Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models

Sarsri, Driss; Azrar, L.; Jebbouri, A.; Hami, Abdelkhalak El

doi:10.1016/j.compstruc.2010.11.009

Cited by 49 publications

(19 citation statements)

References 20 publications

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“…This failure to converge also affects solutions based on perturbation or simulation methods. Although the message of Babuška et al was assimilated by some researchers [12][13][14][15], one finds very recent papers where Gaussian processes are still used to represent the uncertainty in strictly positive mechanical properties [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem

Júnior

Kist

Santos

2014

ISRN Applied Mathematics

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In this paper, the Galerkin method is used to obtain approximate solutions for Kirchhoff plates stochastic bending problem with uncertainty over plates flexural rigidity coefficient. The uncertainty in the rigidity coefficient is represented by means of parameterized stochastic processes. A theorem of Lax-Milgram type, about existence and uniqueness of the theoretical solutions, is presented and used in selection of the approximate solution space. The Wiener-Askey scheme of generalized polynomials chaos (gPC) is used to model the stochastic behavior of the displacement solutions. The performance of the approximate Galerkin solution scheme developed herein is evaluated by comparing first and second order moments of the approximate solution with the same moments evaluated from Monte Carlo simulation. Rapid convergence of approximate Galerkin's solution to the first and second order moments is observed, for the problems studied herein. Results also show that using the developed Galerkin's scheme one gets adequate estimates for accrued probability function to a random variable generated by the stochastic process of displacement.

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Section: Introductionmentioning

confidence: 99%

Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem

Júnior

Kist

Santos

2014

ISRN Applied Mathematics

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“…(4). The subspace Ω is spanned by the columns of the orthogonal projection matrix ∈ × at the mean of random variable [15]. The relationship between the reduced generalized coordinates ∈ and the original generalized coordinates ∈ is = .…”

Section: Nonlinear Model Order Reductionmentioning

confidence: 99%

A stochastic surrogate model for time-variant reliability analysis of flexible multibody system

Kan¹,

Zhang²,

Wang³

2017

Vib. proced.

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Abstract. The dynamic model of the flexible multibody systems (FMS) is usually the differential equations with time-variant, high nonlinear and strong coupling characteristics. The traditional reliability models are inefficient to solve these problems. And the reliability model is poor in accuracy and computational efficiency. Based on this point, a new stochastic surrogate model for time-variant reliability analysis of FMS is proposed. Combined model order reduction with generalized polynomial chaos, the stochastic surrogate model is established and the statistical characteristics of system responses are obtained. The calculation method of kinematic time-variant reliability is given. Finally, the effectiveness of the method is verified by a rotating flexible beam. The results show that this method has high computational accuracy compared with Monte Carlo method.

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“…Component mode synthesis (CMS) is a wellestablished method for efficiently constructing models to analyze the dynamics of large and complex structures that are often described by separate substructure (or components) models. Sarsri et al [22] have coupled the CMS methods with the projection chaos polynomials methods in the first and second orders to compute the frequency transfer functions of stochastic structures. This coupling methodological approach has been used by Sarsri and Azrar in time domain [23] as well as a coupling with the perturbation method [24].…”

Section: Introductionmentioning

confidence: 99%

Numerical Procedures for Random Differential Equations

Said

Azrar

Sarsri

2018

Journal of Applied Mathematics

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Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method 'IRCM' is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the onedimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the superposition method leading to successive random differential equations with the same main random operator and right-hand sides depending only on one random parameter. This methodological approach leads to equations with a reduced number of random variables and thus to a large reduction of CPU time and memory required for the numerical solution. The conditional expectation method is also elaborated for reference solutions as well as the Monte-Carlo procedure. The applicability and effectiveness of the developed methods are demonstrated by some numerical examples.

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Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models

Cited by 49 publications

References 20 publications

Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem

Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem

A stochastic surrogate model for time-variant reliability analysis of flexible multibody system

Numerical Procedures for Random Differential Equations

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