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15th International Symposium on Applied Electromagnetics and Mechanics (ISEM)

作者： Beddek, K. Clenet, S. Moreau, O. Le Menach, Y. L2EP Univ Lille 1 F-59655 Villeneuve Dascq France L2EP Arts & Metiers ParisTech Lille France Electricite France Dept THEMIS Clamart France

In this paper, a spectral stochastic finite element method (SSFEM) is described and applied to quantify uncertainties in an industrial eddy current non destructive testing (NDT) problem. A new iterative solver based on the fixed-point method is proposed to solve the large scale linear system. The efficiency of the suggested iterative solver to tackle the SSFEM computational complexity is demonstrated. The SSFEM results and the computation times obtained with 2 and 4 random variables are compared to those given by the anisotropic adaptive sparse grid non intrusive spectral projection (NISP). On this application, the SSFEM dedicated solver is competitive with the adaptive sparse grids strategy.

关键词： spectral stochastic finite element method fixed-point method eddy current problem polynomial chaos expansion intrusive solver

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spectral stochastic finite element method for Periodic Structure

Spectral Stochastic Finite Element Method for Periodic Struc...

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IEEE International Microwave and RF Conference (IMaRC)

作者： Hemanth, G. Vinoy, K. J. Gopalakrishnan, S. Indian Inst Sci Dept Elect Commun Engn Bangalore Karnataka India Indian Inst Sci Dept Aerosp Engn Bangalore Karnataka India

ISBN: (纸本)9781479963171

In this paper we formulate the finite element matrix equations using spectral stochastic methods for plane wave scattering by a periodic structures with uncertain parameters. The input random variable is discretized by Karhunen-Loeve expansion method and output random solution is expanded using polynomial chaos method. stochastic Galerkin method is employed to get least squares solution. We present the method of coupling the plane wave scattering problem with SSFEM and illustrate with a numerical example.

关键词： Electromagnetic Band Gap finite element method Karhunen-Loeve Polynomial Chaos spectral stochastic finite element method

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Applying the spectral stochastic finite element method in multiple-random field RC structures

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Frontiers of Structural and Civil Engineering 2022年第4期16卷 434-447页

作者： Abbas YAZDANI Civil Engineering Department University of Sistan and BaluchestanZahedan 98167-45845Iran

This paper uses the spectral stochastic finite element method(SSFEM)for analyzing reinforced concrete(RC)beam/slab *** doing so,it presents a new framework to study how the correlation length of a random field(RF)with uncertain parameters will affect modeling uncertainties and reliability *** considers:1)different correlation lengths for uncertainty parameters,and 2)dead and live loads as well as the elasticity moduli of concrete and steel as a multi-dimensional RF in concrete *** show the SSFEM’s efficiency in the study of concrete structures and to evaluate the sensitivity of the correlation length effects in evaluating the reliability,two examples of RC beams and slabs have been *** to the results,the RF correlation length is effective in modeling uncertainties and evaluating reliabilities;the longer the correlation length,the greater the dispersion range of the structure response and the higher the failure probability.

关键词： uncertainty spectral stochastic finite element method correlation length reliability assessment reinforced concrete beam/slab

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A natural frequency sensitivity-based stabilization in spectral stochastic finite element method for frequency response analysis

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STRUCTURAL ENGINEERING AND MECHANICS 2020年第3期75卷 311-325页

作者： Lee, Gil-Yong Jin, Seung-Seop Park, Yong-Hwa Korea Adv Inst Sci & Technol Dept Mech Engn 291 Daehak Ro Daejeon 34141 South Korea Korea Inst Civil Engn & Bldg Technol KICT Sustainable Infrastruct Res Ctr Goyang Si 10223 South Korea

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

关键词： uncertainty quantification spectral stochastic finite element method frequency response natural frequency sensitivity

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A GPU domain decomposition solution for spectral stochastic finite element method

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COMPUTER methodS IN APPLIED MECHANICS AND ENGINEERING 2017年 327卷 392-410页

作者： Stavroulakis, G. Giovanis, D. G. Papadopoulos, V. Papadrakakis, M. Natl Tech Univ Athens Inst Struct Anal & Antiseism Res Athens Greece

