A stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuities

Zakian, Pooya; Khaji, N.

doi:10.1007/s00466-019-01692-5

Cited by 18 publications

(7 citation statements)

References 54 publications

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“…The indicator function, Equation (8), gives the true geometry by ignoring the participation of the fictitious domain, and returns a very small value for the points inside the fictitious domain because a value strictly equal to zero produces ill-conditioned matrices. This very small value ranges from 10 −6 to 10 −14 depending on the problem.…”

Section: Spectral Cell Methodsmentioning

confidence: 99%

“…x ∈ Ω with Ω being the deterministic space describing the system geometry. 8 Furthermore, Ĥ(x, ⋅) represents a random variable for a given x, whereas Ĥ(⋅, 𝜃) indicates the random field realization for a given event 𝜃.…”

Section: Preliminarymentioning

confidence: 99%

“…The present SSCM applies the SCM for eigensolution of the Fredholm integral equation of the second kind needed for the KLE. According to the literature review, several numerical methods have been applied to the solution of this integral equation, such as the finite element method, 2,6 isogeometric analysis, 45,46,49 spectral element method, 7,8,19,50 and finite cell method. 47 Here, the SCM is employed for the solution of Fredholm equation composed of domains with CAD geometry.…”

Section: Numerical Solution Of the Fredholm Equationmentioning

confidence: 99%

“…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%

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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: Spectral Cell Methodsmentioning

confidence: 99%

Section: Preliminarymentioning

confidence: 99%

Section: Numerical Solution Of the Fredholm Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic spectral cell method for structural dynamics and wave propagations

Zakian

2023

Numerical Meth Engineering

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“…Wang and Yeh [17], Zakian et al [18,19], and Yeh and Rahman [20] studied seismic responses considering soil spatial variability. Zakian and Khaji [21,22] used a stochastic spectral finite element method to investigate wave propagation in a stochastic medium. e MCM is both simple and direct.…”

Section: Introductionmentioning

confidence: 99%

A Prediction Method Based on Monte Carlo Simulations for Finite Element Analysis of Soil Medium considering Spatial Variability in Soil Parameters

Tang

Wang

2020

Advances in Materials Science and Engineering

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With the Stochastic Finite Element Method (SFEM), the spatial variability of soil properties can be incorporated into the analysis of geotechnical structures. Although this method is significantly superior in principle to the homogeneous analysis of soil parameters, generalizing the method in engineering practice is difficult due to its computational inefficiency. In this paper, we propose a new method for the fast calculation of convergence results. The proposed method introduces a distance space to the Monte Carlo Method (MCM) random field instances and, considering the importance of a safety margin in structures, uses selected spatial interpolation to predict the MCM instances to be solved. Two case study simulations are presented. The results show that compared to the full Monte Carlo Simulation, the fast calculation method proposed in this paper can achieve very accurate convergence results while substantially reducing the computational cost, and the simulation errors for the structure are on the safer side.

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