Relationship between specified ductility and strength demand reduction for single degree-of-freedom systems under extreme wind events

Gani, Ferawati; Légeron, Frédéric

doi:10.1016/j.jweia.2012.06.006

Cited by 20 publications

(9 citation statements)

References 15 publications

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“…The equivalent statistical linearization, originally introduced by Botoon and Caughey [7,8] can be used for the analysis of largescale nonlinear structures, as encountered in earthquake engineering [14,69,22] or in wind engineering [71,26,24]. The main idea of the equivalent linearization consists in replacing the nonlinear system with an equivalent linear one by minimizing an error criterion depending on the parameters of the equivalent system.…”

Section: Gaussian Equivalent Linearizationmentioning

confidence: 99%

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Canor

Caracoglia

Denoël

2016

Probabilistic Engineering Mechanics

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a b s t r a c tThe analysis of large-scale structures subject to transient random loads, coherent in space and time, is a classic problem encountered in earthquake and wind engineering. The simulation-based framework is usually seen as the most convenient approach for both linear and nonlinear dynamics. However, the generation of statistically consistent samples of an excitation field remains a heavy computational task. In light of this, perturbation techniques are applied to develop and improve evolutionary spectral analysis.Advantageously performed in a standard modal basis, this evolutionary spectral analysis for linear structures requires the computation of the modal impulse response matrix. However, this matrix has no general closed-form expression in the presence of modal coupling. We propose therefore to model it by an asymptotic approximation, obtained by the inverse Fourier transform of an asymptotic expansion of the modal transfer matrix of the structure. This latter expansion considers the modal coupling as a perturbation of a main decoupled system. This strategy leads to an expansion known in a closed-form. Finally, the semi-group property allows the use of an efficient recurrence relation to approximate the modal evolutionary transfer matrix, i.e. the evolutionary extension of the transfer matrix.The asymptotic expansion-based method and the recurrence relation are then applied to nonlinear transient dynamics by using Gaussian equivalent linearization. This extension is formalized by a multiple timescales approach, allowing to consider a linearized structure, namely a time variant system, as piecewise linear time invariant depending on a statistical timescale. The proposed developments are finally illustrated on realistic civil engineering applications.

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Section: Gaussian Equivalent Linearizationmentioning

confidence: 99%

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Canor

Caracoglia

Denoël

2016

Probabilistic Engineering Mechanics

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“…The reason why the derivation ends up with such a simple formulation is that the whole concept is based on linear algebra. Retrospectively, the matrix inversions in (20) are replaced by linear combinations, thanks to the asymptotic expansion, and any operation in the derivation is linear with respect to its arguments. The permutation of these linear operators precisely allows the expression of the response of the coupled systems as a perturbation of the response of the main decoupled system.…”

Section: Derivation Of the Asymptotic Formulationmentioning

confidence: 99%

“…Among them, the equivalent linearization, originally introduced by Botoon and Caughey [13,14] can be used for the analysis of high-dimensional nonlinear structures, as encountered in earthquake engineering [15,16,17] or in wind engineering [18,19,20]. The main idea of the equivalent linearization consists in replacing the nonlinear system with an equivalent linear one by minimizing an error criterion depending on the parameters of the equivalent system.…”

Section: Introductionmentioning

confidence: 99%

An asymptotic expansion-based method for a spectral approach in equivalent statistical linearization

Canor

Blaise

Denoël

2014

Probabilistic Engineering Mechanics

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Equivalent linearization consists in replacing a nonlinear system with an equivalent linear one whose parameters are tuned with regard to the minimization of a suitable function. In particular, the Gaussian equivalent linearization expresses the properties of an equivalent linear system in terms of the mean vector and the covariance matrix of the responses, which are the unknowns of the optimization problem in a spectral approach. Even though the system has been linearized, the resulting set of equations is nonlinear. The computational effort in this method pertains to the solution of a possibly large set of nonlinear algebraic equations involving integrals and inversions of full matrices. This work proposes to develop and apply an asymptotic expansion-based method to facilitate and to improve the statistical linearization for large nonlinear structures. The proposed developments demonstrate that for slightly to moderately coupled nonlinear systems, the equivalent linearization can be applied with an appropriate modal approach and eventually seen as a convergent series initiated with the stochastic response of a main decoupled linear system. With this method, the computational effort is attractively reduced, the conditioning of the set of nonlinear algebraic equations is improved and inversion of full transfer matrices and repeated integrations are avoided. The paper gives a formal description of the method and illustrates its implementation and performances with the computation of stationary responses of nonlinear structures subject to coherent random excitation fields.

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“…The downside of this is that the structural systems of many buildings are designed with no knowledge of their inelastic behavior, potentially leaving them exposed to undesirable collapse scenarios or at least unknown post-yield behavior. From a research perspective, the problem of understanding and modeling the inelastic behavior of wind excited structures has been the subject of a number of works [19][20][21][22][23][24][25][26] including the application of pushover analysis [27]. The main difficulty in defining a modeling procedure that can account for this effect is the extremely long duration of wind storms.…”

Section: Introductionmentioning

confidence: 99%

An efficient framework for the elasto-plastic reliability assessment of uncertain wind excited systems

et al. 2016

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Relationship between specified ductility and strength demand reduction for single degree-of-freedom systems under extreme wind events

Cited by 20 publications

References 15 publications

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

Perturbation methods in evolutionary spectral analysis for linear dynamics and equivalent statistical linearization

An asymptotic expansion-based method for a spectral approach in equivalent statistical linearization

An efficient framework for the elasto-plastic reliability assessment of uncertain wind excited systems

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