The wave finite element method for uncertain systems with model uncertainty

2015 ◽  
Vol 230 (6) ◽  
pp. 974-985 ◽  
Author(s):  
MA Ben Souf ◽  
O Bareille ◽  
M Ichchou ◽  
M Haddar
Keyword(s):  
Finite Element ◽  
Dynamic Systems ◽  
Periodic Structures ◽  
Probabilistic Approach ◽  
Numerical Test ◽  
Maximum Entropy Principle ◽  
Nonparametric Model ◽  
Test Cases ◽  
Entropy Principle ◽  
Random Uncertainties

The random dynamic response of periodic structures with model uncertainties is here studied. For that purpose, a nonparametric model of random uncertainties is used. The present approach is based on the maximum entropy principle optimization and is developed to identify the response of linear and nonlinear dynamic systems. This non-parametric probabilistic approach is implemented in combination with the Wave Finite Element. Numerical test cases are used as examples and for validation purpose.

Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

2014 ◽  
Vol 24 (08) ◽  
pp. 1495-1539 ◽  
Author(s):  
Francesco Bassi ◽  
Lorenzo Botti ◽  
Alessandro Colombo
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Numerical Test ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Element Discretization ◽  
Mesh Free ◽  
Domain Boundaries ◽  
Coarse Grids

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

A new stochastic analysis method for mechanical components

2012 ◽  
Vol 227 (8) ◽  
pp. 1818-1829 ◽  
Author(s):  
YL Zhang ◽  
YM Zhang
Keyword(s):  
Finite Element ◽  
Dimension Reduction ◽  
Probability Density ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Entropy Principle ◽  
Input Variables ◽  
First Four Moments

Univariate dimension-reduction integration, maximum entropy principle, and finite element method are employed to present a computational procedure for estimating probability densities and distributions of stochastic responses of structures. The proposed procedure can be described as follows: 1. Choose input variables and corresponding distributions. 2. Calculate the integration points and perform finite element analysis. 3. Calculate the first four moments of structural responses by univariate dimension-reduction integration. 4. Estimate probability density function and cumulative distribution function of responses by maximum entropy principle. Numerical integration formulas are obtained for non-normal distributions. The non-normal input variables need not to be transformed into equivalent normal ones. Three numerical examples involving explicit performance functions and solid mechanic problems without explicit performance functions are used to illustrate the proposed procedure. Accuracy and efficiency of the proposed procedure are demonstrated by comparisons of the estimated probability density functions and cumulative distribution functions obtained by maximum entropy principle and Monte Carlo simulation.

scholarly journals An Entropic Scheme for an Angular Moment Model for the Classical Fokker-Planck-Landau Equation of Electrons

2014 ◽  
Vol 15 (2) ◽  
pp. 422-450 ◽  
Author(s):  
Jessy Mallet ◽  
Stéphane Brull ◽  
Bruno Dubroca
Keyword(s):  
Discrete Model ◽  
Landau Equation ◽  
Numerical Test ◽  
Test Cases ◽  
Minimum Entropy ◽  
Fundamental Properties ◽  
Direct Numerical Solution ◽  
Entropy Principle ◽  
The Moment ◽  
Fokker Planck

AbstractIn plasma physics domain, the electron transport is described with the Fokker-Planck-Landau equation. The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension. To find a solution compatible with physics conditions, the closure of the moment system is obtained under a minimum entropy principle. This model is proved to satisfy the fundamental properties like a H theorem. Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model. Finally, we validate on numerical test cases the fundamental properties of the full discrete model.

scholarly journals Dynamics of random coupled structures through the wave finite element method

2015 ◽  
Vol 32 (7) ◽  
pp. 2020-2045 ◽  
Author(s):  
Mohamed Amine Ben Souf ◽  
Mohamed Ichchou ◽  
Olivier Bareille ◽  
Noureddine Bouhaddi ◽  
Mohamed Haddar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Structures ◽  
Uncertainty Propagation ◽  
Probabilistic Approach ◽  
Uncertain Parameters ◽  
Content Type ◽  
High Frequencies ◽  
Coupled Structures ◽  
Element Method

