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Mathematics
Volume 13
Issue 16
10.3390/math13162626
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Elastic Contact Between a Transversely, Uniformly Loaded Circular Membrane and a Spring-Reset Rigid Flat Circular Plate: An Improved Closed-Form Solution

by
Xiao-Ting He
1,2,3,
Jing-Miao Yin
1,
Jun-Song Ran
1,
Jun-Yi Sun
1,2,3 and
Ying Guo
1,2,3,*
1
School of Civil Engineering, Chongqing University, Chongqing 400045, China
2
State Key Laboratory of Safety and Resilience of Civil Engineering in Mountain Area, Chongqing 400045, China
3
Key Laboratory of New Technology for Construction of Cities in Mountain Area of Ministry of Education (Chongqing University), Chongqing 400045, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(16), 2626; https://doi.org/10.3390/math13162626
Submission received: 12 July 2025 / Revised: 4 August 2025 / Accepted: 12 August 2025 / Published: 15 August 2025
(This article belongs to the Special Issue Mathematical Models in Mechanics and Engineering)
Versions Notes

Abstract

The closed-form solution of the problem regarding elastic contact between a transversely, uniformly loaded circular membrane and a spring-reset rigid flat circular plate has potential application value in sensor developments or bending-free shell designs, but it still needs to be further improved. In this paper, on the basis of existing studies, the plate/membrane elastic contact problem is reformulated by improving the system of differential equations governing the elastic behavior of a large deflection of a circular membrane. Specifically, the radial geometric equation used in the existing studies is improved by giving up the assumption of a small rotation angle for the membrane, and an improved closed-form solution to the plate/membrane elastic contact problem is presented. The convergence and validity of the improved closed-form solution are analyzed, and the difference between the closed-form solutions before and after improvement is graphically shown. In addition, the effect of changing some important geometric and physical parameters on the improved closed-form solution is investigated.
Keywords: circular membrane; rigid flat plate; transversely uniform loading; elastic contact problem; closed-form solution circular membrane; rigid flat plate; transversely uniform loading; elastic contact problem; closed-form solution

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MDPI and ACS Style

He, X.-T.; Yin, J.-M.; Ran, J.-S.; Sun, J.-Y.; Guo, Y. Elastic Contact Between a Transversely, Uniformly Loaded Circular Membrane and a Spring-Reset Rigid Flat Circular Plate: An Improved Closed-Form Solution. Mathematics 2025, 13, 2626. https://doi.org/10.3390/math13162626

AMA Style

He X-T, Yin J-M, Ran J-S, Sun J-Y, Guo Y. Elastic Contact Between a Transversely, Uniformly Loaded Circular Membrane and a Spring-Reset Rigid Flat Circular Plate: An Improved Closed-Form Solution. Mathematics. 2025; 13(16):2626. https://doi.org/10.3390/math13162626

Chicago/Turabian Style

He, Xiao-Ting, Jing-Miao Yin, Jun-Song Ran, Jun-Yi Sun, and Ying Guo. 2025. "Elastic Contact Between a Transversely, Uniformly Loaded Circular Membrane and a Spring-Reset Rigid Flat Circular Plate: An Improved Closed-Form Solution" Mathematics 13, no. 16: 2626. https://doi.org/10.3390/math13162626

APA Style

He, X.-T., Yin, J.-M., Ran, J.-S., Sun, J.-Y., & Guo, Y. (2025). Elastic Contact Between a Transversely, Uniformly Loaded Circular Membrane and a Spring-Reset Rigid Flat Circular Plate: An Improved Closed-Form Solution. Mathematics, 13(16), 2626. https://doi.org/10.3390/math13162626

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