Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials

Xu, Yanming; Li, Haozhi; Chen, Leilei; Zhao, Juan; Zhang, Xin

doi:10.3390/math10111840

Cited by 15 publications

(7 citation statements)

References 42 publications

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“…Because of the complexity and non-linearity of geotechnical engineering problems, it is often difficult to directly compute the uncertainty and reliability of model outputs. Monte-Carlo-based probabilistic analysis is, therefore, widely used to evaluate the probability of failure or performance of geotechnical structures and systems under uncertain conditions (e.g., [12][13][14]). The Monte Carlo simulation is a computational technique that uses random sampling and probability distributions to simulate the potential outcomes of a complex system or process.…”

Section: Introductionmentioning

confidence: 99%

Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

Zhang

Cui

2023

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The number of random fields required to capture the spatial variability of soil properties and their impact on the performance of geotechnical systems is often varied. However, the number of random fields required to obtain higher-order statistical moments of model outputs has not yet been studied. This research aims to investigate the number of Monte Carlo simulations needed to achieve stationary higher-order statistics of a pore pressure head in an unsaturated soil slope under steady-state infiltration. The study recommends using at least 500 Monte Carlo samples for the probabilistic analysis of geotechnical engineering models. A more conservative choice for up to second-moment analysis is 1000 samples. The analysis reveals significant variations in skewness, which become stationary for all mesh grids when the number of samples exceeds 15,000. Kurtosis stabilizes only when the number of samples reaches 25,000. The pore pressure head in the unsaturated zone is less uncertain. Additionally, the probability density function of the pore pressure head follows a leptokurtic distribution.

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Section: Introductionmentioning

confidence: 99%

Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

Zhang

Cui

2023

Axioms

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“…Therefore, it is widely adopted in piezoelectric materials [20], dynamics [21], and acoustics [22][23][24]. However, the traditional MoM needs to solve huge matrix systems [25][26][27][28], which requires a large amount of calculation and memory [29]. Considering the limitations of the aforementioned methods in rapidly solving the RCS of arbitrary targets, the polynomial chaos expansion method with model universality is adopted.…”

Section: Introductionmentioning

confidence: 99%

The method of moments for electromagnetic scattering analysis accelerated by the polynomial chaos expansion in infinite domains

Yuan

Huang

et al. 2023

Front. Phys.

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An efficient method of moments (MoM) based on polynomial chaos expansion (PCE) is applied to quickly calculate the electromagnetic scattering problems. The triangle basic functions are used to discretize the surface integral equations. The polynomial chaos expansion is utilized to accelerate the MoM by constructing a surrogate model for univariate and bivariate analysis. The mathematical expressions of the surrogate model for the radar cross-section (RCS) are established by considering uncertain parameters such as bistatic angle, incident frequency, and dielectric constant. By using the example of a scattering cylinder with analytical solution, it is verified that the MoM accelerated by PCE presents a considerable advantage in computational expense and speed.

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“…By using IGABEM, geometric mistakes and time-consuming preprocessing steps may be avoided and numerical simulation can be carried out straight from the precise models. Since its inception, IGABEM has been used to address a variety of issues, including those related to elastic mechanics [27][28][29][30], potential issues [15], wave-resistance [31], fracture mechanics [32,33], electromagnetics [34][35][36][37][38][39], and structural optimization [40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

FEM/Wideband FMBEM coupling based on subdivision isogeometry for structural-acoustic design sensitivity analysis

Chen,

Huang,

Zhou

et al. 2023

Front. Phys.

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A computer simulation approach known as the isogeometric (IGA) method may directly use the surface information of geometric model. In 3D computer graphics, Loop subdivision surfaces are a common method for creating complicated shapes. In this study, we propose a coupling algorithm that utilizes Loop subdivision surfaces and a direct differentiation method for the computation of acoustic-fluid-structure interaction and the performance of structural-acoustic sensitivity analysis. This algorithm combines the finite element method (FEM) and wideband fast multipole boundary element method (FMBEM). Because of that the proposed method is of a great ability of integrating the numerical calculation and computer-aided modeling, the current technique can deliver results quickly and accurately. The numerical prediction of the effects of vibrating structures with arbitrary shape within sound field is made feasible by the FEM/Wideband FMBEM technique. Calculation examples are provided to show the applicability and effectiveness of the suggested method.

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Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials

Cited by 15 publications

References 42 publications

Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

Investigating the Number of Monte Carlo Simulations for Statistically Stationary Model Outputs

The method of moments for electromagnetic scattering analysis accelerated by the polynomial chaos expansion in infinite domains

FEM/Wideband FMBEM coupling based on subdivision isogeometry for structural-acoustic design sensitivity analysis

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