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A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation

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)

  • Zhi-Hang Zhao

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

  • Shou-Zhen Li

    (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 well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.

Suggested Citation

  • Xue Li & Jun-Yi Sun & Zhi-Hang Zhao & Shou-Zhen Li & Xiao-Ting He, 2020. "A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation," Mathematics, MDPI, vol. 8(5), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:653-:d:350294
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    References listed on IDEAS

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    1. Ali Rehman & Zabidin Salleh & Taza Gul & Zafar Zaheer, 2019. "The Impact of Viscous Dissipation on the Thin Film Unsteady Flow of GO-EG/GO-W Nanofluids," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
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