Numerical Simulation Of Sheet Metal Forming

Sheet metal forming is one of the most important technique in the manufacturing industry. It is widely used to reduce the costing because of its high efficiency in productivity and the exploitation of the material. The sheet metal forming process is characterized by strong non-linearity, not only in the plastic yielding of the material and the large deformation, but also in the contact and friction between workpiece and die. It makes the control of process more difficult, and it causes the fracture and wrinkling of the workpiece, which results in the failure of the products. In order to improve the processing technology and to raise the quality of products, the numerical simulation of the sheet metal forming has been paid close attention by the engineers and scientists in the world.In this thesis, it is investigated some numerical techniques of nonlinear Finite Element Method, which aims at the key problems in the numerical simulation of sheet metal forming. (1) The tangent stiffness matrix is reconditioned to improve the accuracy of the solution when the deformation state of structure is near the critical points. (2) A modified arc-length approach is introduced to the algorithm with the auto-adaptive loading and unloading schedule. (3) A path-switching technology is presented and it is enhanced the stability of passing through the bifurcation points of the unstable structure based on the mentioned re-conditioning method. (4) Some system parameters are defined to identify the correct deformation direction for the path-following method and it results to an improved arc-length method for the more complex post-buckling path. On these bases, by applying the contact searching algorithm combined with Lagrange multiplier method for friction and contact, finite element analysis is carried out for the numerical simulation of super-plastic forming processes. In addition, it is also presented the FEM and BEM coupled technique for the numerical simulation of sheet metal forming to take the advantages of both methods. All the numerical methods presented and adopted are realized in FORTRAN source codes. The efficiency and the accuracy are demonstrated in numerical examples.