Meshless Method And Its Application In Numerical Analysis Of Injection Filling

Because of the advantages of manufacturing more complex products and realizing automation easily, injection molding occupies an extremely important position in polymer processing, and its products can be seen everywhere in the production and life. As important equipment in injection molding, mold design and manufacture have important effect on the replacement and market competitiveness of plastic products. With the development of computer technology, injection molding CAE technology has become the more important tools and methods in plastic injection molds and production design. Now commonly used and mature CAE technology is mostly based on finite element method by means of the element and grid, which greatly limits the application and development of the finite element method. With the emergence of new injection technologies such as Sequential-Valve-Gate Molding and rapid heat cycle molding, injection products become more complex and thin, which is a challenge for grid and element of FEM. In view of this, the meshless methods will be discussed in this paper, and its application in injection molding will be researched. The main contents are as follows:(1)The research of approximate ability of meshfree shape functions. Several meshfree approximate methods are analyzed and the fitting ability of MLS and RPIM shape functions is emphatically studied. At first, function and its first derivative and second derivative are fitted by using MLS and RPIM shape functions. Secondly, the fitting ability of two kinds of shape functions is compared. Then, by studying the basic functions of MLS shape function, the effect of basic functions on the fitting ability of MLS is investigated. At last, numerical computing of Poisson's equation is used to probe the performance of MLS and RPIM shape functions.(2)The treatment of essential boundary conditions based on hybrid meshless method. In order to solve the problem of imposing the essential boundary conditions in the element free Galerkin (EFG), a hybrid method based on the coupling of the radial point interpolation method (RPIM) and EFG is proposed. The problem domain is divided into two parts in this method. The RPIM is applied to the part that contain the essential boundary and the EFG is employed in the rest domain, then the hybrid method is established by using the relationship between two types of meshless interpolation functions. The results of numerical examples indicate that this method is able to combine the good essential boundary condition processing capability of the RPIM and the high computational accuracy of EFG method, and easy to program.(3)The derivation of control volume meshless method. By establishing expression of conservation equation on control volume and using meshfree approximate methods, a control volume meshless method is development based on the idea of control volume finite element method. Comparing with other meshless methods, CVMM is a kind of local weak-form meshless methods that its weight function is constant, Not only reduces the dimension of the integral operation in system equations, but also improves the computational efficiency, and its physical or mathematical meaning is more explicit.(4)The research of numerical analysis of injection molding based on meshless methods. By using the relationship of pressure gradient and velocity in injection filling, a solution model of mass conservation law is established and a solution method of pressure field based on CVMM is proposed. Temperature field is solved by means of finite difference approximation in the thickness direction and meshfree approximation in flow plane; in order to deal with non-physical penetration phenomenon in Lagrangian flow front tracking, a flow front tracking method is development by coupling control volume with the mobile nodes, which can improve the flow front tracking of injection filling. The influencing factors that impacting the numerical solutions of CVMM are studied by example of disc injection. Comparing with the existing finite element software and the actual injection, Meshless method has considerable computational efficiency with the existing finite element method in injection molding analysis, but completely free from the constraints of grids and the elements, and can be more flexible and effective in analyzing the injection molding process.(5)Control Volume-Direct Collocation (CVDC) meshless method and its application in injection numerical analysis. Firstly, by analyzing the phenomenon of calculating accuracy deterioration cause by derivative boundary conditions in DC method, CVDC meshless method is presented that coupling CVMM and DC meshless method, which can overcome calculating accuracy deterioration of DC meshless method due to the derivative boundary condition, and improve the poor calculating efficiency problem causing by integral operation. Moreover, CVDC extended the approaches for numerical analysis of injection filling. CVDC meshless method is applied in the numerical analysis of injection process first time, which uses CVMM to setup system equations at the injection mold walls and cores boundary where exist pressure derivative boundary condition, and selects DC meshless method at the other nodes, finally, total pressure solve matrix is obtained. The analysis results indicated that CVDC meshless method can obtain the same effect with CVMM, but the calculating efficiency was greatly improve.