Nonlinear dynamics of locally pulse loaded square Föppl–von Kármán thin plates

Abstract

Modern armour graded thin steel plates benefit from significant elastic strength with high elastic energy storage capacity, which contributes to dissipation of total impulse from extensive blast loads within the bounds of the elastic region. Higher elastic energy storage capability mitigates the probability of catastrophic damage and ensuing large deformations compared to the conventional graded metallic panels. While blast assessment of such structures is important to design and application of protective systems, limited studies are available on their response to localised blasts.The present paper aims at deducing, from the minimization of Föppl-von Kármán (FVK) energy functional, the dynamic response of localised blast loaded thin elastic square plates undergoing large deformations. The presumed blast load function is a multiplicative decomposition of a prescribed continuous piecewise smooth spatial function and an arbitrary temporal function which may assume various shapes (e.g. rectangular, linear, sinusoidal, exponential).A kinematically admissible displacement field and the associated stress tensor were considered as a truncated cosine series with multiple Degrees-of-Freedom (DoF's). From the prescribed displacement field, having simply supported boundary conditions, useful expressions for stress tensor components were delineated corresponding to a unique mode and a series of differential equations were derived. The explicit solutions were sought using the Poincaré-Lindstedt perturbation method. The closed form solutions of each mode were corroborated with the numerical FE models and showed convergence when the first few modes were considered. The influence of higher modes, however, on the peak deformation was negligible and the solution with 3 DOF's conveniently estimated the blast response to a satisfactory precision.