Structural stochastic responses determination via a sample-based stochastic finite element method

Zheng, Zhibao; Dai, Hongzhe

doi:10.1016/j.cma.2021.113824

Cited by 23 publications

(17 citation statements)

References 17 publications

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“…Several explorations for solving linear static stochastic problems, linear dynamic stochastic problems and the problems defined on random domains using (25)-like expansions can be found in our previous work. 30,31,33 We also remark that the second part-like expansion in (25) (i.e., ∑ k j=1 𝜆 j (t i , 𝜃) d j (t i )) has been widely used in the context of proper generalized decomposition methods. [34][35][36] However, these classical expansions are not applicable to the stochastic elastoplastic problem.…”

Section: Approximation Of Stochastic Solutionsmentioning

confidence: 99%

“…Each stochastic increment is then decoupled into stochastic and deterministic spaces and approximated by the product of a random variable and a deterministic vector, which are calculated by solving the corresponding linear stochastic finite element equation using a weakly intrusive SFEM. 30,31 In this method, the deterministic vector is computed by solving deterministic linear finite element equations that are obtained by the stochastic Galerkin method, 11,12 and the corresponding random variable is solved by one-dimensional stochastic algebraic equations using a non-intrusive method. Furthermore, since all random sources are embedded into one-dimensional stochastic algebraic equations, the proposed method has low computational complexity and its computational cost is weakly dependent on the stochastic dimensionality.…”

Section: Introductionmentioning

confidence: 99%

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A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties

Zheng

Nackenhorst

2023

Numerical Meth Engineering

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This article presents an efficient nonlinear stochastic finite element method to solve stochastic elastoplastic problems. Similar to deterministic elastoplastic problems, we describe history‐dependent stochastic elastoplastic behavior utilizing a series of (pseudo) time steps and go further to solve the corresponding stochastic solutions. For each time step, the original stochastic elastoplastic problem is considered as a time‐independent nonlinear stochastic problem with initial values given by stochastic displacements, stochastic strains, and internal variables of the previous time step. To solve the stochastic solution at each time step, the corresponding nonlinear stochastic problem is transformed into a set of linearized stochastic finite element equations by means of finite element discretization and a stochastic Newton linearization, while the stochastic solution at each time step is approximated by a sum of the products of random variables and deterministic vectors. Each couple of the random variable and the deterministic vector is also used to approximate the stochastic solution of the corresponding linearized stochastic finite element equation that can be solved via a weakly intrusive method. In this method, the deterministic vector is computed by solving deterministic linear finite element equations, and corresponding random variables are solved by a non‐intrusive method. Further, the proposed method avoids the curse of dimensionality successfully since its computational effort does not increase dramatically as the stochastic dimensionality increases. Four numerical cases are used to demonstrate the good performance of the proposed method.

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Section: Approximation Of Stochastic Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties

Zheng

Nackenhorst

2023

Numerical Meth Engineering

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“…The model utilized the nanofluid joins the impacts of thermophoresis and Brownian motion. Zheng and Dai [15] examined a new stochastic finite element method (FEM) for computing structural stochastic responses to linear problems.…”

Section: Introductionmentioning

confidence: 99%

Hybrid surveying of radiation and magnetic impacts on Maxwell fluid with MWCNT nanotube influence of two wire loops

et al. 2022

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In this paper, the effects of Maxwell nanoliquid transmission with MWCNT nanotube are investigated over two circular wires with opposite currents and a stretching sheet. The innovation of this paper is the examination of MWCNT nanotube temperature and nanofluid velocity and also magnetic potential and magnetic effect in the three different places of two circular wires on the sheet. The finite element method is utilized for calculating differential equations. By increasing the distance from two wires on the stretching sheet, the amount of MWCNT nanotube temperature increased, and a large vortex forms at the bottom of the sheet. Overall, the MWCNT nanotube velocity around the two circular wires at the beginning of the sheet is 46.09% higher than the middle of the sheet and 20% higher than the end of the sheet, also the MWCNT nanotube magnetic potential around the two circular wires at the beginning of the sheet is 13.40% higher than the middle of the sheet and 23% higher than the end of the sheet. The second part of the essay relates to the using response surface methodology (RSM) method in the Design‐Expert software. Based on the results obtained from the MWCNT nanotube velocity graphs and the heat transfer cantors, and magnetism effects in the Design‐Expert software, the best optimization occurred for u = 0.07, T = 1.15, and H = 4.531.

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“…From a mathematical point of view, the stochastic finite element method can be considered a computational method for solving stochastic partial differential equations. In several studies, the problems of convergence and error estimation of this method have been studied in detail [1]- [6]. In fact, these two aspects of the stochastic finite element method are complementary and interdependent.…”

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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Structural stochastic responses determination via a sample-based stochastic finite element method

Cited by 23 publications

References 17 publications

A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties

A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties

Hybrid surveying of radiation and magnetic impacts on Maxwell fluid with MWCNT nanotube influence of two wire loops

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

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