Purpose – The purpose of this paper is to develop a new formulation using spectral approach, which can predict the wave behavior to uncertain parameters in mid and high frequencies. Design/methodology/approach – The work presented is based on a hybridization of a spectral method called the “wave finite element (WFE)” method and a non-intrusive probabilistic approach called the “polynomial chaos expansion (PCE).” The WFE formulation for coupled structures is detailed in this paper. The direct connection with the conventional finite element method allows to identify the diffusion relation for a straight waveguide containing a mechanical or geometric discontinuity. Knowing that the uncertainties play a fundamental role in mid and high frequencies, the PCE is applied to identify uncertainty propagation in periodic structures with periodic uncertain parameters. The approach proposed allows the evaluation of the dispersion of kinematic and energetic parameters. Findings – The authors have found that even though this approach was originally designed to deal with uncertainty propagation in structures it can be competitive with its low time consumption. The Latin Hypercube Sampling (LHS) is also employed to minimize CPU time. Originality/value – The approach proposed is quite new and very simple to apply to any periodic structures containing variabilities in its mechanical parameters. The Stochastic Wave Finite Element can predict the dynamic behavior from wave sensitivity of any uncertain media. The approach presented is validated for two different cases: coupled waveguides with and without section modes. The presented results are verified vs Monte Carlo simulations.

Recent Advances in Test vs Finite Element Correlations Through Design for Six Sigma Tools

2012 ◽  
Author(s):  
Santhosh K. Kompally ◽  
Vinay Ramanath ◽  
Karthikeyan Jeevanandan ◽  
Manoj Kunnil
Keyword(s):  
Finite Element ◽  
Six Sigma ◽  
Material Characterization ◽  
Complex Geometry ◽  
Probabilistic Approach ◽  
Mechanical Tests ◽  
Test Cases ◽  
Design For Six Sigma ◽  
Design Cycle ◽  
Huge Variation

In general, thermal generators have a combination of composites and metals in different assemblies. It is important to note that the material properties and interface stiffnesses change during the assembly process. Added to this change, the complex geometry and assembly procedures result in huge variation in material characterizations. These variabilities triggered a requirement of a unique process for material characterization at both component and assembly levels. This paper covers the details of a 6-stage DFSS methodology, which involves filling the above-stated gaps by performing mechanical tests at component and sub-assembly levels, followed by series of finite element correlations at various stages of design cycle. This paper emphasizes a DFSS-based probabilistic approach, developed with a built-in validation for evaluating finite element variables to match with assembly tests. This paper also discusses the success of this DFSS-based process in bench marking with two test cases.

scholarly journals Some aspects of probabilistic modeling, identification and propagation of uncertainties in computational mechanics

2010 ◽  
pp. 25-40
Author(s):  
Christian Soize
Keyword(s):  
Probabilistic Models ◽  
Polynomial Chaos ◽  
Matrix Theory ◽  
Probabilistic Approach ◽  
Maximum Entropy Principle ◽  
Geometrical Nonlinearities ◽  
Computational Dynamics ◽  
Entropy Principle ◽  
Experimental Validations ◽  
Propagation Of Uncertainties

In this paper, we present some aspects relative to the types of uncertainties, the variability of real systems, the types of probabilistic approaches and of the representations for the probabilistic models of uncertainties, the construction of the probabilistic models using the maximum entropy principle. We then present the nonparametric probabilistic approach of uncertainties for elliptic problems, for 3D continuous dynamical systems with geometrical nonlinearities induced by large displacements and for low- and mediumfrequency vibroacoustics of a complex system with experimental validations. Finally, a generalized probabilistic approach of uncertainties in computational dynamics using the random matrix theory and polynomial chaos decompositions is presented.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

Edge finite element method for periodic structures using random meshes

2021 ◽  
pp. 1-19
Author(s):  
Ouail Ouchetto ◽  
Brahim Essakhi ◽  
Said Jai-Andaloussi ◽  
Saad Zaamoun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Structures ◽  
Element Method

scholarly journals A posteriori error estimates for a multi-scale finite-element method

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Khallih Ahmed Blal ◽  
Brahim Allam ◽  
Zoubida Mghazli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
A Posteriori Error Estimates ◽  
Numerical Test ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Essential Information ◽  
Multi Scale ◽  
Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

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