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Although the rigid plastic finite element method (RPFEM) is extremely efficient and particularly suitable for analyzing the strip rolling, 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 initial guess. In this paper, three different initial guesses are constructed through Engineering Method, G Functional and Neural Network, respectively. Especially, the back propagation neural network model for predicting the relative velocity field (nodal velocities/roll speed) is trained from huge amounts of RPFEM results. Whereafter, the initial guess is calculated by multiplying the predicted relative velocity field by the roll speed. The numerical examples of seven passes hot strip rolling are provided to show the solution efficiency and the accuracy of RPFEM code in the cases of different initial guess. Compared with other two methods, the Neural Network 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 initial guess by the Neural Network can meet the requirements of online control completely in hot strip rolling.

In general, some iterative methods, such as the standard Newton–Raphson method, the modified Newton–Raphson method and so on, have been employed to solve the system of simultaneous equations obtained in rigid–plastic FE analysis. If the stiffness matrix is symmetric and positive definite, it can be solved by the conjugate-gradient method. In this paper, shifted incomplete Cholesky decomposition of the stiffness matrix is combined with the conjugate-gradient method, designated the Shifted ICCG method, to solve the equations arising in the rigid–plastic FEM. The performance of the algorithm in terms of shift parameter ψ , and CPU time under a range of friction conditions has been assessed. The use of higher order time integration is also investigated. The CPU times required for calculation employing the diagonal matrix method, the shifted ICCG method ( ψ =0.0) and the Newton–Raphson method are compared, it being found that the stability is not always good for the diagonal matrix method, and the CPU time required for calculation is very large. Numerical tests show that the shifted ICCG method is stable, and can be used successfully in the application of the rigid–plastic finite element method to the solution of metal forming problems.