Analytical modelling of high-rate elasto-viscoplastic deformation of circular plates subjected to impulsive loads using pseudo-spectral collocation method

Abstract

An analytical methodology is developed to study dynamic elasto-viscoplastic behaviour of moderately thick circular plates subjected to high-intensity impulsive loads, comprehensively. First, incremental kinematic formulations are derived based on the first-order shear deformation theory to take into account viscous damping and rotary inertia. Geometrical and material non-linearities are applied by the complete von Kármán system and a mixed strain hardening law coupled with a physically based viscoplastic model, respectively. A semi-implicit scheme of return-mapping is employed by the cutting-plane algorithm to obtain effective plastic strains apart from satisfying the consistency condition. The subsequent part is devoted to the transformation of this boundary value problem into an initial value problem, to evaluate displacement fields. Spatial and temporal discretizations are carried out by the Chebyshev pseudo-spectral collocation method and Houbolt time-marching scheme, respectively. This transformation has been handled in the compact matrix forms to stabilize the solution and to make it more convenient. Influence of impulsive load and other parameters on plate deflections, effective strain and stress, temperature rise and stresses are considered. Ultimately, good accuracy is achieved through comparison between results and existing experimental data and finite element simulation from the literature. In addition, some challengeable aspects for the modelling are discussed.