Analytical study of plastic deformation of clamped circular plates subjected to impulsive loading

Abstract

This paper presents an analytical method for determining deflection of fully clamped thin circular plates. The plates are made from a rigid perfectly plastic material and subjected to a transverse localized and uniform blast loading. The essence of the model is to describe the deformation profile with the aid of a zero-order Bessel function and to perform energy analysis. This provides a method for predicting the plastic deformation of circular plates under impulsive loading. It can be also regarded as an attempt to use the energy method for different impulsive loading conditions. Calculations of the cases indicate that the proposed analytical models are based on reasonable assumptions. The solutions obtained are in very good agreement with different sets of experimental results.A list of symbols can be found on page 320.

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

“…Babaei and Darvizeh [15] also proposed an analytical model to predict the plastic deformation of clamped circular plates under impulsive loading. Two explosive conditions (i.e.…”

“…Thus, the radial displacement and the rebound deformation are ignored, and the impact responses are approximated to only the radial tensile, and radial and circumferential flexure deformations. In reality, a number of analytical or empirical models [3,9,10,14,15,[18][19][20][21] also neglected the radial displacement in order to simplify these models; despite this, the predicted results using the aforementioned models correlated well with experiments. Thus, the same simplification is adopted in this work to craft a simplified method for preliminary design purposes.…”

“…Like the other mathematical models (e.g., the zero-order Bessel function of the first kind [15] , etc.) for depicting the deflection profile of a circular plate, Equations (1) to (9) seek to craft the deformation profile of the impacted plate, more rationally and more easily.…”

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

“…In the above equation, w ( x , y ), W 0 , a , and b are the transverse displacement profile of the deformed plate, maximum central deflection, half‐length of the plate, and width of the plate, respectively. It is noteworthy to mention that ω is the first root of the zero‐order Bessel function of the first kind, with an approximate amount of 2.404825558 . The important point is that the magnitudes of longitudinal displacements are very small in comparison with transverse ones and can be omitted in the large deformation analysis .…”

“…In recent years, the dynamic response of structural members subjected to blast loading has received much attention . Most studies have focused on the dynamic response of monolithic metal plates and beams against different types of impulsive loads that were either locally distributed at the centre of the plate or uniformly distributed over the entire plate area.…”