Buckling of parabolic shallow arches when support stiffens under compression

The in-plane stability of parabolic shallow arches whose rotational stiffness of supports increases when loaded is investigated. The nonlinear buckling analysis based on the virtual work formulation is carried out to obtain the critical load for both snap-through buckling and bifurcation buckling. It is found that the critical load increases with either the initial stiffness coefficient or the stiffening rate. The influence of the stiffening rate on critical loads decreases with an increase of the initial stiffness. The values of the modified arch slenderness that delineates different buckling modes increase with the stiffening rate.