Lattice domes reliability by the perturbation-based approaches vs. semi-analytical method

Pokusiński, Bartłomiej; Kamiński, Marcin

doi:10.1016/j.compstruc.2019.05.012

Cited by 15 publications

(3 citation statements)

References 18 publications

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“…From the mathematical viewpoint, the SFEM is known as a robust technique for the solution of stochastic partial differential equations. There are different variants of the SFEM such as the perturbation approach, 4 spectral decomposition approach, 2 and Monte Carlo simulation 3,5 which have been applied to numerous research fields consisting of earthquake engineering, [5][6][7][8][9] structural engineering, [10][11][12][13][14] mechanical engineering, [15][16][17] among others. 18 More recently, the stochastic spectral element method (SSEM) has been proposed as a computational framework based on the spectral decomposition.…”

Section: Introductionmentioning

confidence: 99%

Stochastic spectral cell method for structural dynamics and wave propagations

Zakian

2023

Numerical Meth Engineering

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The spectral element method when enriched with the concept of fictitious domain constitutes the spectral cell method which is appropriately able to model geometrically complicated problems by simplifying the mesh generation. In this paper, we propose a new computational framework called stochastic spectral cell method (SSCM) as a stochastic development of the spectral cell method for uncertainty quantification applied to structural dynamics and wave propagations. The stochastic form of spectral cell method has not been developed yet. Hence, the SSCM is a novel stochastic method comprising the advantages of spectral cell method for computational mechanics considering the geometrical complexity resulting from computer‐aided design. The SSCM is established by incorporating the polynomial chaos and Karhunen‐Loève expansions for the uncertainty quantification, and the interpolation functions of spectral elements for the spatial discretization. In the SSCM, the numerical solution of the Fredholm integral equation of the second kind required in Karhunen‐Loève expansion is obtained using the spectral cell method. The use of Cartesian mesh, diagonal mass matrix, and higher order interpolation functions of spectral elements for stochastic dynamic analysis lead to desirable computational efficiency and accuracy of the SSCM. The capability, effectiveness, and accuracy of the proposed SSCM are demonstrated with several numerical examples of wave propagation as well as dynamic analysis of structures.

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Section: Introductionmentioning

confidence: 99%

Stochastic spectral cell method for structural dynamics and wave propagations

Zakian

2023

Numerical Meth Engineering

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“…3 A popular class, on which many proposed literature methods are based, is the family of perturbation methods. [4][5][6] This method is mainly based on a Taylor series expansion in terms of a set of zero-mean random variables (RVs), where different levels of accuracy can be obtained by truncating the series at different terms. Basically, perturbation-based approaches are characterized by computational advantage and easy applicability.…”

Section: Introductionmentioning

confidence: 99%

“…Other stochastic methods are based on the so‐called closure technique, which consists of a truncation of the cumulant series expansion of the response characteristic function (CF) at

k

th term 3 . A popular class, on which many proposed literature methods are based, is the family of perturbation methods 4‐6 . This method is mainly based on a Taylor series expansion in terms of a set of zero‐mean random variables (RVs), where different levels of accuracy can be obtained by truncating the series at different terms.…”

Section: Introductionmentioning

confidence: 99%

A new stochastic method based on the Taylor expansion to compute response probability densities of uncertain systems

Navarro‐Quiles

Laudani

Falsone

2022

Numerical Meth Engineering

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In this article, a new stochastic approach is proposed for the analysis of structural systems with uncertainties. This novel strategy method combines the probability transformation method, expressed in terms of characteristic function with a probabilistic version of the Taylor expansion. Some notes about the convergence and the accuracy of the proposed method are reported. The results of these notes and several examples here reported evidence an optimum level of accuracy, coupled with great simplicity of application of this approach, even for relatively high levels of uncertainties. Hence, this method can be considered a valuable tool for the solution of stochastic analyses of engineering systems. Several examples are performed to show the capability of the results established. These applications show how the method is a useful technique for engineering analysis.

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Stochastic finite cell method for structural mechanics

Zakian

2021

Comput Mech

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Lattice domes reliability by the perturbation-based approaches vs. semi-analytical method

Cited by 15 publications

References 18 publications

Stochastic spectral cell method for structural dynamics and wave propagations

Stochastic spectral cell method for structural dynamics and wave propagations

A new stochastic method based on the Taylor expansion to compute response probability densities of uncertain systems

Stochastic finite cell method for structural mechanics

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