A New Analytical Iterative Method for Analyzing the Effects of Low-Velocity Impacts on Composite Sandwich Plates with Flexible Cores

This work introduces a new systematic iterative analytical method for analyzing the impact of low velocities on composite sandwich plates. This method utilizes the Hertzian contact law to establish an exponential equation. By using the principle of minimal potential energy and the energy-balance model between the indenter and the sandwich plate, the unknown coefficients of the exponential equation are determined analytically. An iterative systematic analytical procedure is used to calculate the maximum contact force in the two-degrees-of-freedom (2DOF) spring-mass model. The current approach not only decreases the execution time but also ensures the problem-solving process achieves suitable convergence. Furthermore, a comprehensive model is constructed using the new analytical contact law to calculate the displacements, strains, and stresses in both the face sheets and the flexibility core. The numerical findings are compared with exiting theoretical and experimental results. According to the revised contact law, the contact coefficients are highly dependent on the geometrical and material properties of the coupled structure-impactor system. By doing further investigation about the effect of the impactor's mass on the maximal normal stress, we found that 55% increase of the impactor's mass resulted in a 40% increase in the maximum normal stress absorbed by the core.