A model reduction approach for real-time part deformation with nonlinear mechanical behavior

Dulong, Jean-Luc; Druesne, Frédéric; Villon, Pierre

doi:10.1007/s12008-007-0028-y

Cited by 20 publications

(17 citation statements)

References 18 publications

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“…It was initially applied in solid mechanics by [27], due to its capability of describing complex phenomena in a reduced dimension. Then, it has been applied in structural non-linear dynamics to analyze a vibro-impact system [25] and, more in general, to the real-time analysis of non-linear mechanical behavior [10]. In this latter paper, the method is divided into a training phase and a real-time phase.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In this case, all of the eigenfunctions corresponding to an eigenvalue λ i > Λλ max are taken, where Λ typically assumes small values, e.g., 10 −4 [10].…”

Section: Choosing Kmentioning

confidence: 99%

“…3, we adopt the functional principal component analysis (FPCA) to express the displacement function u(x, θ ), which is the functional counterpart of the classical principal component analysis (PCA). PCA treats data as multivariate vectors rather than functions, and it is a widespread technique in the context of numerical analysis, where it is equivalently referred as proper orthogonal decomposition (POD) [3,10,30] or as Karhunen-Loeve decomposition [1,20].…”

Section: Introductionmentioning

confidence: 99%

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Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

et al. 2015

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The great influence of uncertainties on the behavior of physical systems has always drawn attention to the importance of a stochastic approach to engineering problems. Accordingly, in this paper, we address the problem of solving a Finite Element analysis in the presence of uncertain parameters. We consider an approach in which several solutions of the problem are obtained in correspondence of parameters samples, and propose a novel non-intrusive method, which exploits the functional principal component analysis, to get acceptable computational efforts. Indeed, the proposed approach allows constructing an optimal basis of the solutions space and projecting the full Finite Element problem into a smaller space spanned by this basis. Even if solving the problem in this reduced space is computationally convenient, very good approximations are obtained by upper bounding the error between the full Finite Element solution and the reduced one. Finally, we assess the applicability of the proposed approach through different test cases, obtaining satisfactory results

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Section: Literature Reviewmentioning

confidence: 99%

“…In this case, all of the eigenfunctions corresponding to an eigenvalue λ i > Λλ max are taken, where Λ typically assumes small values, e.g., 10 −4 [10].…”

Section: Choosing Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

et al. 2015

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“…A popular physics-based meta-modeling technique consists of carrying out the approximation on the full vector fields using PCA and Galerkin projection [5] in CFD [6] as well as in structural analysis [7]. This approach has been successfully applied to a number of areas such as flow modeling [8,9] optimal flow control [10], aerodynamics design optimization [11] or structural mechanics [12]. However, this requires manipulation of the input variablesV .…”

Section: Introduction Literature Reviewed and Motivation For Researchmentioning

confidence: 99%

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

Raghavan¹,

Xia²,

Breitkopf³

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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International audienceEngineering design problems generally involve a high-dimensional input space of design variables yielding an output space by means of costly high-fidelity evaluations. In order to decrease the overall cost, reduced-order models for the output space such as Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) are an active area of research. However, little research has been conducted into alleviating the problems associated with a high-dimensional input space. In addition to higher dimensionality being an impediment to efficient design by itself, complex shapes involve a high number of explicit/implicit constraints restricting the design space. Geometric parameterization methods in traditional CAD present difficulties in expressing these constraints leading to a high failure rate and the generation of inadmissible shapes. In this paper, we propose a simultaneous meta-modeling protocol for both input and output spaces. We perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an alpha-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using metamodeling for both spaces, we facilitate interactive design space exploration for the purpose of design. The proposed approach is applied to the industrial problem of designing a car engine intake port

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“…Dulong et al [5] in this regard had recently proposed an interactive model on real-time part deformation with nonlinear mechanical behaviour. These models are quiet useful in mechanical industries to optimize the parts design.…”

Section: Introductionmentioning

confidence: 99%

On the tool vibration effects during down-cut peripheral milling process

Asad

Mabrouki

Rigal

2010

Int J Interact Des Manuf

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Improvement in machining efficiency requires better comprehension of multiphysical cutting process phenomenon under real dynamic cutting conditions. Present work suggests a multi-scale interaction of mesoscopic level cutting with macroscopic level machine tool dynamics to optimize cutting process parameters and potentially improve interactive design process. For that, the case of an orthogonal down-cut peripheral milling, for an aeronautic aluminium alloy A2024-T351, has been treated. A finite element based multi-scale dynamic cutting model has been conceived with a commercial finite element based code ABA-QUS /EXPLICIT to predict the chip morphology under dynamic cutting conditions. Later, combines the elasticity of a classical high speed milling spindle system (tool, tool-holder and rotor) with the mesoscopic level chip formation process. A qualitative parametric study with various stiffness and damping coefficient values for high speed milling spindle system shows that, a less rigid un-damped milling system generates higher amplitude tool vibrations during cutting. In this situation, the temperature rises at tool-workpiece interface, enhancing material softening. Present study deals with the consequences of this softening on affecting the chip morphology (evolution of segmented chip morphology), and machined surface integrity. Further, numerical simulation results depict that the higher values of cutting speed and uncut chip thickness are associated with higher values of milling cutter vibration amplitudes.

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A model reduction approach for real-time part deformation with nonlinear mechanical behavior

Cited by 20 publications

References 18 publications

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

Efficient uncertainty quantification in stochastic finite element analysis based on functional principal components

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

On the tool vibration effects during down-cut peripheral milling process

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