A stochastic B-spline wavelet on the interval finite element method for beams

Vadlamani, Shashank; Arun, C. O.

doi:10.1016/j.compstruc.2020.106246

Cited by 17 publications

(6 citation statements)

References 42 publications

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“…The construction of B-spline basic functions is determined by the recursive Cox-de Boer formulas [16][17][18][19][20][21]:…”

Section: Some Aspects Of the Construction Of Normalized Basis Functions Of The B-splinementioning

confidence: 99%

Localization of Solution of the Problem for Poisson’s Equation With the Use of B-Spline Discrete-Continual Finite Element Method

Mozgaleva¹,

Akimov²

2021

IJCCSE

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Localization of solution of the problem for Poisson’s equation with the use of B-spline discrete-continual finiteelement method (specificversion of wavelet-based discrete-continual finiteelement method) is under consideration in the distinctive paper. The original operational continual and discrete-continual formulations of the problem are given, some actual aspects of construction of normalized basis functions of a B-spline are considered, the corresponding local constructions for an arbitrary discrete-continual finiteelement are described, some information about the numerical implementation and an example of analysis are presented.

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“…The construction of B-spline basic functions is determined by the recursive Cox-de Boer formulas [16][17][18][19][20][21]:…”

Section: Some Aspects Of the Construction Of Normalized Basis Functions Of The B-splinementioning

confidence: 99%

Localization of Solution of the Problem for Poisson’s Equation With the Use of B-Spline Discrete-Continual Finite Element Method

Mozgaleva¹,

Akimov²

2021

IJCCSE

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“…The finite element method (FEM) [2][3][4][5] is widely used in numerical analysis. However, when faced with problems involving large deformations and high-speed impacts, the grids may deform, leading to non-convergence.…”

Section: Introductionmentioning

confidence: 99%

Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics

Zhou,

Li,

Zhuang

et al. 2024

Mathematics

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This study proposes an innovative meshless approach that merges the peridynamic differential operator (PDDO) with the generalized finite difference method (GFDM). Based on the PDDO theory, this method introduces a new nonlocal differential operator that aims to reduce the pre-assumption required for the PDDO method and simplify the calculation process. By discretizing through the particle approximation method, this technique proficiently preserves the PDDO’s nonlocal features, enhancing the numerical simulation’s flexibility and usability. Through the numerical simulation of classical elastic static problems, this article focuses on the evaluation of the calculation accuracy, calculation efficiency, robustness, and convergence of the method. This method is significantly stronger than the finite element method in many performance indicators. In fact, this study demonstrates the practicability and superiority of the proposed method in the field of elastic statics and provides a new approach to more complex problems.

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“…In 2020, Shashank Vadlamani proposed the stochastic beam element formulation. The results obtained by the perturbation method were compared with those obtained by the MCS [20]. In 2020, Bing Wang analyzed the uncertainty and reliability of thermomechanical problems through MCS.…”

Section: Introductionmentioning

confidence: 99%

Structural Uncertainty Analysis of High-Temperature Strain Gauge Based on Monte Carlo Stochastic Finite Element Method

Zhao,

Zhang,

et al. 2023

Sensors

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The high-temperature strain gauge is a sensor for strain measurement in high-temperature environments. The measurement results often have a certain divergence, so the uncertainty of the high-temperature strain gauge system is analyzed theoretically. Firstly, in the conducted research, a deterministic finite element analysis of the temperature field of the strain gauge is carried out using MATLAB software. Then, the primary sub-model method is used to model the system; an equivalent thermal load and force are loaded onto the model. The thermal response of the grid wire is calculated by the finite element method (FEM). Thermal–mechanical coupling analysis is carried out by ANSYS, and the MATLAB program is verified. Finally, the stochastic finite element method (SFEM) combined with the Monte Carlo method (MCM) is used to analyze the effects of the physical parameters, geometric parameters, and load uncertainties on the thermal response of the grid wire. The results show that the difference of temperature and strain calculated by ANSYS and MATLAB is 1.34% and 0.64%, respectively. The calculation program is accurate and effective. The primary sub-model method is suitable for the finite element modeling of strain gauge systems, and the number of elements is reduced effectively. The stochastic uncertainty analysis of the thermal response on the grid wire of a high-temperature strain gauge provides a theoretical basis for the dispersion of the measurement results of the strain gauge.

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A stochastic B-spline wavelet on the interval finite element method for beams

Cited by 17 publications

References 42 publications

Localization of Solution of the Problem for Poisson’s Equation With the Use of B-Spline Discrete-Continual Finite Element Method

Localization of Solution of the Problem for Poisson’s Equation With the Use of B-Spline Discrete-Continual Finite Element Method

Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics

Structural Uncertainty Analysis of High-Temperature Strain Gauge Based on Monte Carlo Stochastic Finite Element Method

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