scholarly journals Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion— Application to a Finite Element Rotor

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
E. Sarrouy ◽  
O. Dessombz ◽  
J.-J. Sinou
Keyword(s):  
Finite Element ◽  
Stochastic Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Eigenvalues And Eigenvectors ◽  
Campbell Diagram ◽  
Complex Eigenvalues ◽  
Gyroscopic Effects ◽  
Rotor Model

This paper proposes to use a polynomial chaos expansion approach to compute stochastic complex eigenvalues and eigenvectors of structures including damping or gyroscopic effects. Its application to a finite element rotor model is compared to Monte Carlo simulations. This lets us validate the method and emphasize its advantages. Three different uncertain configurations are studied. For each, a stochastic Campbell diagram is proposed and interpreted and critical speeds dispersion is evaluated. Furthermore, an adaptation of the Modal Accordance Criterion (MAC) is proposed in order to monitor the eigenvectors dispersion.

Stochastic Finite Element Method Using Polynomial Chaos Expansion

2011 ◽  
Vol 199-200 ◽  
pp. 500-504 ◽  
Author(s):  
Wei Zhao ◽  
Ji Ke Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polynomial Chaos ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Polynomial Expansion ◽  
Stochastic Finite Element Method ◽  
Chaos Expansion ◽  
Stochastic Finite Element ◽  
Element Method

We present a new response surface based stochastic finite element method to obtain solutions for general random uncertainty problems using the polynomial chaos expansion. The approach is general but here a typical elastostatics example only with the random field of Young's modulus is presented to illustrate the stress analysis, and computational comparison with the traditional polynomial expansion approach is also performed. It shows that the results of the polynomial chaos expansion are improved compared with that of the second polynomial expansion method.

An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion

2013 ◽  
Vol 13 (4) ◽  
pp. 1173-1188 ◽  
Author(s):  
Samih Zein ◽  
Benoît Colson ◽  
François Glineur
Keyword(s):  
Finite Element ◽  
Design Of Experiments ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Computational Time ◽  
Chaos Expansion ◽  
Analysis Model ◽  
Element Analysis ◽  
Analytical Functions ◽  
The Cost

AbstractThe polynomial chaos expansion (PCE) is an efficient numerical method for performing a reliability analysis. It relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by using a regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experiments is large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experiments in the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.

scholarly journals Stochastic Finite Element Analysis using Polynomial Chaos

2016 ◽  
Vol 38 (1) ◽  
pp. 33-43 ◽  
Author(s):  
S. Drakos ◽  
G.N. Pande
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stochastic Analysis ◽  
Polynomial Chaos ◽  
Computational Time ◽  
Chaos Expansion ◽  
Stochastic Finite Element ◽  
Element Analysis ◽  
Stochastic Finite Element Analysis ◽  
Random Finite Element

Abstract This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos. It eliminates the need for a large number of Monte Carlo simulations thus reducing computational time and making stochastic analysis of practical problems feasible. This is achieved by polynomial chaos expansion of the displacement field. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and results of settlement are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.

An Enrichment Scheme for Polynomial Chaos Expansion Applied to Random Eigenvalue Problem

2005 ◽  
Author(s):  
Roger Ghanem ◽  
Debraj Ghosh
Keyword(s):  
Eigenvalue Problem ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Eigenvalues And Eigenvectors ◽  
System Parameters ◽  
Statistical Behavior ◽  
Random Eigenvalue ◽  
Clustered Eigenvalues ◽  
Random Eigenvalue Problem

For a system with the parameters modeled as uncertain, polynomial approximations such as polynomial chaos expansion provide an effective way to estimate the statistical behavior of the eigenvalues and eigenvectors, provided the eigenvalues are widely spaced. For a system with a set of clustered eigenvalues, the corresponding eigenvalues and eigenvectors are very sensitive to perturbation of the system parameters. An enrichment scheme to the polynomial chaos expansion is proposed here in order to capture the behavior of such eigenvalues and eigenvectors. It is observed that for judiciously chosen enrichment functions, the enriched expansion provides better estimate of the statistical behavior of the eigenvalues and eigenvectors.

Sign in / Sign up

Export Citation Format

Share Document