Stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters

Minh, Duy; Gao, Wei; Song, Chongmin

doi:10.1016/j.cma.2015.11.032

Cited by 27 publications

(8 citation statements)

References 47 publications

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“…Thus, an adaptive step size λ(θ) calculated by (11) is introduced herein to adjust the iterative random vector V when (9) cannot be satisfied. And the new iterative random vector V k+1 new is calculated by (12).…”

Section: B the Proposed Ass-hra Methodsmentioning

confidence: 99%

“…The RBDO problems of engineering structures are usually described as either probabilistic or non-probabilistic models [9]- [11]. Specifically, uncertain parameters are usually described as random variables or random fields based on the theory of probability and statistics when the sample data of uncertain factors are abundant [12]- [14], and then the failure probability of an engineering structure can be precisely calculated based on reliability analysis [15], [16]. The probabilistic reliability analysis has two characteristics: 1) It depends on the probability density function (PDF) which relies on a large amount of statistical data; 2) It is very sensitive to the variations of the parameters' probabilistic distributions.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Reliability-Based Design Optimization of Complex Structures With Random and Interval Uncertainties Based on ASS-HRA

Cheng

Lü

et al. 2019

IEEE Access

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In this paper, an efficient hybrid reliability analysis (HRA) method and a hybrid reliability-based design optimization (HRBDO) approach are proposed for realistic complex engineering structures with random and interval uncertainties. First, the HRBDO model for complex engineering structures is constructed with its objective and performance functions described as the implicit functions of design variables and random and interval parameters. Then, an efficient HRA method based on adaptive step size (ASS-HRA) is put forward to calculate the minimum reliability of the structure's performance function under the influences of both random and interval uncertainties, the computational efficiency and accuracy of which are verified by a benchmark test. Subsequently, an efficient HRBDO approach integrating the proposed ASS-HRA method with the polynomial response surface model (PRSM) is developed for solving the HRBDO problems of complex engineering structures, the effectiveness of which is demonstrated by a numerical example. Finally, the HRBDO of a high-speed press slider demonstrates the efficiency, effectiveness, and versatility of the proposed HRBDO approach based on the ASS-HRA in the design of realistic complex engineering structures. INDEX TERMS Hybrid reliability analysis (HRA), adaptive step size (ASS), hybrid reliability-based design optimization (HRBDO), random and interval uncertainties, complex structure.

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Section: B the Proposed Ass-hra Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybrid Reliability-Based Design Optimization of Complex Structures With Random and Interval Uncertainties Based on ASS-HRA

Cheng

Lü

et al. 2019

IEEE Access

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“…Several types of stochastic slope stability analyses have been conducted by Griffiths et al [16], Lo and Leung [17] and Ji et al [18,19]. Do et al [20] considered random field for the Young's modulus and body force in the analysis of structures.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of stability against piping and sliding in diversion dams, considering four cutoff wall configurations

Hekmatzadeh

Zarei

Johari

et al. 2018

Computers and Geotechnics

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The stability against piping and sliding, which is subject to numerous sources of uncertainty, is of great importance in the design of diversion dams. In this study, the performance of four cutoff wall configurations, including a single wall and two walls with half the length of the single wall, was evaluated stochastically using the random finite element method. The Cholesky decomposition technique in conjunction with three types of Auto-Correlation Function (ACF) was employed to generate numerous random fields. The results indicate that the probabilities of failure related to different cutoff wall configurations are similar, considering isotropic hydraulic conductivity. However, there are noticeable differences between the probabilities of failure of these configurations in anisotropic situations. Moreover, the use of a single cutoff wall on the upstream face of an impervious blanket provides the lowest probability of failure for piping. In addition, the exponential ACF ends up with greater exit hydraulic gradients than the second-order Markov and binary noise ACFs. In addition, the sliding stability of the ordinary and earthquake load combinations was examined stochastically using random field theory and Monte Carlo Simulation (MCS). The probability of failure appears to increase with an increase in the autocorrelation distance.

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“…A systematic approach for evaluating the stochastic PDEs on random domain has been well established by Ghanem and Spanos , known as the spectral stochastic finite element method (SSFEM). Some studies based on the framework of SSFEM are listed in . This approach shows great benefits to solve stochastic problems under random‐field consideration .…”

Section: Introductionmentioning

confidence: 99%

The stochastic Galerkin scaled boundary finite element method on random domain

Minh

Gao

Saputra

et al. 2016

Numerical Meth Engineering

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Summary The research work extends the scaled boundary finite element method to non‐deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random‐field uncertainties. The aim is to blend the scaled boundary finite element method into the Galerkin spectral stochastic methods, which leads to a proficient procedure for handling the stress singularity problems and crack analysis. The Young's modulus of structures is considered to have random‐field uncertainty resulting in the stochastic behaviour of responses. Mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses (displacement, strain, and stress) and stress intensity factors of cracked structures. The feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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Stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters

Cited by 27 publications

References 47 publications

Hybrid Reliability-Based Design Optimization of Complex Structures With Random and Interval Uncertainties Based on ASS-HRA

Hybrid Reliability-Based Design Optimization of Complex Structures With Random and Interval Uncertainties Based on ASS-HRA

Reliability analysis of stability against piping and sliding in diversion dams, considering four cutoff wall configurations

The stochastic Galerkin scaled boundary finite element method on random domain

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