Prediction of probabilistic settlements via spectral stochastic meshless local Petrov–Galerkin method

Sheu, Guang-Yih

doi:10.1016/j.compgeo.2011.02.001

Cited by 12 publications

(14 citation statements)

References 8 publications

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“…Therefore, the time spent to create a finite element discretization or background cells for the numerical integration can be saved. Nonetheless, the SSMLPG results of two elastostatic problems approach more satisfactorily to the MCS results than the SSFEM results of the same problems do [5].…”

Section: Introductionmentioning

confidence: 93%

“…Similarly manipulating the published RBF interpolation formula [5], we can approximate u i (i = 1, 2) over Q for x I (I = 1 to N T ) by…”

Section: Discrete Equationsmentioning

confidence: 99%

“…To eliminate these deficiencies thereby improve the computational efficiency, a previous study [5] extended the meshless local Petrov-Galerkin (MLPG) method [6] to the SSMLPG method. Applying the SSMLPG method does not need a finite element discretization.…”

Section: Introductionmentioning

confidence: 99%

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Perturbation-Based Spectral Stochastic Meshless Local Petrov-Galerkin Method in Predicting Probabilistic Settlements

Sheu¹

2012

TOCSJ

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Abstract:In an attempt of solving stochastic boundary-value problems sufficiently accurately without creating a finite element discretization, a previous study (Comput. Geotech. 2011, vol. 38, No. 4, pp. 407-415) developed the spectral stochastic meshless local Petrov-Galerkin (SSMLPG) method. Some different approaches of deriving an SSMLPG formulation have been developed using various random field discretization methods. This study presents the SSMLPG formulation composed of perturbation expansions of random fields and a 2D meshfreee weak-strong (MWS) form in elasticity. A performance evaluation of this SSMLPG formulation is implemented through a stochastic elastostatic problem in which probabilistic settlements are predicted with the uncertainty in the spatial variability of Young`s modulus. The evaluation results demonstrate that SSMLPG-based predicted probabilistic settlements approach more close to the Monte Carlo simulation (MCS) results than spectral stochastic finite element-based predicted probabilistic settlements do. In addition, generating the SSMLPG results is time-saving than completing the MCS does. In conclusion, the SSMLPG method can be an efficient alternative tool to solve stochastic boundary-value problems.

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Section: Introductionmentioning

confidence: 93%

“…Similarly manipulating the published RBF interpolation formula [5], we can approximate u i (i = 1, 2) over Q for x I (I = 1 to N T ) by…”

Section: Discrete Equationsmentioning

confidence: 99%

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Perturbation-Based Spectral Stochastic Meshless Local Petrov-Galerkin Method in Predicting Probabilistic Settlements

Sheu¹

2012

TOCSJ

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“…Nevertheless, the performance of spectral stochastic finite element method is not always satisfactory. For example, the spectral stochastic finite element method predicts less accurate mean values or standard deviations of random fields than the spectral stochastic meshless local Petrov-Galerkin method does [6]. Similar experiences bring about the motive for improving the performance of spectral stochastic finite element method.…”

Section: Introductionmentioning

confidence: 97%

“…Since and f are dependent upon x, y, and , (10) is not ready for use. The generalized polynomial chaos expansion is chosen to estimate the distribution of and f. Similar manipulating the published study [6], generalized polynomial chaos expansions of and f are defined by n P n P   , P is the highest order of Ψ, and n is the total number of uncorrelated random variables.…”

Section: U Tmentioning

confidence: 99%

High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

Sheu¹

2013

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This study presents an experiment of improving the performance of spectral stochastic finite element method using high-order elements. This experiment is implemented through a two-dimensional spectral stochastic finite element formulation of an elliptic partial differential equation having stochastic coefficients. Deriving this spectral stochastic finite element formulation couples a two-dimensional deterministic finite element formulation of an elliptic partial differential equation with generalized polynomial chaos expansions of stochastic coefficients. Further inspection of the performance of resulting spectral stochastic finite element formulation with adopting linear and quadratic (9-node or 8-node) quadrilateral elements finds that more accurate standard deviations of unknowns are surprisingly predicted using quadratic quadrilateral elements, especially under high autocorrelation function values of stochastic coefficients. In addition, creating spectral stochastic finite element results using quadratic quadrilateral elements is not unacceptably time-consuming. Therefore, this study concludes that adopting high-order elements can be a lower-cost method to improve the performance of spectral stochastic finite element method.

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Shock-induced stochastic dynamic analysis of cylinders made of saturated porous materials using MLPG method: considering uncertainty in mechanical properties

2017

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Prediction of probabilistic settlements via spectral stochastic meshless local Petrov–Galerkin method

Cited by 12 publications

References 8 publications

Perturbation-Based Spectral Stochastic Meshless Local Petrov-Galerkin Method in Predicting Probabilistic Settlements

Perturbation-Based Spectral Stochastic Meshless Local Petrov-Galerkin Method in Predicting Probabilistic Settlements

High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

Shock-induced stochastic dynamic analysis of cylinders made of saturated porous materials using MLPG method: considering uncertainty in mechanical properties

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