Elasto-Plastic Response of Impacted Moderatly Thick Rectangular Plates with Different Boundary Conditions

Abstract

Many elements of structures are subject to dynamic loads during their operation. Knowing the structure's dynamic response parameters makes it possible to design the structure with account of design, strength and operational requirements. Impact of a sphere with a plane surface is a common phenomenon in nature. Rectangular plates subjected to external loads with different boundary conditions have undoubtedly been one of the key components in aerospace, civil, automotive, biomechanical, petrochemical, marine industries, nuclear, optical, electronic, mechanical, and shipbuilding industries. This paper introduces semi-analytically solution for the elasto-plastic analysis of the isotropic rectangular plates subjected to transverse normal impact of a small mass. The Hertzian contact law was obtained from the elasto-plastic analysis of contact between a spherical impactor and an elastic rectangular. At this study, the focus is placed on the frictionless normal low velocity impact of a small sphere against an elastic mordantly thick rectangular plate (using Mindlin's plate theory). The natural frequencies and mode shapes of the plate are calculated by using the exact solution based on three coupled equilibrium equations. Finally, the influence of boundary conditions, dimensions of the plate, initial velocity and radius of the spherical impactor on the impact parameters are examined and discussed in detail.