Analytical Solution for Low-Velocity Impact Response of Composite Plates

An analytical model for the impact response of laminated composite plates is presented. The governing equations, which apply to small deflection elastic response of specially orthotropic laminates, include the combined effects of shear deformation, rotary inertia, and the nonlinear Hertzian contact law. For simply supported boundary conditions, a Fourier series solution is presented that, in contrast to previously published work, retains the frequencies associated with rotary inertia effects throughout the analysis. Errors that are incurred in the analysis of impact events, where the contact force history is obtained as part of the solution process, are investigated and guidelines to achieve converged solutions are recommended. For a benchmark impact problem, the present solution converges more rapidly than other analytical solutions available in the literature. Present analytical predictions are also found to agree well with the experimental results for composite fiber-reinforced plastic plates impacted by instrumented projectiles launched from both gas-gun and drop-weight test setups. The efficiency and robustness of the model in handling the complexities of the impact response of composite plates is further demonstrated by comparing the analytical predictions of contact force and fiber strain histories with those generated using detailed finite element analyses. The good agreement obtained instills confidence in using the model as a foundation for predictions of impact damage and response to penetrating impact events.