Stochastic finite element method for non-linear material models

Lacour, Maxime; Macedo, Jorge; Abrahamson, Norman A.

doi:10.1016/j.compgeo.2020.103641

Cited by 12 publications

(7 citation statements)

References 11 publications

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“…One of the most recent advancements includes the truncation preconditioners [21,32,33], which we also use in our numerical experiments. We note that a similar study to ours was recently presented by [34], but here we focus on a more complex nonlinear model that includes a crack development, and we also study efficient solution of the linear systems obtained by use of the stochastic Galerkin method.…”

Section: Introductionmentioning

confidence: 92%

“…Expansion (34) is then used to calculate expansion (18). In general, while by [12] when considering the expansion of the displacement (25) using gPC polynomials of degree p it would be possible to use gPC polynomials of degree up to 2p in expansion (34), in the numerical experiments we used expansions of the same degree and we set n K = n ξ .…”

Section: Example 1: Simply Supported Reinforced Concrete Beammentioning

confidence: 99%

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Stochastic Galerkin finite element method for nonlinear elasticity and application to reinforced concrete members

S.¹,

Sousedík²,

Dabbagh³

et al. 2022

Preprint

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We develop a stochastic Galerkin finite element method for nonlinear elasticity and apply it to reinforced concrete members with random material properties. The strategy is based on the modified Newton-Raphson method, which consists of an incremental loading process and a linearization scheme applied at each load increment. We consider that the material properties are given by a stochastic expansion in the so-called generalized polynomial chaos (gPC) framework. We search the gPC expansion of the displacement, which is then used to update the gPC expansions of the stress, strain and internal forces. The proposed method is applied to a reinforced concrete beam with uncertain initial concrete modulus of elasticity and a shear wall with uncertain maximum compressive stress of concrete, and the results are compared to those of stochastic collocation and Monte Carlo methods. Since the systems of equations obtained in the linearization scheme using the stochastic Galerkin method are very large, and there are typically many load increments, we also studied iterative solution using preconditioned conjugate gradients. The efficiency of the proposed method is illustrated by a set of numerical experiments.

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Section: Introductionmentioning

confidence: 92%

Section: Example 1: Simply Supported Reinforced Concrete Beammentioning

confidence: 99%

Stochastic Galerkin finite element method for nonlinear elasticity and application to reinforced concrete members

S.¹,

Sousedík²,

Dabbagh³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…On the other hand, in systems in which the materials used have nonlinear behavior, it is possible to achieve the solution by incremental methods, which itself requires a lot of computational costs. Therefore, in these cases, finding methods that reduce the computational volume will be inevitable [13], [17]. Researchers have always sought appropriate solutions to this problem, one of which is the SSFEM first proposed by Ghanem and Spanos [18].…”

Section: Introductionmentioning

confidence: 99%

“…Some studies have used the aforementioned strategy to investigate the following topics: wave propagation analysis Vibration analysis of fiber-reinforced composites [19], composite plates [11], [20], random creep failure prediction [21], earth dams [22], shells [10], [11], wooden structures [23], elastodynamic issues in the time domain [24], and a variety of other instances have all been investigated. Lacour et al looked into the nonlinear behavior of uncertain materials without taking into account the loading system's uncertainty, and their findings are provided [17]. However, certain loading was assumed in a wide range from studies presented for the SSFEM, Yazdani et al can be mentioned among the limited researches in which loading is also assumed to be uncertain [13].…”

Section: Introductionmentioning

confidence: 99%

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

rahimibondarabadi¹,

mousaviamjad²

2022

Preprint

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The significance of the influence of uncertainty and stochastic approach-related problems on engineering system analysis is now evident and irrefutable. On the other hand, considering the factors that apply these uncertainties in the findings should need a significant amount of computing cost and effort, which is why researchers are always looking for approaches that combine high calculation accuracy with speed. One of the most useful tools for analyzing systems with uncertainty in computational stochastic mechanics is the spectral stochastic finite element method. In the present paper, by applying uncertainty to the applied loads and elastic modulus, this method has been developed to analyze the structures with nonlinear materials, and a method called the nonlinear spectral stochastic finite element method (NLSSFEM) has been proposed. The results obtained from the used method have been compared with the results obtained from the Monte Carlo simulation method. The accuracy of calculations and the speed of access to the solution of the proposed method are evaluated as desirable.

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“…In this context, Mccarthy and Gray [7] proposed and analyzed a deterministic model for predicting the distribution of loads in multibolt composite joints [8]. In other investigation, Lacour et al [9] have modeled the von Mises stress, stiffness, and displacements by a nonlinear stochastic model at each degree of freedom.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Model of Stress Evolution in a Bolted Structure in the Presence of a Joint Elastic Piece: Modeling and Parameter Inference

Haiek

Ansari

Amrani

et al. 2020

Advances in Materials Science and Engineering

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In this paper, we propose a stochastic model to describe over time the evolution of stress in a bolted mechanical structure depending on different thicknesses of a joint elastic piece. First, the studied structure and the experiment numerical simulation are presented. Next, we validate statistically our proposed stochastic model, and we use the maximum likelihood estimation method based on Euler–Maruyama scheme to estimate the parameters of this model. Thereafter, we use the estimated model to compare the stresses, the peak times, and extinction times for different thicknesses of the elastic piece. Some numerical simulations are carried out to illustrate different results.

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Stochastic finite element method for non-linear material models

Cited by 12 publications

References 11 publications

Stochastic Galerkin finite element method for nonlinear elasticity and application to reinforced concrete members

Stochastic Galerkin finite element method for nonlinear elasticity and application to reinforced concrete members

Generalization of spectral stochastic finite element method for analysis of structures with elastoplastic materials

A Stochastic Model of Stress Evolution in a Bolted Structure in the Presence of a Joint Elastic Piece: Modeling and Parameter Inference

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