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Improved Power Series Solution of Transversely Loaded Hollow Annular Membranes: Simultaneous Modification of Out-of-Plane Equilibrium Equation and Radial Geometric Equation

Author

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  • Xiao-Ting He

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

  • Fei-Yan 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, Ministry of Education (Chongqing University), Chongqing 400045, China)

Abstract

The ability to accurately predict the shape of a transversely loaded hollow annular membrane is essential to the design of bending-free hollow annular shells of revolution, which requires a further improvement in the hollow annular membrane solution to meet the needs of this accurate prediction. In this paper, the large deflection problem of a transversely loaded hollow annular membrane is reformulated by simultaneously modifying the out-of-plane equilibrium equation and radial geometric equation, and a newer and more refined power series solution is derived. The reason why the classical radial geometry equation induces errors is revealed. The convergence and asymptotic behavior of the power series solution obtained is analyzed numerically. The newly derived solution is compared with the two previously derived solutions graphically, showing that the newly derived solution performs basically as well as expected. In addition, the anticipated use of the hollow and not-hollow annular membrane solutions for the design application of bending-free annular shells of revolution is discussed.

Suggested Citation

  • Xiao-Ting He & Fei-Yan Li & Jun-Yi Sun, 2023. "Improved Power Series Solution of Transversely Loaded Hollow Annular Membranes: Simultaneous Modification of Out-of-Plane Equilibrium Equation and Radial Geometric Equation," Mathematics, MDPI, vol. 11(18), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3836-:d:1234899
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    References listed on IDEAS

    as
    1. Qi Zhang & Xue Li & Xiao-Ting He & Jun-Yi Sun, 2022. "Revisiting the Boundary Value Problem for Uniformly Transversely Loaded Hollow Annular Membrane Structures: Improvement of the Out-of-Plane Equilibrium Equation," Mathematics, MDPI, vol. 10(8), pages 1-25, April.
    2. 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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