DYNAMIC BUCKLING OF FIXED SHALLOW ARCHES UNDER STEP LOADING OF INFINITE DURATION

An energy approach is used to investigate the dynamic buckling of shallow fixed arches that are subjected to a step loading. The study is based on the principle of energy conservation and prior knowledge of the nonlinear static equilibrium paths and the static buckling of shallow fixed arches. For static buckling of a fixed arch, symmetric limit point buckling dominates because the bifurcation point for antisymmetric buckling is located on the unstable equilibrium region and so antisymmetric buckling cannot occur before occurrence of the limit point buckling although it is lower than the limit point buckling load. However, dynamic buckling may occur on the primary unstable equilibrium path at a load lower than the static limit point buckling load, or on the unstable equilibrium path after bifurcation buckling at a load lower than both the upper dynamic buckling and the static bifurcation buckling loads. The merit of the energy approach for dynamic buckling is that it allows the dynamic buckling load to be determined Without the need to solve the equations of motion.