A new model for calculating the transient displacement field within a linear elastic isotropic solid with a through hole under dynamic impact: A 3D model is developed and a 2D case study is examined

This paper presents an exact analytical solution in tensor notation for solving the elastic wave propagation for any 3-dimensional shape objects with a hole (from infinitesimal to finite). For validating the proposed model, a case study of an axisymmetric thick walled cylindrical metallic tube with finite length under a dynamic impact, was modeled and computed. The case study was also computed and validated by using an explicit time integration finite element method, LS-Dyna, for comparison purpose. The LS-Dyna simulation results were used to calculate the boundary conditions for the proposed model for obtaining the analytical solution because in the real world applications these boundary conditions can be obtained through measurement data or the signals of sensors. Based on the virtual boundary conditions obtained from simulation, the proposed model can compute the displacement field (transient response) of the object under dynamic impact. Once the displacement field is available, all transient stress, strain, rotation etc. can be computed as needed. The obtained analytical displacement fields as a function of time and coordinates were compared with the simulation results from LS-Dyna. It has been proven in this paper that the efficiency, accuracy and robustness of the proposed model meet the needs of any potential applications.