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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 36
Numerical Modelling of the Effects of a Reliability Indicator for Damaged ElastoDissipative Composites S. Carbillet and M.L. Boubakar
Applied Mechanics Laboratory Raymond Chaléat, FEMTOST Institute, UMR 6174, FrancheComté University, CNRS, Besançon, France S. Carbillet, M.L. Boubakar, "Numerical Modelling of the Effects of a Reliability Indicator for Damaged ElastoDissipative Composites", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 36, 2006. doi:10.4203/ccp.83.36
Keywords: second moment reliability methods, laminates, mesomacro modelling, damage, (visco)elasticity, (visco)plasticity, incremental laws, failure probability.
Summary
Because of the lack of knowledge of the longterm composite materials behaviour,
the building of sufficiently reliable composite structures needs designers to use
very high safety coefficients. As a result, the composite solution in leading
industries, aeronautics for instance, looses a large part of its interest because of over
sizing. This article proposes an objective reliability index for damaged composites
with strongly nonlinear behaviour. To calculate this index, a reliability computation
algorithm is coupled with a finite element code in which the integration of the finite
strain laminate behaviour is perfectly assessed, to minimize the
errors and uncertainties of the modelling response.
Within the context of a mesoscopic approach to model the nonlinear behaviour of laminate composites made of a polymer matrix reinforced with long fibres, the simple ply constitutive law, including damage, (visco)plasticity and (visco)elasticity by Boubakar et al. [1,2] is recalled. Its integration within a context of spaceshell finite elements has been realised using a multistep predictioncorrection algorithm. Modelling the identification parameters has been executed using the method of Carbillet [3] with a hybrid algorithm and the experimental data is obtained using cylindrical tubes subject to traction and internal pressures. To evaluate laminate reliability, one can calculate its failure probability, defined as the joint probability density integral on the failure domain in the Xspace (physical parameters space), by taking into account the failure scenarios and the nominal parameter uncertainties. An estimation of the failure probability can be obtained using a secondmoment method such as the first order reliability method (FORM) due to Breitung [4], which determines the first order reliability index due to Hasofer et al. [5]. In order to compute , the Yspace of the reduced centered Gaussian variables is employed. To assess the Yspace from the Xspace, the Nataf [6] transformation is used. The value of and the conception point (failure surface point) are classically obtained by solving a minimisation problem using the RackwitzFiessler algorithm [7]. To introduce the space conception parameters' variability, an exponential type autocorrelation is applied. The numerical integration parameters' influence, on the reliability index, is studied in the case of a laminated squared tube [+55, 55, +55, 55, 90] clamped at one of its edges and loaded by a deviated force acting on the other edge. The geometric, loading and material data are defined as being Gaussian uncorrelated random variables. References
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