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Volume 10
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Article

A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

by
Fei-Yan Li
1,
Xue Li
1,
Qi Zhang
1,
Xiao-Ting He
1,2 and
Jun-Yi Sun
1,2,*
1
School of Civil Engineering, Chongqing University, Chongqing 400045, China
2
Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(16), 3025; https://doi.org/10.3390/math10163025
Submission received: 24 July 2022 / Revised: 15 August 2022 / Accepted: 18 August 2022 / Published: 22 August 2022
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)
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Abstract

Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate.
Keywords: circular membranes; large deflections; plate/membrane contact; power series method; closed-form solution circular membranes; large deflections; plate/membrane contact; power series method; closed-form solution

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MDPI and ACS Style

Li, F.-Y.; Li, X.; Zhang, Q.; He, X.-T.; Sun, J.-Y. A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation. Mathematics 2022, 10, 3025. https://doi.org/10.3390/math10163025

AMA Style

Li F-Y, Li X, Zhang Q, He X-T, Sun J-Y. A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation. Mathematics. 2022; 10(16):3025. https://doi.org/10.3390/math10163025

Chicago/Turabian Style

Li, Fei-Yan, Xue Li, Qi Zhang, Xiao-Ting He, and Jun-Yi Sun. 2022. "A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation" Mathematics 10, no. 16: 3025. https://doi.org/10.3390/math10163025

APA Style

Li, F.-Y., Li, X., Zhang, Q., He, X.-T., & Sun, J.-Y. (2022). A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation. Mathematics, 10(16), 3025. https://doi.org/10.3390/math10163025

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