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A Stochastic Galerkin Cell-based Smoothed Finite Element Method (SGCS-FEM)
Tittu Varghese Mathew, Lars Beex, Stéphane PA Bordas,
Published in World Scientific Publishing Co. Pte Ltd
2019
Abstract
In this paper, the cell-based smoothed finite element method is extended to solve stochastic partial differential equations with uncertain input parameters. The spatial field of Young's Modulus and the corresponding stochastic results are represented by Karhunen-Loéve expansion and polynomial chaos expansion, respectively. Young's Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of the static displacements and the free vibration frequencies. The feasibility and the effectiveness of the proposed SGCS-FEM method in terms of accuracy and lower demand on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework yields accurate results. © 2019 World Scientific Publishing Company.
About the journal
JournalInternational Journal of Computational Methods
PublisherWorld Scientific Publishing Co. Pte Ltd
ISSN02198762
Open AccessYes
Concepts (14)
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    Elastic moduli
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    Galerkin methods
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    Numerical methods
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    Stochastic systems
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    Uncertainty analysis
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    Cell-based
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    Free vibration
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    Mathematical expressions
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    Polynomial chaos expansion
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    RANDOM MATERIALS
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    SMOOTHED FINITE ELEMENT METHOD
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    STATISTICAL CHARACTERISTICS
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    Stochastic partial differential equation
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    Finite element method