A NR–BFGS method for fast rigid-plastic FEM in strip rolling

RPFEM (rigid-plastic finite element method) has been widely applied in rolling process with the development of computer technology. However, it is unavailable for online application due to the large computational time. During iterative solution of RPFEM, the convergence speed is greatly determined by the optimization method. In order to improve computational efficiency and convergence, the NR (Newton–Raphson) method and BFGS (Broyden–Fletcher–Goldfarb–Shanno) quasi-Newton method are discussed, respectively, and an NR–BFGS (NR and BFGS) method is proposed and constructed for fast calculation of RPFEM. Moreover, the RPFEM code is developed using Compaq Visual Fortran language and the different strip rolling processes have been solved successfully to show the efficiency and accuracy with the different optimization methods. The calculated results have a good agreement with the measured value and the RPFEM has higher accuracy. Compared with other two methods, the NR–BFGS method has the remarkable advantages to reduce the CPU time and the iterations of RPFEM code. From the numerical results, it is found that the CPU time, stability and the accuracy of RPFEM code in the solution procedure by the NR–BFGS method can meet the requirements of online application of FEM in the strip rolling process.