AUTHOR=Zhang Zixiang , Wang Weile , Liu Yuanyuan , Pan Junjie , Xin Weijin 
  
TITLE=HDQ-based solution strategy for in-plane nonlinear buckling of shallow steel arches with linear elastic supports
  
JOURNAL=Frontiers in Physics
  
VOLUME=Volume 13 - 2025
  
YEAR=2025
  
URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1717268
  
DOI=10.3389/fphy.2025.1717268
  
ISSN=2296-424X
  
ABSTRACT=This paper investigates the in-plane nonlinear buckling of shallow steel arches with linear elastic supports. Differential equations of equilibrium are built considering a virtual work principle. To balance computational accuracy, efficiency, and cost, a harmonic differential quadrature method (HDQ)-based solution strategy combined with an iterative process is utilized to follow the complete buckling path. The corresponding critical buckling load is obtained. The convergence of HDQ algorithm is then examined, and the accuracy of presented solutions is validated by comparing the FE predictions. It was found that the nonlinear behavior of circular arches with linear elastic supports can be precisely predicted by the presented HDQ-based solution strategy. The arch could buckle either in a limit point mode or a bifurcation mode, depending on the modified slenderness ratio.