Linking Of Smoothed Particle Hydrodynamics Methods To Standard Finite Element Methods And Its Application In Impact Dynamics

In this thesis the basis theory and discretization method of Lagrange Finite Element Method(FEM), Smoothed Particle Hydrodynamics(SPH) and a coupling method (linking of Smoothed Particle Hydrodynamics methods to standard finite element methods) are described. Some related problems are discussed, such as discretization forms and sliding surface in FEM; discretization forms, kernel functions and smoothing length in SPH; conversion of elements to particles, sliding algorithms on the interface between elements and particles and the computation of the particles near the interface in coupling method. Finally, the coupling method is applied to the study of one-dimensional strain wave propagation and hyperveiocity impact phenomenon, the results show that the method has good performance in the numerical study of impact dynamics.First, the basic idea of the discretization method of conservation equations in continuum mechanics with Lagrange Finite Element Method and the flowchart of computations are described. The problems of sliding surface and severely distorted element in hyperveiocity impact simulations are discussed, and the corresponding solving ways are proposed.Kernel estimate of a function and its derivatives are the key point in SPH method and their various forms are obtained by kernel interpolation theory. Based on the analysis of SPH method, the discretization formations of conservation equations in continuum mechanics are established. In addition, several topics, such as kernel function properties, the choice of smoothing length, artificial viscosity, constitution relations, conservative smoothing method and flowchart of computations, are discussed in details.Then a coupling method (linking of Smoothed Particle Hydrodynamics methods to standard finite element methods) is proposed, which creates the model with finite element at the beginning and automatically convert distorted elements into smoothed particles during dynamic deformation. Three difficulties in the coupling method are discussed, such as the conversion of elements to particles, the contact and sliding algorithms between elements and particles and the computation of the particles near the interface, and some ways are proposed to solve these problems.Particle searching algorithm plays a very important role in coupling method and SPH computations since it takes most computational time and hence it determines the computation efficiency. Considering kernel function as a strong compact support function, a subdomain searching algorithm is suggested, which is a simple method and increases computation efficiency greatly. One problem in coupling method and SPH is hard to define the boundary. In order to solve the problem, we use the concept of particle boundary circle to determine it and the boundary particle is identified by whether the particle circle is...