Study Of Some Impact Dynamics Problems Based On Smoothed Particle Hydrodynamics Method

Smoothed particle hydrodynamics (SPH) method is a new numerical method solving partial differential equations, which is one of meshless methods. The most attractive feature of SPH method is that the field variable approximation is performed at each time step based on a current local set of arbitrarily distributed particles, not on nodes of elements, therefore it can naturally handle problems with extremely large deformation. Since the SPH particle is connected to the moving material similar to the Lagrangian description, the entire time history of all the field variables at a material point can be naturally obtained and thus it is easy to trace material boundaries, free surfaces and moving fluid-structure interfaces of fluids. SPH method, as a meshless, adaptive, stable and Lagrangian solver for dynamic problems, has distinct advantages over the conventional grid-based numerical methods, so SPH method is one of most attractive and hopeful numerical method in impact dynamics. In this thesis, the theory of SPH method has been studied and applied to different complex engineering problems, such as penetration of ship hull plates, shearing action of energy absorber, dropping emulation of fluid-filled tank, penetration of submerged double shells and fluid-structure interaction of hydrodynamic damper, which were supported by fund project of national natural science foundation of China combined with china academy of engineering physics.The basic concept and the essential formulations of SPH method are introduced firstly. The SPH approximations are studied, which include the strategy of the SPH method, the continuous kernel approximation and the discrete particle approximation. The description and major properties of the smoothing functions are also discussed. The detailed SPH formulations is derived by discretizing the partial differential equations in continuity mechanics spatially, leading to a set of ordinary differential equations with respect to time. The numerical aspects in implementing the SPH formulations, including artificial viscosity, artificial heat, equation of state, constitutive relations and integration method, are also discussed. A three-dimensional SPH source code written by FORTRAN is provided to solve the problems, which is a base in the further research.The capability of the SPH method has been demonstrated through solving a number of example functions. It is noted that the calculation accuracy is influenced by smoothing function, smoothing length and initial distribution of particles, and boundary deficiency problem and tensile instability problem are inevitable in the traditional SPH method. Some derivative SPH methods, such as improved SPH, CSPH and DSPH, are discussed to improve the traditional SPH. Numerical studies show that the derivative SPH methods not only remedy the boundary deficiency problem but also well simulate the discontinuity of field variable functions. Some special boundary treatments are needed in the SPH method. Three classical physical problems are solved by my SPH codes and it can be seen that the SPH method is suitable for solving the impact problems.SPH method has been applied to simulate the fracture and failure of solid materials in the impact successfully. In simulation of ship hull plates penetrated by projectile with low velocity, the results of SPH method are consistent with results of finite element method or ballistic experiment. In simulation of ship hull plates penetrated by projectile with high velocity, the large deformation of ship hull plates and the debris cloud of materials same as experimental literatures are easily obtained with the SPH method, which is the most outstanding advantage over other grid-based methods. Subsequently, SPH method is applied to simulate the shearing actions of new type energy absorber, because the large number of elements and the large CPU time are unacceptable if using finite element method. By reason of structure design, energy absorber can switch the impact to thousands of shearing actions among thin ring plates inside the absorber and the impact energy will be decentralized and dissipated gradually. The results of SPH method show that the impact velocity, thickness and material of ring plates are important related factors of energy absorption ability and the energy absorber is effective for collision that impact velocity is lower than 40 km/h. The sled crash test is carried out to validate the result of simulations.SPH method has been applied to simulate the large deformation of fluid and the fluid-structure interaction successfully. A new idea of SPH method coupled FE method is proposed, which creates SPH particles in fluid domain, divides FE elements in solid domain and calculates the fluid-structure interaction through the contact force between SPH particles and FE elements. The coupled method makes full use of SPH method to solve large deformation problem and FE method to treat complex shapes or boundary conditions, which is an attractive and promising numerical algorithm in engineering.SPH method coupled with FE method is used to simulate the dropping of rectangular fluid-filled tank firstly. Compared with ALE method, the slosh of fluid and the deformation of tank simulated by SPH method are more close to the truth. Secondly, penetration of submerged double shells is simulated using SPH method coupled with FE method. When the projectile at high speed penetrates the fluid-filled tank, the water hammer effect will obviously change the deformation or stress level of the frontal and back walls along the impact direction, so the interaction between the water and the double shells can not be neglected in structural security analysis. Subsequently, the dynamic characteristics of hydrodynamic damper during the rush into the water channel with high velocity are successfully simulated by SPH method coupled with FE method. The water resistance, the pressure in the interface and the stress of structure are investigated, and the relationship among the peak of water resistance, initial velocity and actual draught is also discussed. The pressure or stress concentration is the main risk during the impact and an empirical formula is put forward to predict the water resistance of hydrodynamic damper in engineering.In this thesis, the fracture and failure of structures is simulated by SPH method and some fluid-structure coupling problems are successfully solved by SPH method coupled with FE method. It can be concluded that the SPH method is a kind of new potential numerical method and has a bright future in the research of impact dynamics.