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

Xiao-Ting He, Jing-Miao Yin, Jun-Song Ran, Jun-Yi Sun and Ying Guo ()
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Xiao-Ting He: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jing-Miao Yin: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jun-Song Ran: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Jun-Yi Sun: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Ying Guo: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Mathematics, 2025, vol. 13, issue 16, 1-40

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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