Research On Numerical Simulation Of Metal Forming By Meshfree Methods

The metal plastic forming technique is very important to the manufacturing process of metal parts. In order to predict the influence of various processing parameters to metal flow, the numerical simulation technique is necessary. But the metal forming is a very complex physical process, including non-linear geometry, physical and contact, etc. In present, finite element analysis technique is widely applied in the research of plastic forming. But the finite element method is a numerical method based on mesh. When the mesh distorted seriously, the computation accuracy will lost, even the computation process can not be continued. Remesh process for the distorted mesh is necessary in order to continue the simulation. The remesh procedure is a very time consuming process especially to three dimensions remesh technique.According to finite element method depends on the mesh, more and more researchers begin to focus on the meshfree method. The shape function of meshfree method is without employment of mesh, which is very suitable for solving the large deformation problems such as high speed impact, dynamic crack expand, plastic forming, solid-liquid coupled, etc.Based on the detailed explain of basic theory and numerical procedure of meshfree method, the application of metal plastic forming numerical simulation procedure using collocation meshfree method based on reproducing kernel particle functions is researched deeply. Corresponding simulation code is developed, two dimensional symmetric and three dimensional problems are solved. Satisfied results show the feasibility of the method mentioned in this paper.The basic theory of collocation meshfree method and realization procedure in two dimensional symmetric problem of metal bulk forming are explained, including the construction of shape function and its first-order and second-order derivation, the treatment of friction and contact, etc. The collocation equations of elastic-plastic material and rigid-plastic material are deduced. The feasibility of the method is proved from two numerical examples.The explicit dynamic and heat transfer equations of metal plastic forming process using meshfree method are explained. Thermal-mechanical coupled meshfree analysis of ring compress process is realized combined with the commonly used metal deformation and heat transfer coupling algorithm in finite element method. The feasibility is proved compared with the experimental results of Male.The three dimensional equations of reproducing kernel particle function and its first-order and second-order derivation is deduced. The numerical implement procedure of three dimensional collocation meshfree method based on elastic-plastic material is given. Some key problems such as the control of time step, the treatment of friction-contact, the control of nodal influence radio, etc are explained in detail. A C-shape profile metal extrusion process using collocation meshfree method is analyzed and compared with the simulation results by finite element method. Using color plasticine, physical simulation model is carried out for the extrusion process. A method of layer-built billet has been proposed and effectively used. A good agreement of numerical simulation results and physical simulation results show the validity of the meshfree method.According to the absence of mesh and lack of connection information between the sprinkled nodes, on the other hand, make post-processing of meshfree results such as displacement, stress and strain in the whole domain an issue needs additional effort. A mold interpenetration and mesh quality control method based on incremental algorithm to build Delaunay tetrahedrons are proposed. The detailed flowchart of realizing the method is given. The numerical result shows the topological relationship produced by this method can describe the real shape of the discrete nodes very well.A new shape function is proposed. The construction procedure of this shape function is discussed. The characteristic of this shape function is proved. The equivalent integral weak form of discrete scheme based on Galerkin is derivated. Detailed implementary steps and the elimination of singularity are given. Without solving the complex anti-matrix, the procedure is simplified. Because of the interpolation property of this function, the essential boundary conditions can be imposed directly. According to a numerical example, the effects of the influence radio of domain to the accuracy are analyzed. Compared with the moving least square function, the effective and accuracy are proved of this shape function. A new way of researching shape function of meshfree method is proposed.