2005 .

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

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

[12]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

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

[14]  Leon Cohen,et al.  Time Frequency Analysis: Theory and Applications , 1994 .

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

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

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

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

[19]  Manolis Papadrakakis,et al.  The effect of material and thickness variability on the buckling load of shells with random initial imperfections , 2005 .

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

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

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

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

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

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

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

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

[28]  Joseph Morlier,et al.  Smart monitoring of aeronautical composites plates based on electromechanical impedance measurements and artificial neural networks , 2013 .

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