Meshless Method And Its Application In Metal Plastic Forming

The technology of metal plastic forming plays a crucial role in the mechanical product manufacturing process, it not only has the advantages of high productivity、stable quality and low cost of materials, but also can effectively improve the microstructure performance. With the development of computer technology and computation methods, metal plastic forming gained great achievement and was applied wildly in metal forming processing. While the metal forming is a very complex physical process, and the finite element method is a numerical method based on mesh which tend to be distorted in large forming. Distorted meshes lead to the deterioration of computational accuracy and even the half of simulation. As a result, burdensome remeshing procedures have to be implemented. Nevertheless, remeshing remains as a challenging task for3D problems. In addition, extra loss of accuracy and efficiency is inevitable.In order to solve the deficiency of classical finite element method in large deformation problems, the meshless method, a new numerical method, was proposed. This method requires only node information and a description of the boundary conditions, and no element connectivity is needed totally or partly which avoids the problem of the mesh distortion. It has broad application prospects in the large deformation problems and three-dimensional calculations.As a new numerical method, meshless method is not yet mature in the field of theoretical research and engineering application. Based on the summarization of the present literatures, theory of meshless method has been studied, and some effective exploration has been made in the application of metal plastic forming. This dissertation includes the following contents.Firstly the research history and the current research status of meshless method have been reviewed, the characteristics and the superiority of meshless method, and its problems existed recently have also been presented in this study.Secondly, the key technology of meshless method was described in detail. The calculation program of radial point interpolation method (RPIM) and element free Galerkin method (EFGM) has been written by FORTRAN language. A two-dimensional cantilever beam was taken as the research object. The influence of calculation accuracy has been studied from the shape coefficient, the size of nodal supports, the weight function and analyses the influence of parameters, shape coefficient, and the Gauss integral order. Then the optimal parameter range was determined, which improved the theoretical basis for the future study.Then, the metal elastic-plastic theory was introduced in detail. Combined the element free Galerkin method with the elastic-plastic theory, an elastic-plastic meshless method was established. Then the Taylor bar experiment was used to verify the accuracy of the elastic-plastic meshless method, the results showed that as long as the size of nodal supports is large, the calculation precision of the meshless method is higher than that of the finite element simulation.Finally, the cylinder upsetting and rolling forming were analyzed by using elastic-plastic meshless method compared with the finite element simulation process, results show that, when the deformation is small, the meshless method is very close to the results of finite element simulation. Along with the deformation increasing, the mesh distortion of finite element method is Serious which lead to a great calculation error. While the node distribution of the meshless method is very uniform and the distribution of stress and strain is very smooth, which embodies the superiority of meshless method in the large deformation.