A nonintrusive proper generalized decomposition scheme with application in biomechanics

Zou, Xi; Conti, Michele; Dı́ez, Pedro; Auricchio, Ferdinando

doi:10.1002/nme.5610

Cited by 42 publications

(34 citation statements)

References 32 publications

(49 reference statements)

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“…As an alternative, the purpose of this work is to build a resolution scheme based on the use of some variable separation techniques widely encountered in numerical simulations [2,25,19,12,10,42]. The interest of extending such methods to DIC has already been illustrated in previous works [27,17], where the dimensions of space were separated in order to speedup computation time.…”

Section: The Proposed Space-time Pgd-dic Formulationmentioning

confidence: 99%

A Space-Time PGD-DIC Algorithm:

2018

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The aim of this study is to develop a new regularized Digital Image Correlation (DIC) method for time dependent measurements. The correlation problem is written as a minimization problem over the space-time domain in a general formulation including 2D-DIC and Stereo DIC (SDIC). The unknown time-resolved displacement field is found as a sum of products of space and time functions, similarly to the Proper Generalized Decomposition in computational mechanics. It is shown that the space fields are less sensitive to noise as time regularity acts as a physical regularization of the space fields. The proposed method is illustrated by vibration measurement under harmonic excitation in 2D-DIC and SDIC.

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Section: The Proposed Space-time Pgd-dic Formulationmentioning

confidence: 99%

A Space-Time PGD-DIC Algorithm:

2018

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“…according to Zou et al [61] is used. If the tolerance is reached the enrichment loop stops and the final solution is given with M = m summations.…”

Section: Proper Generalized Decomposition For Structural Reliabilitymentioning

confidence: 99%

Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema

Robens-Radermacher

Unger

2020

Adv. Model. and Simul. in Eng. Sci.

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One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of 10 −4 to 10 −6. Generally, it is not possible to compute the failure probability analytically. Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a full FE simulation. Additionally, an adaptive importance sampling scheme is used to minimize the total number of required samples. The accuracy of the failure probability depends on the accuracy of the PGD model (mainly influenced on mesh discretization and mode truncation) as well as the number of samples in the sampling algorithm. Therefore, a general iterative PGD reliability procedure is developed to automatically verify the accuracy of the computed failure probability. It is based on a goal-oriented refinement of the PGD model around the adaptively approximated design point. The methodology is applied and evaluated for 1D and 2D examples. The computational savings compared to the method based on a FE model is shown and the influence of the accuracy of the PGD model on the failure probability is studied.

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“…5.3.1. Construction of the reduced order model For this particular example, the so-called non-intrusive PGD method has been employed [49,50]. In particular, we have employed the formulation introduced in [50], that employs adaptive samplings of the parametric domain and collocation approaches.…”

Section: Neo-hookean Hyperelasticitymentioning

confidence: 99%

Reduced order modeling for physically-based augmented reality

Badías

Alfaro

González

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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In this work we explore the possibilities of reduced order modeling for augmented reality applications. We consider parametric reduced order models based upon separate (affine) p arametric d ependence s o a s t o s peedup t he a ssociated d ata assimilation problems, which involve in a natural manner the minimization of a distance functional. The employ of reduced order methods allows for an important reduction in computational cost, thus allowing to comply with the stringent real time constraints of video streams, i.e., around 30 Hz. Examples are included that show the potential of the proposed technique in different situations.

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A nonintrusive proper generalized decomposition scheme with application in biomechanics

Cited by 42 publications

References 32 publications

A Space-Time PGD-DIC Algorithm:

A Space-Time PGD-DIC Algorithm:

Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema

Reduced order modeling for physically-based augmented reality

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