‘On-the-fly’ snapshots selection for Proper Orthogonal Decomposition with application to nonlinear dynamics

Phalippou, Pierre; Bouabdallah, Salim; Villon, Pierre; Zarroug, Malek

doi:10.1016/j.cma.2020.113120

Cited by 22 publications

(10 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some recent examples include non-intrusive interpolation methods for evaluating nonlinear functions with hypersurfaces [34,35] and use of Gaussian Processes and machine learning for error evaluation and refinement of the pROM [36] or interpolation on the Grassmann manifold via tangent spaces [37]. Alternatively, many of these methods approximate the nonlinear function using hyperreduction methods as the discrete empirical interpolation method (DEIM) [38,39] to speed up the evaluation, and in this sense, online basis selection and adaptive algorithms were studied [40,41]. However, as mentioned above, POD (and DEIM) needs a number of FOM simulations to construct the ROM.…”

Section: Introductionmentioning

confidence: 99%

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

et al. 2021

View full text Add to dashboard Cite

We present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

show abstract

Section: Introductionmentioning

confidence: 99%

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Once the sampling points are selected, the computation of the snapshots is generally performed in parallel, exploiting the independence of each set of parameters to one another, to reduce the computational cost of the offline phase. Recently, an alternative strategy aiming to reduce the number of required full-order solutions was proposed via an incremental algorithm [24].…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms

Giacomini

Borchini

Sevilla

et al. 2021

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

“…Some recent examples include non-intrusive interpolation methods for evaluating nonlinear functions with hypersurfaces [35,36] and use of Gaussian Processes and machine learning for error evaluation and refinement of the pROM [37] or interpolation on the Grassman manifold via tangent spaces [38]. Alternatively, many of these methods approximate the nonlinear function using hyper-reduction methods as the Discrete Empirical Interpolation Method (DEIM) [39,40] to speed up the evaluation, and in this sense online basis selection and adaptive algorithms were studied [41,42]. However, as mentioned above, POD (and DEIM) needs a number of FOM simulations to construct the ROM.…”

Section: Introductionmentioning

confidence: 99%

An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion

Marconi,

Tiso,

Quadrelli

et al. 2021

Preprint

View full text Add to dashboard Cite

We present an enhanced version of the parametric nonlinear reduced order model for shape imperfections in structural dynamics we studied in a previous work [1]. The model is computed intrusively and with no training using information about the nominal geometry of the structure and some user-defined displacement fields representing shape defects, i.e. small deviations from the nominal geometry parametrized by their respective amplitudes. The linear superposition of these artificial displacements describe the defected geometry and can be embedded in the strain formulation in such a way that, in the end, nonlinear internal elastic forces can be expressed as a polynomial function of both these defect fields and the actual displacement field. This way, a tensorial representation of the internal forces can be obtained and, owning the reduction in size of the model given by a Galerkin projection, high simulation speed-ups can be achieved. We show that by adopting a rigorous deformation framework we are able to achieve better accuracy as compared to the previous work. In particular, exploiting Neumann expansion in the definition of the Green-Lagrange strain tensor, we show that our previous model is a lower order approximation with respect to the one we present now. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

show abstract

‘On-the-fly’ snapshots selection for Proper Orthogonal Decomposition with application to nonlinear dynamics

Cited by 22 publications

References 17 publications

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms

An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion

Contact Info

Product

Resources

About