Closed-form analytical analysis on the effect of coupled membrane and bending strains on the dynamic plastic behaviour of fully clamped thin quadrangular plates due to uniform and localized impulsive loading

Abstract

The problem of studying plastic response of structures loaded dynamically has been extensively investigated over many years. A survey of literature on dynamic plastic behaviour of plates subjected to impulsive loading reveals that most analytical studies on fully clamped thin quadrangular plates consider bending moments and membrane forces separately and the coupled yielding analysis is ignored. Therefore, this paper investigates large plastic deformation of thin quadrangular plates due to both uniform and localized loading when the coupled interaction between membrane and bending strains has been incorporated into the closed-form analytical analysis. The present closed-form analytical analysis is developed by pursuing the energy approach based on upper bound solution in which the Cowper-Symonds constitutive equation is employed to take into account strain-rate effects. The material coefficients in Cowper-Symonds equation have been considered as functions of plate thickness based on Jones' experiments on steel materials. The analytical predictions are compared with different set of experiments in terms of maximum permanent transverse deflections, in addition to Jones' theoretical model and our previous analytical model. It is found that incorporating the coupled yielding into the analysis leads to reduce the error value in predicting the maximum permanent transverse deflections.