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

Fei-Yan Li, Xue Li, Qi Zhang, Xiao-Ting He and Jun-Yi Sun ()
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Fei-Yan Li: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Xue Li: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Qi Zhang: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Xiao-Ting He: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jun-Yi Sun: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Mathematics, 2022, vol. 10, issue 16, 1-32

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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