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International audience; In previous work, the nonlinear localization was first presented and studied in the case of large displacements but only for globally stable structural responses. In this paper, the influence of the local error criterion on the performance of the strategy is investigated in structures exhibiting more complex behaviour, such as snap-through and snap-back. Second, a path following method is implemented in the domain decomposition framework of the strategy in order to track the solution around a critical point (snap-through and snap-back).

As an extension of safety factors, the Lack-Of-Knowledge theory (LOK) is an answer to model validation issues in structural mechanics. The approach is based on a decomposition of the model into several substructures and a global description of uncertainties at that level through basic LOK on stiffness matrices. These uncertainties are introduced using intervals with probabilistic bounds. The theory then enables to propagate uncertainties on a quantity of interest. Previous work presented results for linear static and dynamic problems. We introduce in this paper a propagation method of the basic LOKs on buckling loads of structures and present its application on academical and industrial examples.

International audience; The finite element simulation of structures subjected to post-buckling still faces computational limits, especially for large stiffened structures. Several solving strategies have already been proposed in response to this issue. Among them are the adaptive model reduction solving techniques which demonstrated their ability to drastically reduce the number of unknowns as well as to control the approximation error of solving non-linear problems like post-buckling. The challenges regarding these techniques are the computation of a reduced basis at lower cost, the use of an efficient adaptive procedure and the limitation of the number of call to the adaptive procedure. This paper proposes a Post-Buckling Adaptive Model Reduction (PBAMR) strategy, which requires only two initial Ritz vectors without compromising the accuracy of the simulation. This solving method is tested in the case of shear of a stiffened panel.

International audience; An efficient approach is proposed in order to predict the mechanical response of complex industrial parts. As these structures are usually composed of massive and thin parts, different models have to be mixed together (plate, shells, solid). The transition between these different kinematic assumptions can be problematic and non-linear models cannot be employed depending on the plate model that is considered. Moreover, Finite Element analysis in the case of large and complex assemblies implies tedious meshing steps. The idealization and simplification of these structures into a mix of 2D and 3D Finite Elements usually takes therefore significantly more time than the analysis itself. The objective of the present contribution is to explore a calculation process that enables a simple automation of the meshing steps. Even though potentially computationally more expensive, the meshing automation may lead to drastic time reduction for the CAD to mesh process and a much tighter link between CAD and calculated assembly. Finally, easier and faster design explorations would be allowed. This strategy relies on the use of a non-conforming quadratic approximation that is defined on a sufficiently fine mesh. The eXtended Finite Element Method is used in order to alleviate meshing issues. The mesh and Level-Set function are built from the CAD input, by means of an automated approach. The strategy is verified against analytical solutions and real aerospace substructures.

In this study, we explore the possibilities offered by new multilevel nonlinear strategies with domain decampasitian far the past-buckling analysis of large shell smcrures. This work is based an the methads fust introduced in [1] far beam frames and aims at validating them far mare complex smcrures such as stiffened panels, far instance. These shategies are based an the classical damaindecampasitian methods (DDM) such as BDD or FETI, which have been much studied aver the past decade far the resolution of linear systems [2][3]. These classical methads have alsa been used in a Newtan-bphsan scheme far the resolution of large-scale nan-linear problems [3], but they proved to have rather poor convergence far unbalanced nan-linear effects, ie. when the nan-linewity has a significant spatial variation [4] Following same of the ideas developed in the LATIN method [5], we aimed at concentrating the computational efforts an the mast demanding zones of the smcrure while reducing communications and decoupling local phenamena. A first version of the proposed strategies applies local non-linear iterations per substructure, after each global computation, with fixed displacement conditions over the boundaries, while a second version makes use of mixed conditions. A new macro problem obtained through a micro/macro separation of boundary unknowns is also introduced.

International audience; The study was focused on the primal and mixed domain decomposition methods, showing that the mixed method is the best choice, because it can reduced the number of global iterations increasing the load step size, and as a consequence of these, reducing also the number of total local iterations.Another important point is the capability, when choosing the appropriate Robin parameter, of passing critical points much more easily than for the primal version. Different options are presented for choosing the Robin parameter, in this work the Schur complement of the neighbouring substructures was used. An analysis of the influence of this parameter was carried out. In order to describe the complete behaviour of the structure an "arc-length" method was implemented at the global level.The method was tested over a wing-box type structure made of triangular plate elements, the final configuration shows some parts of the structure buckling.Finally the method is parallelized; a BDDC method was implemented, solved by a GMRES algorithm, because of the non-symmetry of the operator as a result of the corotationnal formulation used.