无网格法研究进展及其应用

Research progress and application of meshless method

从加权残量法的角度出发,系统地总结了现有各种无网格法的基本格式,阐明了无网格法的特点,论述了无网格法的研究进展,给出了无网格法在碰撞、动态裂纹扩展、金属加工成型、流体力学以及其它领域中的应用。

The finite element method (FEM) has been the most frequently used and the most powerful numerical method in engineering during the past thirty years. However, the lack of robust and efficient 3D mesh generators makes the solution of 3D problems a difficult task. Furthermore, mesh-based methods are also not well suited to the problems associated with extremely large deformation and problems associated with frequently remeshing. To avoid these drawbacks of the FEM, considerate effort has been devoted during recent years to the development of the meshless method, and more than 10 different meshless methods have been developed. In this paper, the basic formulations of meshless methods are first summarized from the weighted residual method point of view, and then compared with FEM, classical weighted residual method and finite difference to show their characteristics. The research progress in meshless methods is discussed in detail, and their applications to impact, dynamic fracture, metal forming and fluid flow are given.