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A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

Author

Listed:
  • Fei-Yan Li

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

  • Xue Li

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

  • Qi Zhang

    (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)

  • 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)

Abstract

Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate.

Suggested Citation

  • Fei-Yan Li & Xue Li & Qi Zhang & Xiao-Ting He & Jun-Yi Sun, 2022. "A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equat," Mathematics, MDPI, vol. 10(16), pages 1-32, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3025-:d:894807
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    References listed on IDEAS

    as
    1. Teng-fei Wang & Xiao-ting He & Yang-hui Li, 2018. "Closed-Form Solution of a Peripherally Fixed Circular Membrane under Uniformly Distributed Transverse Loads and Deflection Restrictions," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, May.
    2. Xiao-Ting He & Xue Li & Bin-Bin Shi & Jun-Yi Sun, 2021. "A Closed-Form Solution without Small-Rotation-Angle Assumption for Circular Membranes under Gas Pressure Loading," Mathematics, MDPI, vol. 9(18), pages 1-29, September.
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