A finite element study on bifurcation and limit point buckling of elastic-plastic arches

Abstract

The technique of continuum finite element modeling is used to discretize elastic-plastic circular arches which show nonlinear deformation behavior under external load. Response history curves for different arch models which have the same range angle and thickness, but different radii are updated by using the incremental/iterative procedure. In the incremental/iterative procedure, an accelerated modified Newton-Raphson scheme is used to obtain converged finite element solutions. The response history curves change depending on the radii. There are three types of response history curves, one of which has no buckling. The second one has limit point buckling, but does not have bifurcation buckling. The third one has both limit point buckling and bifurcation buckling. For the third type, the limit point buckling may appear before or after the bifurcation buckling, following the increase of the lateral displacement of the central point. The ratios of bifurcation buckling load to limit point buckling load, and bifurcation buckling displacement to limit point buckling displacement are obtained. They are plotted for different arch models with different radii.