Behavior of variable length elastica with frictional support under follower force

The same problem as the one studied by Wang et al was presented, except that the support is not frictionless. The problem is solved using the principle of elastic similarity, where the deformed shape of the beam is compared to that of the standard compression rod. This approach was found to be simpler in solving the problem and can show the existence of other possible instability modes that are not shown in Wang's paper. Results of the analysis show that the friction at the sliding support increases the buckling load. It also makes the initial slopes of the buckling path positive, with changes into negative, compared to the frictionless cases, which are always negative.