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Article
Publication date: 1 October 2005

Marcin Kamiński and Graham F. Carey

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

Abstract

Purpose

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

Design/methodology/approach

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

Findings

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

Research limitations/implications

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Practical implications

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

Originality/value

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 15 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 5 October 2015

Ali Johari, Jaber Rezvani Pour and Akbar Javadi

Liquefaction of soils is defined as significant reduction in shear strength and stiffness due to increase in pore water pressure. This phenomenon can occur in static…

Abstract

Purpose

Liquefaction of soils is defined as significant reduction in shear strength and stiffness due to increase in pore water pressure. This phenomenon can occur in static (monotonic) or dynamic loading patterns. However, in each pattern, the inherent variability of the soil parameters indicates that this problem is of a probabilistic nature rather than being deterministic. The purpose of this paper is to present a method, based on random finite element method, for reliability assessment of static liquefaction of saturated loose sand under monotonic loading.

Design/methodology/approach

The random finite element analysis is used for reliability assessment of static liquefaction of saturated loose sand under monotonic loading. The soil behavior is modeled by an elasto-plastic effective stress constitutive model. Independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are selected as stochastic parameters which are modeled using a truncated normal probability density function (pdf).

Findings

The probability of liquefaction is assessed by pdf of modified pore pressure ratio at each depth. For this purpose pore pressure ratio is modified for monotonic loading of soil. It is shown that the saturated unit weight is the most effective parameter, within the selected stochastic parameters, influencing the static soil liquefaction.

Originality/value

This research focuses on the reliability analysis of static liquefaction potential of sandy soils. Three independent soil parameters including saturated unit weight, peak friction angle and initial plastic shear modulus are considered as stochastic input parameters. A computer model, coded in MATLAB, is developed for the random finite element analysis. For modeling of the soil behavior, a specific elasto-plastic effective stress constitutive model (UBCSAND) was used.

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Article
Publication date: 1 June 1997

Jaroslav Mackerle

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

Abstract

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 4 September 2018

Muhannad Aldosary, Jinsheng Wang and Chenfeng Li

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely…

Abstract

Purpose

This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy subject for novice researchers/practitioners, where many different methods and techniques coexist with inconsistent input/output requirements and analysis schemes.

Design/methodology/approach

This confusing status significantly hampers the research progress and practical application of UQ methods in engineering. In the context of engineering analysis, the research efforts of UQ are most focused in two largely separate research fields: structural reliability analysis (SRA) and stochastic finite element method (SFEM). This paper provides a state-of-the-art review of SRA and SFEM, covering both technology and application aspects. Moreover, unlike standard survey papers that focus primarily on description and explanation, a thorough and rigorous comparative study is performed to test all UQ methods reviewed in the paper on a common set of reprehensive examples.

Findings

Over 20 uncertainty quantification methods in the fields of structural reliability analysis and stochastic finite element methods are reviewed and rigorously tested on carefully designed numerical examples. They include FORM/SORM, importance sampling, subset simulation, response surface method, surrogate methods, polynomial chaos expansion, perturbation method, stochastic collocation method, etc. The review and comparison tests comment and conclude not only on accuracy and efficiency of each method but also their applicability in different types of uncertainty propagation problems.

Originality/value

The research fields of structural reliability analysis and stochastic finite element methods have largely been developed separately, although both tackle uncertainty quantification in engineering problems. For the first time, all major uncertainty quantification methods in both fields are reviewed and rigorously tested on a common set of examples. Critical opinions and concluding remarks are drawn from the rigorous comparative study, providing objective evidence-based information for further research and practical applications.

Details

Engineering Computations, vol. 35 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 9 October 2019

Hui Chen and Donghai Liu

The purpose of this study is to develop a stochastic finite element method (FEM) to solve the calculation precision deficiency caused by spatial variability of dam…

Abstract

Purpose

The purpose of this study is to develop a stochastic finite element method (FEM) to solve the calculation precision deficiency caused by spatial variability of dam compaction quality.

Design/methodology/approach

The Choleski decomposition method was applied to generate constraint random field of porosity. Large-scale laboratory triaxial tests were conducted to determine the quantitative relationship between the dam compaction quality and Duncan–Chang constitutive model parameters. Based on this developed relationship, the constraint random fields of the mechanical parameters were generated. The stochastic FEM could be conducted.

