Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses

Cresta, Philippe; Allix, Olivier; Rey, Christian; Guinard, Stéphane

doi:10.1016/j.cma.2006.03.013

Cited by 58 publications

(79 citation statements)

References 15 publications

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“…The efficiency of the simple approximation (11) has been studied, in the context of nonlinear substructuring and condensation, in some research works [10,16,13], and has given good results when tested on rather homogeneous structures of standard shape.…”

Section: Quick Reviewmentioning

confidence: 99%

“…This article focuses on the nonlinear substructuring and condensation method, which has been investigated in previous studies [10,11,12,13]. The substructured formulation involves a choice of interface transmission conditions, which can be either primal, dual or mixed, referring either to interface displacements, nodal interface reactions, or a linear combination of the two previous types -i.e.…”

Section: Introductionmentioning

confidence: 99%

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Substructured formulations of nonlinear structure problems - influence of the interface condition

Negrello

Gosselet

Rey

et al. 2016

Int. J. Numer. Meth. Engng

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An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is usally too expensive to be computed exactly in practice: an approximate version has to be sought, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

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Section: Quick Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Substructured formulations of nonlinear structure problems - influence of the interface condition

Negrello

Gosselet

Rey

et al. 2016

Int. J. Numer. Meth. Engng

Self Cite

View full text Add to dashboard Cite

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“…which was investigated in nonlinear relocalization techniques [14][15][16]38], but which is in general not possible in the non-invasive framework. Anyhow, in the case of a linear Global model, it is possible to derive a quasi-Newton approach.…”

Section: Quasi-newton's Approaches For Linear Global Modelmentioning

confidence: 99%

“…In [12] the method was used in order to implement a nonlinear domain decomposition method [13][14][15][16] in a non-invasive manner with Code_aster. The extension of the approach to explicit dynamics was proposed in [17], improved in [18] and applied to the prediction of delamination under impact in [19].…”

Section: Introductionmentioning

confidence: 99%

Non-invasive global–local coupling as a Schwarz domain decomposition method: acceleration and generalization

Gosselet

Blanchard

Allix

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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“…However, it is mainly reserved for cases in which the local detail has little or no influence on the rest of the structure at global level. The weak point of such a strategy is thus that it is only applied in one direction (from global to local), without considering the repercussions of local, non-linear effects on the global model: this may lead to severe disturbances of the overall balance of the structure [9,10].…”

Section: Introductionmentioning

confidence: 99%

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

Guinard

Bouclier

Toniolli

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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The multiscale analysis of large composite aeronautical structures involves the development of robust coupling strategies. Among the latter, non-intrusive coupling is attractive, since it is able to consistently connect a global simplified linear model to a local detailed one, using features available in commercial software. Up to now, such coupling methods were still limited to academic situations where global and local meshes are geometrically and/or topologically conforming and of low geometric complexity. To meet the goal of merging a complex non-planar global shell to a local detailed 3D model, an extension of these techniques is proposed to handle meshes of complex shapes that are not only non-matching but also geometrically and topologically non-conforming. The implemented strategy is original and robust: the innovative nature of the approach is to expand the initial local solid model by generating transitional shell meshing. The generated model incorporates two distinct coupling interfaces: (i) non-intrusive global-local coupling and (ii) shell-solid coupling. The multiscale strategy was successfully validated through different numerical experiments using standard Input/Output of a commercial finite element software. In particular, a representative use-case involving a realistic fuselage section of an aircraft was computed.

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Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses

Cited by 58 publications

References 15 publications

Substructured formulations of nonlinear structure problems - influence of the interface condition

Substructured formulations of nonlinear structure problems - influence of the interface condition

Non-invasive global–local coupling as a Schwarz domain decomposition method: acceleration and generalization

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

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