Practical Application of the Stochastic Finite Element Method

Arregui-Mena, José David; Margetts, Lee; Mummery, Paul

doi:10.1007/s11831-014-9139-3

Cited by 120 publications

(62 citation statements)

References 113 publications

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“…The SFEM was already successfully applied to problems involving diffusion, stochastic nanomechanics, stochastic plasticity, and thermomechanics . For an overview of the existing applications and modifications, we refer to the works of Stefanou and Arregui‐Mena et al…”

Section: Introductionmentioning

confidence: 99%

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Pivovarov

Oberleiter

Willner

et al. 2018

Numerical Meth Engineering

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Summary Uncertainties in the macroscopic response of heterogeneous materials result from two sources: the natural variability in the microstructure's geometry and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted aleatoric uncertainty and may be characterized by a known probability density function. The second type of uncertainty is denoted epistemic uncertainty. This kind of uncertainty cannot be described using probabilistic methods. Models considering both sources of uncertainties are called polymorphic. In the case of polymorphic uncertainties, some combination of stochastic methods and fuzzy arithmetic should be used. Thus, in the current work, we examine a fuzzy‐stochastic finite element method–based homogenization framework for materials with random inclusion sizes. We analyze an experimental radii distribution of inclusions and develop a stochastic representative volume element. The stochastic finite element method is used to obtain the material response in the case of random inclusion radii. Due to unavoidable noise in experimental data, an insufficient number of samples, and limited accuracy of the fitting procedure, the radii distribution density cannot be obtained exactly; thus, it is described in terms of fuzzy location and scale parameters. The influence of fuzzy input on the homogenized stress measures is analyzed.

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Section: Introductionmentioning

confidence: 99%

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Pivovarov

Oberleiter

Willner

et al. 2018

Numerical Meth Engineering

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“…However, even if the performance function is explicit, the nonlinearity of the function and the non-Gaussian distribution of random variables always make it impossible to obtain the exact solution of this multi-fold integral [1], [2]. Various methods have been used to analyze the failure probability of structures subjected to random material parameters, such as the first-and second-order reliability methods (FORM/SORM) [3], [4], the simulation methods [5]- [7], the traditional perturbation stochastic finite element methods (PSFEM) [8], [9], the response surface method [10], [11], and so on. However, more or less problems exist in the above mentioned methods.…”

Section: Introductionmentioning

confidence: 99%

Structural Reliability Analysis Using Orthogonalizable Power Polynomial Basis Vector

Huang

2017

MATEC Web Conf.

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Abstract.A new method for structural reliability analysis using orthogonalizable power polynomial basis vector is presented. Firstly, a power polynomial basis vector is adopted to express the initial series solution of structural response, which is determined by a series of deterministic recursive equation based on perturbation technique, and then transferred to be a set of orthogonalizable power polynomial basis vector using the orthogonalization technique. By conducting Garlekin projection, an accelerating factor vector of the orthogonalizable power polynomial expansion is determined by solving small scale algebraic equations. Numerical results of a continuous bridge structure on reliability analysis shows that the proposed method can achieve the accuracy of the Direct Monte Carlo method and can save a lot of computation time at the same time, it is both accurate and efficient, and is very competitive to be used in structural reliability analysis.

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“…A study on the effects of material variability in nuclear graphite can be found in reference [7]. For more information about stochastic finite element modelling the reader is referred to [8].…”

Section: Introductionmentioning

confidence: 99%

Spatial variability in the mechanical properties of Gilsocarbon

Arregui-Mena

Bodel

Worth

et al. 2016

Carbon

Self Cite

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The objective of this study is to investigate whether there is significant spatial variability in the mechanical properties of Gilsocarbon nuclear graphite at different sections of the billet; specifically the dynamic Poisson's ratio, dynamic shear modulus, dynamic Young's modulus and density. Similar studies have been done, usually in the context of manufacturing, to assess the quality of graphite components for nuclear reactors. In this new study, the measurements have been carried out at a much higher spatial resolution than previously. A Torness/Heysham B billet was machined into cubes so that measurements could be made across the circumference and height of the billet. ASTM standards were followed to assess the measurements of the samples. The spatial variability of material properties is described and analysed statistically. The study shows that material variability is present at different heights and circumferential locations of the billet. This discovery will have a significant impact on the structural integrity and through life performance predictions made in industry; both in current and future nuclear reactors. The computer modelling of graphite components may predict different outcomes to standard analyses (that use mean values) if this variability is incorporated into the analysis workflow; specifically through stochastic modelling.

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Practical Application of the Stochastic Finite Element Method

Cited by 120 publications

References 113 publications

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Structural Reliability Analysis Using Orthogonalizable Power Polynomial Basis Vector

Spatial variability in the mechanical properties of Gilsocarbon

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