On dimensionless numbers for the dynamic plastic response of quadrangular mild steel plates subjected to localized and uniform impulsive loading

Abstract

This paper studies the dynamic plastic response of thin quadrangular mild steel plates subjected to uniform and localized impulsive loading. For this, two new dimensionless numbers based on dimensionless governing equation of plates have been suggested. Four different effective parameters such as plate geometry, inertia of applied load, mechanical properties of material and strain rate sensitivity have been considered in suggested dimensionless numbers. The unknown coefficients of these numbers have been calculated by using singular value decomposition method. In order to illustrate the ability of empirical constitutive equations for predicting the maximum deflection, these equations are compared with different sets of experimental results that have been performed by various researchers. The comparison between the results of present empirical equations and the other theoretical and experimental ones shows that these models are more accurate than the other ones and are suitable to use for predicting the maximum deflection of all quadrangular mild steel plates subjected to uniform and localized loading.

Experimental and theoretical study on large ductile transverse deformations of rectangular plates subjected to shock load due to gas mixture detonation

“…According to experimental section, the thickness of steel specimens varied from 1 to 3 mm. In recent publications, Babaei and his co‐authors found an accurate and usable relationship for material parameter q as a function of plate thickness based on Jones' experiments . The results have shown that q approximately varies from 7.8 to 6.1 when the thickness of the steel plate is changed from 1 to 3 mm respectively.…”

“…However, in 1993, by assuming a rigid–perfectly plastic behaviour for the material and neglecting the strain rate effects, an upper bound solution and a lower bound solution were reported for quadrangular plates due to impulsive loading based on the dynamic equilibrium equations of plate and energy conservation. Later on in 2016, on the basis of dimensional analysis and a singular value decomposition method, two new dimensionless formulas were suggested by Babaei and his co‐workers in order to predict central deflection of circular and quadrangular plates due to a different distribution of impulsive loads. The analytical or theoretical models proposed in the literature are presented in Table in an attempt to compare the experimental results of this study to the theoretical ones.…”

“…It is noteworthy to mention that the material coefficients ( q and D ) in Equation 5 and 6 were considered as functions of plate thickness according to Jones' experiments and investigations. More details and further information on the theoretical or empirical procedure have been reported in the literature …”

An analytical model for predicting permanent plastic deflection and strain distributions in aluminium-alloy plates under low velocity impact loading

“…Substituting Equation (19) into Equation (18) Equation (20) is the one-dimensional Tresca yield criterion (i.e. the maximum principal stress yield criterion).…”

“…Several analytical approaches/models have been proposed to predict the response and permanent plastic deflection of the metallic plate under low velocity impact loading by means of strain energy approach and non-linear strain-hardening behaviour depicted by the exponential Cowper-Symonds function [6][7][8][9]15,[18][19][20][21] , or the Johnson-Cook model [10] . FE analysis [11][12][13] is also important for understanding the impact characteristics and permanent plastic deformation mechanism of metallic plates.…”