Research On One-step Inverse Quasi-conforming And Isogeometric Analysis For The Simulation Of Sheet Metal Forming

The research and design of automobile panel molds accounts for about two-third of the cost of the entire vehicle design.At the same time,the industrial manufacturing level of the mold is also one of the important factors affecting the development of the automobile manufacturing industry.The application of numerical simulation technology for sheet metal forming has greatly improved the design efficiency and shortened the cycle of the design.The one-step inverse method based on plastic deformation theory is applied to the stamping part forming design because of its high solution speed.This method ignores the forming loading process from the final configuration of the part,determines the corresponding positions of each node in the initial blank configuration under certain boundary conditions by finite element method,and compares the positions between the two nodes to obtain the stress,strain and thickness distribution of the part.The finite element method is the core and foundation of numerical simulation technology.The quasi-conforming(QC)and the isogeometric analysis(IGA)are the two different type methods in the finite element method.The basic idea of the QC method is to integrate weakening the geometric and equilibrium equations,which are applied to many fields because the stiffness matrix is a display form and can effectively avoid the shear blocking phenomenon.The IGA method based on NURBS basis function is widely used because of its geometric representation,meshes needless,and high element continuity,etc.This paper mainly studies the application of two finite element methods in one-step inverse forming method.The main research contents are as follows:(1)Two quadratic multi-node high-order QC plane elements are constructed by using initial assumed stress QC framework and fundamental analytical solutions method.First,the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements.Then,the stress-function matrices are used as the weighted functions to weaken the strain displacement equations,which makes only string-net functions on the boundary of the elements are needed in the process of strain integration.The results of the numerical tests have proven that both elements are simple and concise,and the elements are immune to the distorted mesh and possess high accuracy.Finally,applying the new element to the one-step inverse initial solution prediction algorithm,the numerical examples proved that the new initial solution prediction algorithm can accurately predict the initial shape of the stamping parts(2)Applied the IGA method to the sheet metal forming to develop the one-step inverse isogeometric analysis method based on the total deformation theory of plasticity,the NURBS element stiffness and internal force and equivalent force solution algorithm in one-step inverse method has been derived.Adopted an isogeometric membrane element to predict the flattened contour of the initial blank from the energy-based initial solution estimation approach.Finally,used the Newton-Raphson algorithm for nonlinear plastic iterations to evaluate the thickness and equivalent strain and stress of the final stamping parts.The results for examples illustrate that this one-step inverse IGA method show good performance in both no external force constraint and withstanding blank holder force constraint conditions.