Nonlinear Reduced Order Modeling of Isotropic and Functionally Graded Plates

Kim, Kwangkeun; Wang, XIao Quan; Mignolet, Marc P.

doi:10.2514/6.2008-1873

Cited by 40 publications

(81 citation statements)

References 17 publications

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“…From observation (b), it is further concluded that the loading in these analyses should excite primarily the modes from the linear basis which are transverse dominated. An intuitive approach (see [8] for further discussion) to achieve this condition is to rely on the linear situation. That is, the applied load (8).…”

Section: Basis Selectionmentioning

confidence: 99%

“…An intuitive approach (see [8] for further discussion) to achieve this condition is to rely on the linear situation. That is, the applied load (8). In fact, a detailed discussion of the linear combinations to be used is presented in [8] but, in all validations carried out, it has been sufficient to consider the cases…”

Section: Basis Selectionmentioning

confidence: 99%

“…depend only on the point X considered and can be obtained non-intrusively from finite element computations [8].…”

Section: Reduced Order Model Form and Governing Equationsmentioning

confidence: 99%

“…Equation (5) (4) and imposing the condition that the error be orthogonal to the basis (Galerkin approach), a set of nonlinear ordinary differential equations for the generalized coordinates ( ) t q n can be obtained [8], they are the reduced order model equations [8]. They can be used for their estimation (see [26]) but an indirect evaluation of many of these coefficients from the finite element model is also possible (see [1,8,22,29]) and is adopted here.…”

Section: Reduced Order Model Form and Governing Equationsmentioning

confidence: 99%

“…Notwithstanding the above difficulties, the ROM capabilities have progressed from applications to flat structures (see [2][3][4][5][6][7][8][9]), to moderately large motions of curved structures (see [10][11][12][13][14]). Further, the coupling of these nonlinear structural reduced order models with aerodynamics, either full or reduced order model has also been successfully demonstrated in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

Perez

Wang

Mignolet

2014

Journal of Sound and Vibration

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The focus of this investigation is on a first assessment of the predictive capabilities of nonlinear geometric reduced order models for the prediction of the large displacement and stress fields of panels with localized geometric defects, the case of a notch serving to exemplify the analysis. It is first demonstrated that the reduced order model of the notched panel does indeed provide a close match of the displacement and stress fields obtained from full finite element analyses for moderately large static and dynamic responses (peak displacement of 2 and 4 thicknesses). As might be expected, the reduced order model of the virgin panel would also yield a close approximation of the displacement field but not of the stress one. These observations then lead to two "enrichment" techniques seeking to superpose the notch effects on the virgin panel stress field so that a reduced order model of the latter can be used. A very good prediction of the full finite element stresses, for both static and dynamic analyses, is achieved with both enrichments.

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Section: Basis Selectionmentioning

confidence: 99%

Section: Basis Selectionmentioning

confidence: 99%

“…depend only on the point X considered and can be obtained non-intrusively from finite element computations [8].…”

Section: Reduced Order Model Form and Governing Equationsmentioning

confidence: 99%

Section: Reduced Order Model Form and Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

Perez

Wang

Mignolet

2014

Journal of Sound and Vibration

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Multi‐expansion modal reduction: A pragmatic semi–a priori model order reduction approach for nonlinear structural dynamics

Naets

Gregoriis

Desmet

2019

Numerical Meth Engineering

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A novel model order reduction scheme for nonlinear finite element (NL-FE) structural dynamics models is proposed in this work, which enables an overall accelerated model evaluation. The proposed multi-expansion modal (MEM) reduction employs a set of modal bases evaluated for a number of representative statically deformed configurations, combined with these static deformation patterns, to obtain a reduced order basis (ROB). This ROB is then exploited in an a priori element sampling to obtain a hyper-reduced model based on the energy-conserving sampling and weighting approach. The proposed element sampling scheme uses a nonnegative L 1 optimization of the element weights where an equality between the projected and hyper-reduced linearized stiffness matrix or static deformation forces is added. A procedure and several guidelines on the reduced order model setup and evaluation are presented, with specific attention to how the presented approach allows to exploit existing NL-FE frameworks. The MEM approach is validated numerically on an academic cantilever beam model and is shown to provide good accuracy and consistent convergence properties. KEYWORDS nonlinear, model order reduction, structural dynamics Int J Numer Methods Eng. 2019;118:765-782.wileyonlinelibrary.com/journal/nme

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Calibration of System Parameters Under Model Uncertainty

Absi

Mahadevan

2014

Model Validation and Uncertainty Quantification, Volume 3

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Nonlinear Reduced Order Modeling of Isotropic and Functionally Graded Plates

Cited by 40 publications

References 17 publications

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

Multi‐expansion modal reduction: A pragmatic semi–a priori model order reduction approach for nonlinear structural dynamics

Calibration of System Parameters Under Model Uncertainty

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