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

Xue Li, Jun-Yi Sun, Zhi-Hang Zhao, Shou-Zhen Li and Xiao-Ting He
Additional contact information
Xue Li: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jun-Yi Sun: School of Civil Engineering, Chongqing University, 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

Mathematics, 2020, vol. 8, issue 5, 1-19

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.

Keywords: circular membrane; axisymmetric deformation; large deflection; equilibrium equation; power series method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/5/653/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/5/653/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:5:p:653-:d:350294

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().