Dynamic elastic‐plastic behaviour of a frame

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Abstract
The full time response of a space frame under impact loading perpendicular to the frame plane is discussed. Theoretical solutions and experimental results are presented and compared. A space frame clamped at its two ends is loaded by a 0.22 lead bullet that hits a mass in the middle of the transversal beam of the frame. The loading time is about 40 to 60 ?sec and the impact impulses in experiment from 0.5 to 1 Ns. The time response of this frame can be divided into four phases where different physical effects are dominant: (a) the ‘loading’ phase where elastic wave motion dominates the time response. Because of the high impact impulses, plastic deformation occurs in the vicinity of the mass and must be included in a theoretical model. The influence of reflections at the corners on the time response is shown; (b) the ‘evolution’ phase. Within this phase, a plastic collapse mechanism develops. Most of this phase is dominated by elastic deformation but local plastic deformations beside the mass are also present. Because many reflections at the corners and the clampings occur within this phase, a modal analysis method is used to predict time histories; (c) the ‘plastic’ phase with plastic zones at the clampings. This phase sets in after the bending wave reaches the clampings. It is characterized by plastic deformation near the clampings and elastic deformation of the other parts of the frame. We used a modal analysis including plastic ‘modes’ to get accurate results; (d) the ‘elastic vibration’ phase.