For a dynamically loaded system made of stable materials, it is found that a dynamically admissible solution, one that satisfies all but the initial conditions, is a definitely convergent solution in time, with geometry changes and discontinuities taken into account. A new and simpler definition for weak and strong discontinuities is proposed. Solutions using simple mode approximations or the more general time-dependent changing mode approximations are described. For rigid, perfectly plastic beams under impulsive loadings, the latter method indeed gives better results, as there are more parameters available to optimize the initial difference energy.

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