The Application Research Of Meshless Methods In Rheological Processing

The numerical methods, such as the Finite Element Method and the Boundary Element Method, have been successful so far. The formation and existence of the grids of these methods, however, are posing some difficulties in their actual applications. For example, there is a great number of large elastic-plastic deformation in engineering field such as rheological forming, structure collision, etc. When simulating these processes by Finite Element Method, we need to adopt the element-remeshing technique to solve the problem of element distortion, so that the efficiency and precision of computation will decrease. Now the element free method can work completely or partly without grids. It is used in simulation of crack propagation, elastic-plastic deformation analysis and impact process, etc. and shows broad developing and applying prospects in the field of scientific research and engineering calculation.Pioneering achievements have been made in recent years by world experts in element free method investigation. The Element Free Galerkin Method and the Reproducing Kernel Particle Method, for example, are two new representative element free numerical methods which have appeared lately. As they don't need any finite element or boundary element grid, they turn out to be more flexible and convenient in numerical calculations in many fields. On the basis of studying these two element free methods, and successfully applied them into the numerical simulation of rheological forming of metal, the concrete researching work and achievements as follows.At the beginning of the dissertation, recent developments of element free methods are briefly summarized. Several kinds of element free methods are reviewed and commented. And the advantages and disadvantages for a variety of element free methods are outlined.Secondly, the effect on the precision of calculation by weight functions, basis functions, the size of support domain radius and the parameters of node, and factors involved in the Element Free Galerkin Method are inquired in detail. The relevant parameters are chosen.Thirdly, the simulation of metal rheological forming were successfully done by using Galerkin element free method in the paper, and the interface of software Tecplot were designed which made the computation results visual and heightened the efficiency of post-processing. Lastly, the variational principle of rigid-plastic element free method was introduced and developed reproducing kernel particle method program which analyzed cylinder compressing. By discussing the influences of node number and size factors to the solution, it obtained the suitable size influence factor range. The feasibility and the validity were validated by comparing with finite element method result and it proved element free method offers tremendous potential supplement in industrial applications, so that it provides guidance and reference in the application of element free method in actual engineering.This study was supported by the key project of the National Education Department of China (No. 02103), the Education Department of Hunan Province (No. 02A008).