Research On The Computational Methods For The Dynamic Responses Of Laminated Plates Subjected To Underwater Explosions

Research on the behavior of composites and laminated structures subjected to underwater explosion load are of great importance. This dissertation investigates the computation theory, analytical and semi-analytical solutions of the elastic dynamic responses of laminated plates subjected to underwater explosion load considering of the fluid-structure-interaction (FSI).A new algorithm is presented to modify the numerical method (Qing,2007) of the Laplace transform inversion at the initial point. Two new numerical inversion methods of Laplace transform are developed, which reduce the computational complexity without loss of the accuracy.Based on Taylor's FSI theory, Laplace transform and inversion method, the analytical solution of monolithic Kirchhoff thin plates' response to air or underwater explosion are derived. The results show that the analytical solution based on Kirchhoff plate theory is accurate enough for thin plates. According to the momentum and energy analysis, the FSI mechanism is investigated.An analytical procedure for solving the elastic dynamic response of the monolithic Ressner-Mindlin plates subjected to air or underwater explosion is proposed. The analytical procedure is verified by comparison with finite element analysis (FEA) results. The analytical solution of the work done by each force component in the motion equations is derived. It is shown that the FSI effect and the energy output efficiency due to the rarefaction wave decrease with the increase of the plate thickness.Based on state space method. precise integration method and numerical inversion method of Laplace transform a semi-analytical procedure for solving the elastic dynamic response of laminated plates subjected to air or underwater explosion are derived with considering the FSI. Results of monolithic plates show that the semi-analytical procedure is more accurate than FEA method. As the thickness of the plate increases, errors of Kirchhoff and Reissner-Mindlin plate theory increase. Results for laminated plates show that the distributions of the rigid panels and flexible layers in the laminated plates have a great influence on the extreme responses of the laminated plates.The responses of monolithic functional graded laminated plates subjected to impulsive load (without considering FSI) are investigated. A semi-analytical impulsive response solution for monolithic functional graded plates with exponential law distribution along the thickness coordinate is derived. Based on the semi-analytical impulsive response solution, the exponential layer model (ELM) is used to approximate monolithic functional graded plates with arbitrary distribution along the thickness coordinate, and an approximated solution is derived. The two solutions are verified by comparisons with the approximated results of homogeneous layer model (HLM). It is shown that as the layer counts increase, exponential layer model reach the exact solution faster than homogeneous layer model. Furthermore, based on the solutions for monolithic functional graded laminated plates subjected to impulsive load, and with considering the FSI, the solutions for the responses of laminated functional graded plates subjected to air and underwater explosions loads are derived.The spring layer model is used to simulate the weak-bonding interface. With considering the FSI, the elastic dynamic response of laminated functional graded plates with weak-bonding interface subjected to air and underwater explosions loads is investigated, and a procedure for solving the response problem is proposed. It is shown that the weak-bonding interface has a relatively great influence on the responses of the laminated plates. As the flexibility of the weak-bonding interface increase, the interface slip also increase.