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

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## Abstract

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## 1. Introduction

## 2. Membrane Equation and Its Solution

## 3. Results and Discussion

## 4. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 3.**Variations of w with r calculated by the solution presented in [25] for q = 0.0554 MPa (the dash-dotted line) and by the solution presented here for q = 0.0556 MPa and g = 2.5 mm (the solid line).

**Figure 4.**Variations of w with r for the gap g = 0.5 mm and the contact radius b = 4 mm corresponding to q = 0.001327 MPa and 0.001322 MPa calculated by the solutions presented in [28] (the dash-dotted lines) and presented here (the solid lines), and for g = 2.5 mm and b = 4 mm corresponding to q = 0.1654 MPa and 0.1576 MPa calculated by the solutions presented in [28] (the dash-dotted lines) and presented here (the solid lines).

**Figure 5.**Variations of ${\sigma}_{r}$ with r for the gap g = 0.5 mm and the contact radius b = 4 mm corresponding to q = 0.001327 MPa and 0.001322 MPa calculated by the solutions presented in [28] (the dash-dotted lines) and presented here (the solid lines), and for g = 2.5 mm and b = 4 mm corresponding to q = 0.1654 MPa and 0.1576 MPa calculated by the solutions presented in [28] (the dash-dotted lines) and presented here (the solid lines).

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**MDPI and ACS Style**

Mei, D.; Sun, J.-Y.; Zhao, Z.-H.; He, X.-T. A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates. *Mathematics* **2020**, *8*, 1017.
https://doi.org/10.3390/math8061017

**AMA Style**

Mei D, Sun J-Y, Zhao Z-H, He X-T. A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates. *Mathematics*. 2020; 8(6):1017.
https://doi.org/10.3390/math8061017

**Chicago/Turabian Style**

Mei, Dong, Jun-Yi Sun, Zhi-Hang Zhao, and Xiao-Ting He. 2020. "A Closed-Form Solution for the Boundary Value Problem of Gas Pressurized Circular Membranes in Contact with Frictionless Rigid Plates" *Mathematics* 8, no. 6: 1017.
https://doi.org/10.3390/math8061017