Study Of Finite Element Method And Application For High Velocity Impact

The research of high velocity impact and penetration has great significance both in military and engineering, and so that it always attracts the attention of scholars at home and abroad. After a series of study of numerical method related to impact dynamics, such as the transient finite element discretization method of conservation equations, numerical quadrature and hourglass control, the identification and redefinition of sliding interface and so on, the dissertation is aimed at to study a high efficient and practical numerical method for high velocity impact and to develop a easy to learn and easy to use software in impact engineering. Therefore, the research achievements we obtained in this paper are valuable for the development of high function weapons and modernization of military equipments.The basic steps to discretize conversation equations of continuum with semi-discretization method of finite element are described in detail and clearly. The features and requirements of finite element numerical computation in impact dynamics are discussed, and an explicit algorithm by the aid of lumped mass matrix is proposed. Based on the theoretical frame of hydro-elastoplastic constitutive model, lots kinds of constitutive equations are considered and inserted in HVP-3D, a software we developed. Several hourglass modes induced by one-point quadrature of hexahedral element with eight nodes are analyzed and a measure to avoid the development of hourglass deformation is proposed. A kind of artificial volumetric viscosity is used in HVP-3D, and it eliminates effectively local vibration resulted from shock wave. Besides, a technique to simulate sliding interface in oblique penetration is studied. The key point of the new method is focused on the treatment of slave elements which were used in most contact computations but replaced by slave nodes in HVP-3D. As a result, many difficulties we have to solve in 3D penetration simulation, such as the intersection of master elements and slave elements, the search and identification of slide interface, modification and redefinition of the master/slave elements and the slide interface and so on, are solved thoroughly. Therefore, the computational efficiency of the software we developed is improved greatly. The software HVP-3D is introduced briefly, in which several measures to improve computation efficiency are used, for instance, the method of searching cells is a typical example which is confirmed to be very effective.By hydro-elastoplastic model including damage and rate effect, a series of penetration simulations of ogive-nosed steel rod impacting at aluminum target are carried out with the program HVP-3D, and the physical details in penetration are described. The simulation results are qualitatively and quantitatively analyzed in detail, and numerical examples of ogive-nosed steel rod penetration in aluminum target indicate that the computational results are in good agreement with publication for both normal and oblique impact. Therefore, it is concluded that the method discussed in the paper and the program we developed are reasonable and available. With increasing of the initial velocity, the residual velocity of normal perforation is nearly proportional to initial velocity. After normally perforating target, steel rod has no mass consume and distortion, and it is in good agreement with experiment. Numerical examples shown that HVP-3D is effective and powerful software in the study of penetration and perforation phenomena, and its value and significance is strengthened greatly since we have the full property of initiative intelligence.Influence of attack angle on penetration process is also discussed, and the physical details for penetration with attack angle are obtained. The results shown that the effect of small attack angle (no more than five degrees) in normal penetration can be neglectable, but for large attack angle the residual velocity will be decreased evidently. If the initial velocity remains constant, the attack angle will play a more important rule for oblique penetration than normal one. Furthermore, attack angle also decreases average velocity, and influence of down attack angle is more than up attack angle in oblique penetration. Jumping of a bullet in oblique penetration is discussed and simulated with different impact velocities, and the critical jump angles are obtained. The results shown that the critical jump angles are decreased with the increasing of impact velocities.Based on the Lagrange finite element, the appearance and control of hourglass phenomenon in one-point quadrature are described in detail, moreover, the numerical method and computation process of using 2×2×2 Gauss quadrature to avoid hourglass deformation are discussed. One-point quadrature will lead the development of hourglass deformation and zero energy mode, so it will result in intersecting and overturn of griddings and the stop of computation. Two kinds of methods to solve hourglass deformation are discussed: 2×2×2 Gauss quadrature and hourglass control. 2×2×2 Gauss quadrature can describe non-linearly displacement modes of hexahedral element with eight nodes, and its computation process is described. By one-point quadrature and 2×2×2 Gauss quadrature, the propagation of one dimensional strain wave in aluminum plate are simulated, and the results shown that 2 ×2×2 Gauss quadrature is much better than one-point quadrature. The computation results of flat-nosed rod penetration in target also shown that 2×2×2 Gauss quadrature can control effectively hourglass deformation.Based on cavity-expansion theory, the analytical equation for normal penetration resistance and depth with different nosed rods is obtained by a simple mode, and the results of penetration depth are in good agreement with experiments. By momentum equation and momentum moment equation, the relation of centroid velocity and attack angle is obtained after spherical-nosed rod impacting at spherical target. Four experiential formulas for penetration depth on concrete are presented, and main features and parameters in the formulas are analyzed in detail.