The paper is concerned with the dynamic response of impulsively loaded rigid-perfectly plastic structures. By combining the mode approximation technique with the upper and the lower bound theorems, we have derived a set of sequential inequalities on the final displacement of the structure. This can be applied to give a reasonable explanation for the criterion of choosing an optimal mode proposed by Symonds (1980). In addition, an approximate expression of the final displacement of the structure is suggested in cases where the “mode approximation” apparently works poorly. Finally, the suggested expression is also illustrated by examples.

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