Snap-Through of Shallow Circular Arches with Variable Horizontal Supports under Unilateral Displacement Control

Abstract

This study proposes a numerical method to solve the snap-through problem of elastic shallow inextensible circular arches. Specifically, the snap-through behavior of arches subjected to a downward load at a point along the span was systematically evaluated for variable elastic horizontal supports under unilateral displacement control. Through theoretical analysis based on a dimensionless formulation, the critical state of snap-through can be determined by embedding ordinary differential equations into the nonlinear unconstrained optimization. Then, critical stiffness lines for horizontal springs and snap regions with varying loading position were systematically analyzed to judge whether a snap-through phenomenon will occur. Parametric analysis was further carried out to investigate the influence of variable horizontal spring stiffness and different arch length on the overall deformation and the critical displacement of critical states. The results show that the critical stiffness increases with the decrease of arch length and the decrease of horizontal stiffness and arch length can both expand the snap region. This study highlights the important role of stiffness of supports in snap-through behavior control and provides a numerical method for more accurate evaluation of the snap-through behavior of arches under various supports and loading conditions in engineering applications.