Bifurcation and hysteresis analysis of the non-degenerate Euler beam problem

In this work, the bifurcation and hysteresis phenomena of the Euler beam problem are focused on from the singularity theory viewpoint. Confirming the continuity of the problem is a necessary condition for performing a bifurcation and hysteresis analysis. A bifurcation problem is transformed from an infinite dimension to a finite dimension by applying the Lyapunov equations. A suitable central force minimizes our considered model and makes the problem stable. Moreover, we perform numerical investigations and interpret the results obtained from the bifurcation and hysteresis analysis geometrically with suitable values of the new unfolding parameters and with different lengths.