A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates
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 conta...
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MDPI AG
2020-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/6/1017 |
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| author | Dong Mei Jun-Yi Sun Zhi-Hang Zhao Xiao-Ting He |
| author_facet | Dong Mei Jun-Yi Sun Zhi-Hang Zhao Xiao-Ting He |
| author_sort | Dong Mei |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T18:58:47Z |
| format | Article |
| id | doaj.art-eb9141a11c4a46a089b7faaa2d230460 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:58:47Z |
| publishDate | 2020-06-01 |
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| series | Mathematics |
| spelling | doaj.art-eb9141a11c4a46a089b7faaa2d2304602023-11-20T04:33:44ZengMDPI AGMathematics2227-73902020-06-0186101710.3390/math8061017A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid PlatesDong Mei0Jun-Yi Sun1Zhi-Hang Zhao2Xiao-Ting He3School of Civil Engineering, Chongqing University, Chongqing 400045, ChinaSchool of Civil Engineering, Chongqing University, Chongqing 400045, ChinaSchool of Civil Engineering, Chongqing University, Chongqing 400045, ChinaSchool of Civil Engineering, Chongqing University, Chongqing 400045, ChinaIn 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.https://www.mdpi.com/2227-7390/8/6/1017circular membranegas pressure loadingdeflection restrictionboundary value problemclosed-form solution |
| spellingShingle | Dong Mei Jun-Yi Sun Zhi-Hang Zhao Xiao-Ting He A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates Mathematics circular membrane gas pressure loading deflection restriction boundary value problem closed-form solution |
| title | A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates |
| title_full | A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates |
| title_fullStr | A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates |
| title_full_unstemmed | A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates |
| title_short | A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates |
| title_sort | closed form solution for the boundary value problem of gas pressurized circular membranes in contact with frictionless rigid plates |
| topic | circular membrane gas pressure loading deflection restriction boundary value problem closed-form solution |
| url | https://www.mdpi.com/2227-7390/8/6/1017 |
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