Dynamic instability of cylindrical elasto-plastic shell under combined static load and dynamic short pulse

Many thin walled structures like shells can be subjected to dangerous loading, as example: a dead loads qo and a short-time dynamic pulse, namely a load q, applied dynamically in the axial direction, during an interval of time [0, τ]; we shall summarize this action with the notation (qτ). The following conditions must be satisfied: qo << q and q > qe, where qe is the maximum value of the static load at which the shell loses its stability. When we apply dynamic pulse the shell does not react immediately as shown by experiments, thus process of buckling has a delay in comparison with the static case. This case of a 'delay' causes the change of the load under which the same buckling of the middle shell surface takes place in comparison with the Euler static load q. As we will see further, for shells the critical dynamic load can surpass the maximum static load qe. The problem arising here is: s it possible to predict theoretically the critical values of the amplitude q of the pulse together with the value of the static load qo such that the shell can go back to the initial undeformed configuration, making oscillations around it? Is it possible to find the curve (q, qo) dividing the zones of stability and instability of the shell? The method used follows Pogorelov's investigations, but will be extended to the problem of dynamic shell stability