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

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  • Yanming Xu

    (School of Architecture and Civil Engineering, Huanghuai University, Zhumadian 463000, China)

  • Haozhi Li

    (College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang 464000, China)

  • Leilei Chen

    (School of Architecture and Civil Engineering, Huanghuai University, Zhumadian 463000, China
    College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang 464000, China
    Henan International Joint Laboratory of Structural Mechanics and Computational Simulation, Huanghuai University, Zhumadian 463000, China)

  • Juan Zhao

    (College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang 464000, China)

  • Xin Zhang

    (School of Architecture and Civil Engineering, Huanghuai University, Zhumadian 463000, China)

Abstract

In this study, a Monte Carlo simulation (MCs)-based isogeometric stochastic Finite Element Method (FEM) is proposed for uncertainty quantification in the vibration analysis of piezoelectric materials. In this method, deterministic solutions (natural frequencies) of the coupled eigenvalue problem are obtained via isogeometric analysis (IGA). Moreover, MCs is employed to solve various uncertainty parameters, including separate elastic and piezoelectric constants and their combined cases.

Suggested Citation

  • Yanming Xu & Haozhi Li & Leilei Chen & Juan Zhao & Xin Zhang, 2022. "Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1840-:d:825445
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    References listed on IDEAS

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    1. Pedro González-Rodelas & Miguel Pasadas & Abdelouahed Kouibia & Basim Mustafa, 2022. "Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions," Mathematics, MDPI, vol. 10(2), pages 1-15, January.
    2. Nguyen, Vinh Phu & Anitescu, Cosmin & Bordas, Stéphane P.A. & Rabczuk, Timon, 2015. "Isogeometric analysis: An overview and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 89-116.
    3. Liang Wang & Chunguang Xiong & Xinpeng Yuan & Huibin Wu, 2021. "Discontinuous Galerkin Isogeometric Analysis of Convection Problem on Surface," Mathematics, MDPI, vol. 9(5), pages 1-12, February.
    4. Dariush Khezrimotlagh & Yao Chen, 2018. "The Optimization Approach," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 107-134, Springer.
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    Cited by:

    1. Baorang Cui & Jingxiu Zhang & Yong Ma, 2023. "Adaptive Load Incremental Step in Large Increment Method for Elastoplastic Problems," Mathematics, MDPI, vol. 11(3), pages 1-14, January.

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