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Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations

Author

Listed:
  • Xue Li

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Jun-Yi Sun

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, Chongqing 400045, China)

  • Xiao-Chen Lu

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Zhi-Xin Yang

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Xiao-Ting He

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, Chongqing 400045, China)

Abstract

In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.

Suggested Citation

  • Xue Li & Jun-Yi Sun & Xiao-Chen Lu & Zhi-Xin Yang & Xiao-Ting He, 2021. "Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations," Mathematics, MDPI, vol. 9(10), pages 1-24, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1105-:d:553921
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    References listed on IDEAS

    as
    1. Yong-Sheng Lian & Jun-Yi Sun & Zhi-Hang Zhao & Xiao-Ting He & Zhou-Lian Zheng, 2020. "A Revisit of the Boundary Value Problem for Föppl–Hencky Membranes: Improvement of Geometric Equations," Mathematics, MDPI, vol. 8(4), pages 1-15, April.
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    Cited by:

    1. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.
    2. Jun-Yi Sun & Ning Li & Xiao-Ting He, 2023. "An Improved Mathematical Theory for Designing Membrane Deflection-Based Rain Gauges," Mathematics, MDPI, vol. 11(16), pages 1-32, August.

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