A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates

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

Mathematics, 2020, vol. 8, issue 6, 1-16

Abstract: In this paper, the static problem of equilibrium of contact between an axisymmetric deflected circular membrane and a frictionless rigid plate was analytically solved, where an initially flat circular membrane is fixed on its periphery and pressurized on one side by gas such that it comes into contact with a frictionless rigid plate, resulting in a restriction on the maximum deflection of the deflected circular membrane. The power series method was employed to solve the boundary value problem of the resulting nonlinear differential equation, and a closed-form solution of the problem addressed here was presented. The difference between the axisymmetric deformation caused by gas pressure loading and that caused by gravity loading was investigated. In order to compare the presented solution applying to gas pressure loading with the existing solution applying to gravity loading, a numerical example was conducted. The result of the conducted numerical example shows that the two solutions agree basically closely for membranes lightly loaded and diverge as the external loads intensify.

Keywords: circular membrane; gas pressure loading; deflection restriction; boundary value problem; closed-form solution (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/2227-7390/8/6/1017/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/6/1017/ (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:6:p:1017-:d:374583

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 ().