Elasticity Solutions for Hertzian Loaded Composite Sandwich Plates

Abstract

The elasticity solutions for composite laminates in bending originally developed by Pagano are extended for Hertzian contact-type loading in this paper. Two solutions are obtained, corresponding to cylindrical bending and three-dimensional bending of a rectangular plate. Loads simulating contact with a spherical indentor are obtained by superposition of the elasticity solutions for individual terms of truncated Fourier sine series representations of Hertzian contact stresses. In this way, a benchmark for models of impact loaded plates is provided in which the loading is more representative of contact than the solutions often used for that purpose. The solutions provide insight into the interpretation of experimental data from low-velocity impact tests and are used to judge the performance of finite-element–based low-velocity impact algorithms in predicting stress under the impactor.