Research On Key Techniques Of Finite Element Method With Large Step For Sheet Metal Forming

At present,finite element simulation for sheet metal forming has been used widely in automobile production,and the finite element simulation of explicit formulation has been studied because it can trace the history of forming process accurately.However,the explicit finite element simulation is not suitable for the conceptual design period of the product,because it is difficult to provide the analysis results quickly due to its heavy computation problem.In order to reduce the time of conceptual design period of product,the finite element simulation of implicit formulation for sheet metal forming has been more and more researched and emphasized,the finite element method with large step is an implicit finite element method by decoupling equations.The finite element method with large step for sheet metal forming is studied in this dissertation.Through the research of several key technical issues,the design of finite element method with large step for sheet metal forming is realized,which improves the prediction efficiency of sheet metal forming and reduces the time of conceptual design period.The main contribution of this dissertation can be concluded as following:(1)The software framework for finite element simulation with large step for sheet metal forming is proposed.The finite element method with large step for sheet metal forming is studied,which decouples the forming simulation process into two successive processes: bending deformation process and tensile deformation process.The result of the bending deformation is called the initial solution of any forming simulation process.The incremental theory is introduced into the tensile deformation process,and the implementation of tensile deformation is given.The frame system of finite element method with large step for sheet metal forming is constructed,three key technical issues in the system are described.(2)The gravity modeling based on DKT shell element and the holding modeling of binder surface for sheet metal forming are studied.In view of the characteristics of the gravity modeling and the basic assumptions of thin plate deformation,the formulas of the curvature field,stress and internal force in the case of DKT12 shell element are given.The gravity modeling based on DKT shell element is established with the aid of the idea of finite element method with large step.On the basis of the mathematical theory of Riemannian manifold space,the holding modeling of sheet metal based on Laplace-Beltrami operator equation is implemented.The differences of DEK12 shell element method and Laplace-Bletrami operator equation in the application of boundary conditions and computational efficiency aspects are obtained.(3)The waterfall-mix contact search and the technology of mesh refinement in finite element method with large step are studied.According to the characteristics of the contact search problem in the finite element method with large step,a local-global contact search algorithm is proposed,which is efficient in both local and global aspects.Considering the Gauss-Bonnet theorem of surface a mathematical tool,the curvature formula on discrete mesh manifold is established,and the technology of mesh refinement is implemented.(4)The initial guess of intermediate configuration by form-finding method of cable and membrane structures are studied.By the virtual displacement principle with the Green-Lagrange strain and the second Piola-Kirchhoff stress,the nonlinear equation with the constraint condition of nodes for form-finding method is constructed.The features of geometric intuition,free modeling and large displacement and small strain with cable and membrane structures are considered in this method.The initial guess of intermediate configuration is obtained through solving a series of nonlinear equations to reach the equilibrium state.(5)There are some researches on pre-process and post-process of software system for finite element method with large step.The data structure of refine mesh in pre-process,the solvers of large-scale finite element sparse linear euqations in post-process and parallel realization are studied.On the basis of the above studies,the design of finite element method with large step for sheet metal forming is realized.The application research of finite element simulation with large step for sheet metal forming is carried out.The validity of this design in running time and accuracy for some cases is verified by comparison with other commercial software.