In intrusive methods for the stochastic analysis of engineering systems, the solution of the stochastic partial differential equations leads to an augmented algebraic system of equations, with respect to the corresponding deterministic problem. The solution of this augmented system can become quite challenging or even impossible due to the increased computational resources and effort required, especially in large-scale problems with large parameter variability. Recent developments in computer hardware regarding graphics processing units (GPU)-accelerated computing have been proven very promising due to their advanced capabilities and have been used in a number of scientific fields in order to enhance the solution of computationally high demanding problems. In this work, the benefits achieved with the exploitation of the GPU capabilities are demonstrated, in addressing intrusive stochastic mechanics problems where the solution of the resulting finite element algebraic equations is performed with the dual domain decomposition method, implementing specifically tailored preconditioners. The results show a significant enhancement of the spectral stochastic finite element method in terms of computational performance as well as of the consumed energy efficiency when applying the proposed methodology. (C) 2017 Published by Elsevier B.V.

关键词： spectral stochastic finite element method Multi-core processing Graphics processing units Domain decomposition methods

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A consistently linearized spectral stochastic finite element formulation for geometric nonlinear composite shells

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COMPUTATIONAL MECHANICS 2025年第5期75卷 1655-1683页

作者： Panther, Lukas Wagner, Werner Freitag, Steffen Karlsruhe Inst Technol KIT Inst Struct Anal Kaiserstr 12 D-76131 Karlsruhe Germany

Material and geometrical properties have a major influence on the structural behavior of geometric nonlinear shell structures. Therefore, uncertain structural parameters have to be considered within the context of stochastic structural analysis. The Monte Carlo simulation (MCS) is a widely used method for estimating statistical properties of the random structural response. Considering the computation time, however, this technique is challenging for complex finite element (FE) models and requires numerical efficient surrogate modelling approaches. An efficient way to propagate parametric uncertainties through complex models is the polynomial chaos expansion (PCE). Within the spectral stochastic finite element method (SFEM), the PCE is integrated into the FE formulation of structural elements. The application of the SFEM to geometrical nonlinear mechanical structures remains comparatively unexplored. In this paper, we present a geometric nonlinear spectral stochastic shell formulation. We use a layerwise formulation of the linear elastic material law to describe the behavior of composite materials. In order to apply Newton's method during the nonlinear solution procedure, all equations are consistently linearized to achieve a quadratic convergence in the iteration behavior. Two numerical examples show the applicability and efficiency of the presented spectral stochastic FE formulation. The SFEM results show a very good agreement compared to the results of the MCS. Special focus is set on the polynomial basis, which has a significant influence on the quality of the results, but also on the computational effort. We show, that the SFEM calculation provides a surrogate model, that can be used efficiently for further post-processing computations.

关键词： Nonlinear shell formulation spectral stochastic finite element method Polynomial chaos expansion Uncertainty quantification Composite materials

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Seismic analysis of gravity dam-foundation systems using stochastic spectral finite element method

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SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 2024年 182卷

作者： Zeng, Qing-Pei Wang, Jin-Ting Zhang, Meng-Zhong Wang, Xiang-Chao Huang, Hai-Long Pan, Jian-Wen Tsinghua Univ Dept Hydraul Engn Beijing 100084 Peoples R China China Three Gorges Construct Management Co Ltd Chengdu 610000 Peoples R China

Seismic analysis of dam-foundation systems is inherently complex due to uncertainties in material properties. This study investigates the effects of material randomness and heterogeneity on the seismic response of gravity dam-foundation systems using the stochastic spectral finite element method (SSFEM) based on the Karhunen Loe`ve expansion and the polynomial chaos expansion. The Pine Plane dam is taken as an analysis example. First, the appropriate Karhunen Loe`ve expansion modes and polynomial chaos order are determined for SSFEM by comparing them with the Monte-Carlo simulations. Subsequently, the seismic response of the dam is analyzed in the stochastic and deterministic models, respectively. Results indicate that material randomness and heterogeneity may reduce the seismic response of gravity dams, and the deterministic model may overestimate dynamic responses. Subsequently, the parametric analysis of the correlation length, which measures the spatial correlation between variables in different positions and indicates the size of heterogeneity material patches, is conducted. It is demonstrated that the correlation length would not significantly affect the mean responses, but a larger correlation length leads to greater dispersions in responses. Finally, the effects of randomness in the foundation are investigated. The heterogeneities in the foundation affect the response of the dam in the high-frequency range. Therefore, the uncertainty in material properties should be fully considered in a structural assessment and risk analysis.

