Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading
The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane bef...
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MDPI AG
2021-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/11/1238 |
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| author | Bin-Bin Shi Jun-Yi Sun Ting-Kai Huang Xiao-Ting He |
| author_facet | Bin-Bin Shi Jun-Yi Sun Ting-Kai Huang Xiao-Ting He |
| author_sort | Bin-Bin Shi |
| collection | DOAJ |
| description | The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence. |
| first_indexed | 2024-03-10T10:57:04Z |
| format | Article |
| id | doaj.art-ef10cfc42dc54163bb280b9791338365 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:57:04Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-ef10cfc42dc54163bb280b97913383652023-11-21T21:48:39ZengMDPI AGMathematics2227-73902021-05-01911123810.3390/math9111238Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure LoadingBin-Bin Shi0Jun-Yi Sun1Ting-Kai Huang2Xiao-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, ChinaThe large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.https://www.mdpi.com/2227-7390/9/11/1238circular membraneinitial stressgas pressure loadinglarge deflectionclosed-form solution |
| spellingShingle | Bin-Bin Shi Jun-Yi Sun Ting-Kai Huang Xiao-Ting He Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading Mathematics circular membrane initial stress gas pressure loading large deflection closed-form solution |
| title | Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading |
| title_full | Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading |
| title_fullStr | Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading |
| title_full_unstemmed | Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading |
| title_short | Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading |
| title_sort | closed form solution for circular membranes under in plane radial stretching or compressing and out of plane gas pressure loading |
| topic | circular membrane initial stress gas pressure loading large deflection closed-form solution |
| url | https://www.mdpi.com/2227-7390/9/11/1238 |
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