On the adequacy of energy criteria for dynamic buckling of arches.

T dynamic conditions under which thin shell structures will become unstable and exhibit large changes in response for small changes of loading are of particular interest in blast loading situations. If a pressure load is applied for a very short time, as a pulse, the structure may be able to withstand levels far higher than the static buckling condition. One possible line of attack to the analytical prediction of such dynamic instability levels deals only with the energy of the system. If the deflection shape is assumed a priori, the internal elastic strain energy can be found as a function of the shape amplitudes. If the loading is very brief and intense, it may be postulated that the response will depend only on the amount of impulse imparted to the structure and not on the exact shape of the loading pulse. Then the load may be identical to an initial velocity distribution that gives directly an initial kinetic energy imparted to the structure. The maximum strain energy achievable in the system will be just equal to this input energy (assuming no dissipation). A relative maximum in the strain energy as a function of deflection shape amplitude will correspond to a state of unstable equilibrium and can be used to define a dynamic buckling criterion. A small increase in input energy beyond that needed to reach the unstable equilibrium point will produce a large increase in response. This was done for lowestmode symmetrical buckling by Humphreys and Bodner