Deformation and stability of a circular-arc arch compressed by a rigid plate: incorporating tension, shear, and bending

doi:10.1007/s10483-026-3330-9

摘要/Abstract

Abstract:

The contact deformation and buckling of elastic rods against rigid surfaces represent a prevalent phenomenon in applications such as oil drilling, arterial stents, and energy harvesting. This has attracted widespread attention from researchers. In this paper, the deformation and buckling behaviors of a circular arch subject to compression by a rigid plate are investigated with a planar elastic rod model that incorporates tension, shearing, and bending. In comparison with the existing models that solely consider the bending energy, the deflection curve, the internal force distribution, and the critical load of the present model show good agreement with the finite element results. Through the dimensional analysis and order-of-magnitude estimation, we examine the factors influencing the critical load. The study reveals that the semi-central angle of the arch has the most significant effect. The dimensionless geometric parameter describing arch slenderness becomes prominent when the semi-central angle is less than 30 $∘,$ while Poisson’s ratio and the cross-sectional shear correction factor exhibit negligible influence. Furthermore, the variation in the proportions of strain energy components during critical buckling is presented with respect to the semi-central angle and the geometric parameter, thereby delineating the applicable ranges of both the original model (OM) and the modified model (MM).

Key words: circular-arc arch, elastic rod, finite deformation, buckling, critical load

中图分类号:

O343.9

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(1): 19-38.

Yunkai TANG, Shengyi TANG, Kai LING, Donghui LIU, Huadong YONG, Youhe ZHOU. Deformation and stability of a circular-arc arch compressed by a rigid plate: incorporating tension, shear, and bending[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(1): 19-38.

图/表 13

Variable	$P s cr$	$E$	$R$	$b$
$M$	1	1	0	0
$L$	1	$− 1$	1	1
$T$	$− 2$	$− 2$	0	0

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