Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13162626

Authors: Xiao-Ting He, Jing-Miao Yin, Jun-Song Ran, Jun-Yi Sun, Ying Guo

Institution: Chongqing University

Language: English

Topic: Contact Mechanics and Variational Inequalities

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China