关键词： Gravity dam-foundation system Dynamic analysis spectral stochastic finite element method Correlated length Heterogeneity

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Effect analysis of 3D material randomness on seismic response of arch dams using a customizable code

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STRUCTURES 2025年 75卷

作者： Zeng, Qing-Pei Wang, Jin-Ting Zhang, Meng-Zhong Wang, Xiang-Chao Pan, Jian-Wen Jiang, Hui Tsinghua Univ State Key Lab Hydrosci & Engn Beijing 100084 Peoples R China Beijing Univ Technol Coll Architecture & Civil Engn Beijing 100124 Peoples R China

This study investigates the impact of material randomness on the seismic response of arch dams based on the spectral stochastic finite element method (SSFEM). Firstly, a customizable computational code is developed within an open-source finite element toolbox to implement the SSFEM for simulating the seismic response incorporating 3D material random fields. Second, the framework is applied to the Pacoima Dam as a case study under the 1994 Northridge earthquake and validated by the comparative analysis based on observational records. Finally, comparative analyses are conducted to quantify the influence of material randomness. The comparison between deterministic and stochastic responses reveals that deterministic models tend to overestimate the peak acceleration responses as the dam height increases. Nonlinear analyses considering homogeneous and heterogeneous material indicate that the material heterogeneity will intensify the local damage and disrupt the continuity of the damage paths. In addition, by comparing cases with independent and crosscorrelated material properties, it is found that the cross-correlation will further exacerbate the damage with increasing the total damage volume by up to 6 %. These results highlight the necessity of incorporating the spatial variability and randomness of materials in seismic safety assessments for arch dams.

关键词： Seismic analysis 3D material random field spectral stochastic finite element method Arch dam

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Efficient numerical strategies for spectral stochastic finite element models

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2005年第10期64卷 1334-1349页

作者： Chung, DB Gutiérrez, MA Graham-Brady, LL Lingen, FJ Delft Univ Technol Fac Aerosp Engn NL-2600 GB Delft Netherlands Johns Hopkins Univ Dept Civil Engn Baltimore MD 21218 USA Habanera Numer Software NL-2629 HT Delft Netherlands

The use of spectral stochastic finite element models results in large systems of equations requiring specialized solution strategies. This paper discusses three different numerical algorithms for solving these large systems of equations. It presents a trade-off of these algorithms in terms of memory usage and computation time. It also shows that the structure of the spectral stochastic stiffness matrix can be exploited to accelerate the solution process, while keeping the memory usage to a minimum. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： spectral stochastic finite element method numerical solution strategies element-by-element algorithms

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stochastic strain and stress computation of a higher-order sandwich beam using hybrid stochastic time domain spectral element method

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MECHANICS OF ADVANCED MATERIALS AND STRUCTURES 2022年第4期29卷 525-538页

作者： Sharma, Himanshu Mukherjee, Shuvajit Ganguli, Ranjan Indian Inst Sci Dept Aerosp Engn Bangalore 560012 Karnataka India

In this work, a combination of the spectral stochastic finite element method (SSFEM) and the time-domain spectral element method (TSEM), referred to as the stochastic time domain spectral element method (STSEM), is presented to compute the stochasticity of strain and stress of a higher-order sandwich composite beam with spatial variability in the material properties. The method proposed in this work employs the efficiencies of both SSFEM and TSEM for the uncertainty analysis of a sandwich beam. The material properties of face sheets and core are considered as Gaussian random fields, which are discretized using the Karhunen-Loeve expansion, and polynomial chaos expansion is used to represent the response quantity. A numerical example is considered for which, first, a sensitivity analysis is performed to identify the most sensitive material properties. Then, the proposed STSEM is used to demonstrate the computational efficiency and numerical accuracy in comparison with Monte-Carlo simulation. Moreover, the effect of core depth on strain and stress variability is also examined.

关键词： Karhunen-Loeve expansion polynomial chaos expansion sandwich composite beam sensitivity analysis spectral stochastic finite element method time domain spectral element method

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