A nonlinear high order theory for analysis of sandwich beam with flexible core under low velocity impact

A novel geometrically nonlinear high order sandwich panel theory for a sandwich beam under low velocity impact is presented in this paper. The equations are derived based on high order sandwich panel theory in which the Von-Karman strains are used. The model uses Timoshenko beam theory assumptions for behavior of the face sheets. The core is modeled as a two dimensional linear elastic continuum that possessing shear and vertical normal and also in-plane rigidities. Nonlinear equations for a simply supported sandwich beam are derived using Ritz method in conjunction with minimum potential energy principle. After obtaining nonlinear results based on this enhanced model, simplification was applied to derive the linear model in which kinematic relations for face sheets and core reduced based on small displacement theory assumptions. A parametric study is done to illustrate the effect of geometrical parameters on difference between results of linear and nonlinear models. Also, to verify the analytical predictions some low velocity impact tests were carried out on sandwich beams with Aluminum face sheets and Nomex cores. In all cases good agreement is achieved between the nonlinear analytical predictions and experimental results.