Remarks on the efficiency of POD for model reduction in non‐linear dynamics of continuous elastic systems

Sampaio, Rubens; Soize, Christian

doi:10.1002/nme.1991

Cited by 33 publications

(34 citation statements)

References 14 publications

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“…Many different methods have been proposed in the past, one of the most popular being the Proper Orthogonal Decomposition (POD) method [3][4][5]29]. In this paper, the NNMs of the unforced structure are tested as basis functions for reducing the dynamics for shell models with harmonic forcing.…”

Section: Discussionmentioning

confidence: 99%

“…This is realized by imposing the invariance of sub-spaces as the key property that must be conserved when non-linearities come into play, and leads to the definition of NNMs as invariant manifolds of the phase space [1]. As the method used for computing the NNMs is purely non-linear, it is expected to give better results than using the LNMs, or modes obtained via the proper orthogonal decomposition (POD) method [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

Touzé

Amabili

Thomas

2008

Computer Methods in Applied Mechanics and Engineering

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. Reduced-order models for large-amplitude vibrations of shells including in-plane inertia. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197 (21-24) AbstractNon-linear normal modes (NNMs) are used in order to derive reduced-order models for large amplitude, geometrically non-linear vibrations of thin shells. The main objective of the paper is to compare the accuracy of different truncations, using linear and non-linear modes, in order to predict the response of shells structures subjected to harmonic excitation. For an exhaustive comparison, three different shell problems have been selected: (i) a doubly curved shallow shell, simply supported on a rectangular base; (ii) a circular cylindrical panel with simply supported, in-plane free edges; and (iii) a simply supported, closed circular cylindrical shell. In each case, the models are derived by using refined shell theories for expressing the strain-displacement relationship. As a consequence, in-plane inertia is retained in the formulation. Reduction to one or two NNMs shows perfect results for vibration amplitude lower or equal to the thickness of the shell in the three cases, and this limitation is extended to two times the thickness for two of the selected models.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

Touzé

Amabili

Thomas

2008

Computer Methods in Applied Mechanics and Engineering

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“…(54), p W|X (w exp ℓ |x) is the value, for the experimental data, of the conditional probability density function w → p W|X (w|x) of the random observation W given X = x in C par . Equation (54) shows that the likelihood function L must verify the following equation,…”

Section: Estimation Of the Parameters Of The Prior Stochastic Model Omentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

139

106

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To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

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“…The above nonlinear reference solution is then used for determining a projection basis with the Proper Orthogonal Decomposition method (PODmethod), which is known to be particularly relevant for nonlinear problems [23,25,42,43,24,44]. Let u(s) be the Ê n -displacement vector corresponding to the finite element discretization of the displacement field {u(x, s) , x ∈ Ω}.…”

Section: Construction Of the Mean Nonlinear Reduced Static Computatiomentioning

confidence: 99%

“…This basis can be obtained by one of several techniques such as the Proper Orthogonal Decomposition method (POD method) [23,24,25], which is known to be particularly efficient for nonlinear static cases. One can also rely on linear elastic modes of vibration [26,27], or selected linear elastic modes appropriately enriched, e.g.…”

Section: Introductionmentioning

confidence: 99%

Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation

Capiez‐Lernout

Soize

Mignolet

2014

Computer Methods in Applied Mechanics and Engineering

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The paper presents a complete experimental validation of an advanced computational methodology adapted to the nonlinear post-buckling analysis of geometrically nonlinear structures in presence of uncertainty. A mean nonlinear reduced-order computational model is first obtained using an adapted projection basis. The stochastic nonlinear computational model is then constructed as a function of a scalar dispersion parameter, which has to be identified with respect to the nonlinear static experimental response of a very thin cylindrical shell submitted to a static shear load. The identified stochastic computational model is finally used for predicting the nonlinear dynamical post-buckling behavior of the structure submitted to a stochastic ground motion.

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Remarks on the efficiency of POD for model reduction in non‐linear dynamics of continuous elastic systems

Abstract: To cite this version:R. Sampaio, Christian Soize. Remarks on the efficiency of POD for model reduction in non-linear dynamics of continuous elastic systems. International Journal for Numerical Methods in Engineering, Wiley, 2007, 72 (1)

Cited by 33 publications

References 14 publications

Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

Reduced-order models for large-amplitude vibrations of shells including in-plane inertia

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation

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