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
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,...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/3025 |
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| author | Fei-Yan Li Xue Li Qi Zhang Xiao-Ting He Jun-Yi Sun |
| author_facet | Fei-Yan Li Xue Li Qi Zhang Xiao-Ting He Jun-Yi Sun |
| author_sort | Fei-Yan Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T09:52:40Z |
| format | Article |
| id | doaj.art-36322abacb5b4f3db19ce3500c819721 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:52:40Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-36322abacb5b4f3db19ce3500c8197212023-12-01T23:58:14ZengMDPI AGMathematics2227-73902022-08-011016302510.3390/math10163025A 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 EquationFei-Yan Li0Xue Li1Qi Zhang2Xiao-Ting He3Jun-Yi Sun4School 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, ChinaSchool of Civil Engineering, Chongqing University, Chongqing 400045, ChinaEssential 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.https://www.mdpi.com/2227-7390/10/16/3025circular membraneslarge deflectionsplate/membrane contactpower series methodclosed-form solution |
| spellingShingle | Fei-Yan Li Xue Li Qi Zhang Xiao-Ting He Jun-Yi Sun 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 circular membranes large deflections plate/membrane contact power series method closed-form solution |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | circular membranes large deflections plate/membrane contact power series method closed-form solution |
| url | https://www.mdpi.com/2227-7390/10/16/3025 |
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