A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters

Falsone, G.; Impollonia, N.

doi:10.1016/s0045-7825(02)00437-1

Cited by 116 publications

(54 citation statements)

References 4 publications

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“…Thus, direct MCS is today a powerful (and perhaps the only universal) tool for treating complex SFEM applications. This is why it is often used as a reference approach for validating the results of other methods [4,9,44,51,138,173,176,177,179].…”

Section: Direct Mcsmentioning

confidence: 99%

“…For a dynamic problem with geometric non-linearity, the results were satisfactory only for small coefficients of variation of the input stochastic field. Falsone and Impollonia [51] proposed an improved method based on the perturbation approach which overcomes its drawbacks. The accuracy of the method is remarkable in the evaluation of higher order moments and PDF of the response even for high amount of uncertainty of the input (Fig.…”

Section: First and Second-order Approximation Of The Response Variabimentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

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Section: Direct Mcsmentioning

confidence: 99%

Section: First and Second-order Approximation Of The Response Variabimentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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“…To the best of our knowledge, there are no published results for this detailed stochastic finite element analysis of the free vibration of laminated composites. Most publications deal with static problems only, [8,10,11], or calculate only second order statistics (COV), [12,15]. Accordingly, results of the present work are compared to those of the well-established Monte Carlo simulation technique.…”

Section: Full Stochastic Analysis Of a Square Asymmetric Laminatementioning

confidence: 99%

“…In their work, Salim et al [5][6][7] have employed a First Order Perturbation Technique FOPT to perform static analysis of composite plates using classical laminated plate theory with random material properties. The static response of uncertain FEM discretised structures was evaluated by Falsone and Impollonia [8], while Chamis et al [9,10] combined optimization techniques with probabilistic structural analysis to reduce the maximum deflection of a composite simulated fuselage by a factor of 4.5.…”

Section: Introductionmentioning

confidence: 99%

Stochastic finite element analysis of the free vibration of laminated composite plates

et al. 2007

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Using the Stochastic Finite Element Method (SFEM) to perform reliability analysis of the free vibration of composite plates with material and fabrication uncertainties has received much attention lately. In this work the stochastic analysis is performed using the First Order Reliability Method (FORM-method 2) and the Second Order Reliability Method (SORM). The basic random variables include laminae stiffness properties and material density, as well as the randomness in ply orientation angles. Modeling of the composite behavior utilizes a nine-noded isoparametric Lagrangian element based on the third order shear deformation theory. The developed code utilizes MATLAB capabilities to derive the derivatives of the reduced stiffness and mass matrices symbolically with a considerable reduction in calculation time. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using available data in the literature, in addition to comparisons with results of the well-established Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of composite plates, when compared to the slower Monte Carlo simulation techniques.

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“…This fact and a similar one for the evaluation of variances and covariances has been noted and used to evaluate the statistics of dynamic systems with uncertainty and for frequency averaging in the last decade or so. Detailed description can notably be found in [14,15,16,17,18,19] and [20,21,7] and in the references therein.…”

Section: General Averaging or Filteringmentioning

confidence: 99%

TRAX: An approach for the time rational analysis of complex dynamic systems

Lecomte

2015

Numerical Meth Engineering

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SUMMARYThis paper introduces a theoretical and algorithmic reduced model approach to efficiently evaluate time responses of complex dynamic systems. The proposed approach combines four main components: analytical expressions of the average of the system's transfer functions in the frequency domain, precise and convergent rational approximations of these exact expressions, exact evaluation of these approximations through model reduction in rational Krylov subspaces, and semi-analytical interpolation at just a few frequency points. The resulting algorithmic principles to evaluate the time response of a particular system are relatively straightforward: one first evaluates the response of the system with slight additional damping at a few frequencies and one then projects or reduces the system in the subspace spanned by these responses. The time response of the reduced model implicitly provides a precise evaluation of that of the original system. The properties of the reduced models and the precision of the proposed approach are studied and applications on complex matrix systems are presented and discussed. While the theory and numerical algorithms are presented in a matrix context, they are also transposable in a continuous functional context.

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A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters

Cited by 116 publications

References 4 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Stochastic finite element analysis of the free vibration of laminated composite plates

TRAX: An approach for the time rational analysis of complex dynamic systems

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