A multiparametric strategy for the two step optimization of structural assemblies

Soulier, Bruno; Boucard, Pierre-Alain

doi:10.1007/s00158-012-0854-9

Cited by 6 publications

(7 citation statements)

References 40 publications

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“…The main idea consists in reusing a previous solution for a given set of parameters to start LATIN iterations for a new set of parameters. This way, a large amount of relaxations (LATIN iterations on the FOM) can be spared as it is described in [46,48,49]. On the other hand, reduced basis methods are also used to accelerate solutions [50][51][52].…”

Section: Parametric Studymentioning

confidence: 99%

A multiscale large time increment/FAS algorithm with time‐space model reduction for frictional contact problems

Giacoma

Dureisseix

Gravouil

et al. 2013

Numerical Meth Engineering

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A multiscale strategy using model reduction for frictional contact computation is presented. This new approach aims to improve computation time of finite element simulations involving frictional contact between linear and elastic bodies. This strategy is based on a combination between the LATIN (LArge Time INcrement) method and the FAS multigrid solver. The LATIN method is an iterative solver operating on the whole time-space domain. Applying an a posteriori analysis on solutions of different frictional contact problems shows a great potential as far as reducibility for frictional contact problems is concerned. Timespace vectors forming the so-called reduced basis depict particular scales of the problem. It becomes easy to make analogies with multigrid method to take full advantage of multiscale information. A. GIACOMA ET AL. in large-scale elasticity problems with contact and friction. Once again, because of the nonsmooth property of contact problems, convergence proof of generalized Newton's methods are hard to provide. Another method consists in casting the contact problems into a linear complementarity problem (LCP) and using specific solvers such as active-set methods, Lemke's algorithm, projected successive over relaxation. In [20], an LCP formulation is used to solve a frictional contact problem by faceting the Coulomb's cone. Nevertheless, this approximation is tough and not efficient (the problem to solve becomes larger). Nowadays, LCP formulations are suited to frictionless problems.Generally speaking, and even within a quasi-static context, all these nonlinear solvers can lead to prohibitive time of computations. Acceleration strategies based on multigrid methods were proposed [21,22]. Computational costs spur recent and intensive works on efficient model reduction techniques in various fields [23][24][25][26]. But because of the nondifferentiable nature of frictional contact, application of such methods seems to be heretic.The aim of this work is to propose a strategy accelerating solution for frictional contact problems in the finite element framework, embedding model reduction techniques also well-suited for parametric studies. Linear elastic, homogeneous, isotropic behavior, and quasi-static evolution are assumed for the bodies. Frictional contact laws involve a nonlinear and nonsmooth behavior at the boundary of the body. To solve this mechanical problem, the nonincremental LArge Time INcrement (LATIN) method is used. This method is well-known for its ability to solve difficult nonlinear large problems (nonlinear material, contact problems...) [27,28] with a global time-space approach. This method is closed to augmented Lagrangian methods. Its great advantages are non refactorization of matrices (stiffness matrix remains constant through LATIN iterations) and explicit subsequent iterations (no iterations to handle the nonlinear behavior solved only on the contacting boundary). So the cost of a LATIN iteration is low even if the number of iterations can be elevated as augmented Lagrangian method...

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Section: Parametric Studymentioning

confidence: 99%

A multiscale large time increment/FAS algorithm with time‐space model reduction for frictional contact problems

Giacoma

Dureisseix

Gravouil

et al. 2013

Numerical Meth Engineering

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“…It is largely problem independent with manual regulation. Besides the cases given in the literature in last section, refer to references [111][112][113][114][115][116][117] for the studies in empirical-based solving.…”

Section: Empirical-based Methodsmentioning

confidence: 99%

Recent Advances of Intelligent Optimization Algorithm in Manufacturing

Tao

Laili

Zhang

2014

Springer Series in Advanced Manufacturing

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Due to its good versatility and independence, intelligent optimization algorithm has largely shortened the time of decision-making in large-scale optimization problems of manufacture. However, lower searching time often conflicts with the searching accuracy in most cases. To improve the problem solving capability, research in intelligent optimization algorithm based on different domain characteristics never stopped. From the view of manufacturing, this chapter classified and comprehensively analyzed all kinds of manufacturing optimization problems and their general methods, illustrated the application features and challenges of intelligent optimization algorithm in manufacturing, and summarized the development needs and trends of intelligent optimization algorithm in the field of manufacturing system.

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“…In this work, the restarting point is chosen to be the nearest point in a Euclidean space. For further details, see [35].…”

Section: Multiparametric Strategymentioning

confidence: 99%

“…In order to improve the computation time, we use a specific feature of the LATIN iterative solver, called the "multiparametric strategy", which enables one to reuse previously calculated data when performing new calculations [33].…”

Section: Introductionmentioning

confidence: 99%

Variable-fidelity modeling of structural analysis of assemblies

2015

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This paper deals with the advantages of using variable-fidelity metamodeling strategies in order to develop a valid metamodel more rapidly than by using traditional methods. In our mechanical assembly design, we use the term "variable-fidelity" in reference to the convergence (or accuracy) level of the iterative solver being used. Variable-fidelity metamodeling is a way to improve the prediction of the output of a complex system by incorporating rapidly available auxiliary lower-fidelity data. This work uses two fidelity levels, but more levels can be added. The LATIN iterative algorithm is used along with a "multiparametric" strategy to calculate the various data and their different fidelity levels by means of an error indicator. Three main categories of variable-fidelity strategies are currently available. We tested at least one method from each of these categories, which comes to a total of five methods for calculating a valid metamodel using low-and high-fidelity data. Here, our objective is to compare the performances of these five methods in solving three mechanical examples.

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A multiparametric strategy for the two step optimization of structural assemblies

Cited by 6 publications

References 40 publications

A multiscale large time increment/FAS algorithm with time‐space model reduction for frictional contact problems

A multiscale large time increment/FAS algorithm with time‐space model reduction for frictional contact problems

Recent Advances of Intelligent Optimization Algorithm in Manufacturing

Variable-fidelity modeling of structural analysis of assemblies

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