PERTURBATION APPROACH TO ELASTIC POSTBUCKLING ANALYSIS

PERTURBATION APPROACH TO ELASTIC POST- BUCKLING ANALYSIS* R. Casciaro$}, G. Garcea$, G. Attanasio% and F. Giordano% $Dipartimento Strutture, Universita` della Calabria, Cosenza, Italy %ALENIA Aeronautica, Pomigliano d’Arco, Italy (Received 21 February 1997; accepted 21 August 1997) Abstract—This paper aims to show that eective and reliable computer codes can be obtained by a suit- able finite element implementation of the Koiter’s perturbation method. However, careful attention has to be paid to all the implementation details in order to avoid kinematical inconsitencies that can strongly aect the results. # 1998 Elsevier Science Ltd. All rights reserved Key words—finite elements, nonlinear analysis, perturbation method INTRODUCTION The analysis of slender structures characterized by complex buckling and post-buckling phenomena and by a strong imperfection sensitivity is largely penalized by a lack of adequate computational tools. Standard algorithms, based on the incre- mental–iterative approach, are extremely expensive for both hardware needs and computational times. As a consequence of the high costs of the single run, it becomes practically impossible to perform the large number of successive runs necessary to the sensitivity analysis, that is, to evaluate the reduction in load capability of the structure due to all possible imperfections. This circumstance usually prevents any optimal design process based on a global safety analysis from being performed. Koiter’s perturbation approach [1, 2] gives a po- tentially convenient alternative process. In fact, this method is characterized by several relevant advan- tages: . a fully automated finite element analysis can be implemented; . the results are qualitatively and quantitatively accurate; . a complete synthetic description of the structural behavior is obtained, including the deterioration due to load imperfections, geometrical defects and damages; . the analysis is very fast, of the same order as a linearized stability analysis; . re-analyses for dierent imperfections require only a small fraction of the first analysis time; . the approach allows the a priori knowledge of the most dangerous defect or damage shapes with respect to the load capability of the structure. It is worth mentioning that as a result of some unsatisfactory experiences in the past, the perturbation method is usually considered by the computational people as a powerful tool for getting analytical ‘at hand’ solutions in particular cases (see Ref. [3]), but unsuitable to be implemented within a general finite element context that would provide reliable results (the general opinion does not diers substantially from that expressed in Ref. [4]). As a consequence, while finite element method (FEM) adaptations of Koiter’s approach started from the early 1970s [5–17], it is not used yet in any commercial code. The main objective of the present paper is to show that the draw- backs that were experienced are due to implementation mistakes more than to intrinsic defects of the method itself. By an adequate attention to some ‘minor’ details, finite element implemen- tations of the perturbation method can be both accurate and reliable [18–42]. Globally ecient codes could be obtained by implementing the method into general purpose host codes. THE PERTURBATION METHOD The method aims to produce an accurate evalu- ation of the nonlinear equilibrium path of an elastic nonlinear structure subjected to proportional load- ing and defined by the stationary condition of the potential energy: Computers & Structures Vol. 66, No. 5, pp. 585–595, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0045-7949/98 $19.00 + 0.00 PII: S0045-7949(97)00112-0 *The paper is a slightly revised version of that presented at the MSC 22nd European Users’ Conference, Rome, September 1995. }To whom all correspondence should be addressed. 585

PERTURBATION APPROACH TO ELASTIC POSTBUCKLING ANALYSIS

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