A Method Study To Speed Up The Finite Element Calculation In The Flat Rolling Simulation

Finite element method (FEM) has been widely applied in the analysis of flat rolling processes with the development of commercial finite element software. The ANSYS is powerful software for FEM analysis, and it can simulate the rolling process, predict the related parameters. However, it also involves the some drawbacks, e.g. its solving speed can not accommodate to the requirements of online analysis. The FEM is excellent in the accuracy of simulation results, but it also faced with some disadvantages such as lower efficiency and higher cost for calculation which has became a bottleneck for on-line application. The key issue for FEM on-line application is the solving speed. In this thesis, a numerical computation method is studied to speed up the solving speed of FEM in the flat rolling process. The main contents are as follows.1) By tracking CPU time consumption for main components in the N-R method which is employed in FEM analysis, it was found that linear search of damping factor occupies the most of CPU time. Thus, more efforts should be put on the linear search of damping factor to speed up the solving procedure, so that the online application of FEM is possible.2) The DN-Brent method, a combination of Damped Newton method, and one-dimensional Brent method, is employed in the rigid plastic finite element method to solve the flat rolling problem. This method tries to find the proper damping factor such that the total energy function closes to its minimum point quickly. Comparing with the N-R method where damping factor is found based on the Golden method, the complexity of the proposed approximate method is reduced, and thus more CPU time is saved.3) The performance of the proposed algorithm has been analyzed in terms of the number of iterations, CPU time and mesh size. The computed rolling forces are also examined. The proposed DN-Brent method is compared with Newton-Raphson (N-R) method, and numerical results show that the DN-Brent method can obtain the exact solution with less iteration number and CPU time, which verify the validity and stability of the DN-Brent method in the application of the rigid-plastic finite element method to the solution of flat rolling problem.