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

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  • Xiao-Ting He

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    State Key Laboratory of Safety and Resilience of Civil Engineering in Mountain Area, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area of Ministry of Education (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
    State Key Laboratory of Safety and Resilience of Civil Engineering in Mountain Area, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area of Ministry of Education (Chongqing University), Chongqing 400045, China)

  • Ying Guo

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    State Key Laboratory of Safety and Resilience of Civil Engineering in Mountain Area, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area of Ministry of Education (Chongqing University), Chongqing 400045, China)

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.

Suggested Citation

  • Xiao-Ting He & Jing-Miao Yin & Jun-Song Ran & Jun-Yi Sun & 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, MDPI, vol. 13(16), pages 1-40, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2626-:d:1725631
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