Findings

When the fully random field was simulated without the restriction effect of experimental data on test pits, the spatial variabilities of both displacement and stress results were all overestimated; however, when the stochastic FEM was performed disregarding the correlation between mechanical parameters, the variabilities of vertical displacement and stress results were underestimated and variation pattern for horizontal displacement also changed. In addition, the method could produce results that are closer to the actual situation.

Practical implications

Although only concrete-faced rockfill dam was tested in the numerical examples, the proposed method is applicable for arbitrary types of rockfill dams.

Originality/value

The value of this study is that the proposed method allowed for the spatial variability of constitutive model parameters and that the applicability was confirmed by the actual project.

Details

Engineering Computations, vol. 36 no. 9
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 November 2002

Herbert Martins Gomes and Armando Miguel Awruch

In this paper, special emphasis is given to uncertainties in the evaluation of the structural behavior, looking for a better representation of the system characteristics…

Abstract

In this paper, special emphasis is given to uncertainties in the evaluation of the structural behavior, looking for a better representation of the system characteristics and quantification of the significance of these uncertainties in structural design. The reliability analysis of reinforced concrete structures is performed taking into account the spatial variability of material properties. The finite element method is used to analyze reinforced concrete structures. A multidimensional non‐Gaussian stochastic field generation model (independent of the finite element mesh) is developed and used. The reliability analysis is carried out employing the first order reliability method. Numerical examples are presented to study how to generate correlated non‐Gaussian stochastic fields and determine the reliability of a reinforced concrete structure with respect to a limit state function.

Details

Engineering Computations, vol. 19 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 16 June 2010

Jhojan Enrique Rojas, Othmane Bendaou, Abdelkhalak El Hami and Domingos Rade

The purpose of this paper is to present a deterministic, stochastic and reliability analysis through numerical simulations in 2D and 3D dynamic fluid‐structure interaction…

Abstract

Purpose

The purpose of this paper is to present a deterministic, stochastic and reliability analysis through numerical simulations in 2D and 3D dynamic fluid‐structure interaction problems.

Design/methodology/approach

The perturbation methods allied to reliability analysis are applied to fluid‐structure finite element models. Reliability analysis couples finite element analysis with first and second order reliability methods and ant colony optimization in a modified first order reliability method.

Findings

Results obtained show the potentialities of the proposed methodology and encourage improvement of this procedure for use in complex coupled fluid‐structure systems.

Originality/value

The understanding of the mechanical interaction between a fluid and an elastic solid has a capital importance in several industrial applications. In order to couple the behaviour of two different media, deterministic models have been proposed. However, stochastic analysis has been developed to deal with the statistical nature of fluid‐structure interaction parameters. Moreover, probabilistic‐based reliability analysis intends to find safe and cost‐effective projects.

Details

Multidiscipline Modeling in Materials and Structures, vol. 6 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 1 October 2006

C.F. Li, Y.T. Feng, D.R.J. Owen and I.M. Davies

To provide an explicit representation for wide‐sense stationary stochastic fields which can be used in stochastic finite element modelling to describe random material properties.

Abstract

Purpose

To provide an explicit representation for wide‐sense stationary stochastic fields which can be used in stochastic finite element modelling to describe random material properties.

Design/methodology/approach

This method represents wide‐sense stationary stochastic fields in terms of multiple Fourier series and a vector of mutually uncorrelated random variables, which are obtained by minimizing the mean‐squared error of a characteristic equation and solving a standard algebraic eigenvalue problem. The result can be treated as a semi‐analytic solution of the Karhunen‐Loève expansion.

Findings

According to the Karhunen‐Loève theorem, a second‐order stochastic field can be decomposed into a random part and a deterministic part. Owing to the harmonic essence of wide‐sense stationary stochastic fields, the decomposition can be effectively obtained with the assistance of multiple Fourier series.

Practical implications

The proposed explicit representation of wide‐sense stationary stochastic fields is accurate, efficient and independent of the real shape of the random structure in consideration. Therefore, it can be readily applied in a variety of stochastic finite element formulations to describe random material properties.

Originality/value

This paper discloses the connection between the spectral representation theory of wide‐sense stationary stochastic fields and the Karhunen‐Loève theorem of general second‐order stochastic fields, and obtains a Fourier‐Karhunen‐Loève representation for the former stochastic fields.

Details

Engineering Computations, vol. 23 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 May 2000

Jaroslav Mackerle

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

Abstract

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

Details

Engineering Computations, vol. 17 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1996

Jaroslav Mackerle

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix…

Abstract

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

Details

Engineering Computations, vol. 13 no. 1
Type: Research Article
ISSN: 0264-4401

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