Abstract
A comprehensive non-linear stability analysis has been performed on an one-degree-of freedom arch for establishing its dynamic (elastic) snap-through buckling strength under impact loading. Such a loading consists of a falling body striking centrally the joint mass of the arch in such a way that a completely plastic impact can be postulated. It has been found that the dynamic buckling load of such a kind of loading—associated with an unbounded motion—can be established by using a static stability analysis. More specifically, it has been shown that the dynamic buckling load corresponds unstable static equilibrium state where the total potential of the system is zero. Furthermore, it has been proved that the second variation of the total potential energy at the foregoing unstable equilibrium state is negative definite. This implies that the curves “loading versus displacement” resulting by vanishing the total potential has always a maximum on the above-mentioned unstable state. These findings have been verified by employing a non-linear dynamic analysis.
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