An analytical model for calculating final plastic deformation of rectangular plates under impulsive loading based on membrane modal method

Abstract

This paper deduces an analytical model for calculating the final plastic deformation of rectangular plates under impulsive loading using the membrane modal method. Modal shape and acceleration are derived from field equations under simple membrane action, incorporating average strain rate effects via a post-corrected strategy. A new dimensionless damage number is introduced, and a formula for dimensionless final plastic deformation with strain rate consideration is established. Predicted deflections are compared with experimental data for steel square and rectangular plates, showing an average absolute error of approximately 9.3% between model solutions and experimental results meeting engineering calculation requirements. Additionally, a linear fitting empirical formula based on the dimensionless damage number is proposed, enabling determination of the critical loading impulse for membrane-dominated plastic deformation initiation in rectangular plates. Compared to Jones’s model, the present model demonstrates superior agreement with experimental data. This research provides valuable reference for studying and evaluating the dynamic plastic response of rectangular plates under impulsive loading.