Solution of the equations of rigid-plastic FE analysis by shifted incomplete Cholesky factorisation and the conjugate gradient method in metal forming processes

In general, some iterative methods, such as the standard Newton-Raphson met hod, the modified Newton-Raphson method and so on, have been employed to so lve the system of simultaneous equations obtained in rigid-plastic FE analy sis. 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 conjuga te-gradient method, designated the Shifted ICCG method, to solve the equati ons arising in the rigid-plastic FEM. The performance of the algorithm in t erms of shift parameter psi, and CPU time under a range of friction conditi ons has been assessed. The use of higher order time integration is also inv estigated. The CPU times required for calculation employing the diagonal ma trix method, the shifted ICCG method (psi=0.0) and the Newton-Raphson metho d are compared, it being found that the stability is not always good for th e diagonal matrix method, and the CPU time required for calculation is very large. Numerical tests show that the shifted ICCG method is stable, and ca n be used successfully in the application of the rigid-plastic finite cleme nt method to the solution of metal forming problems. (C), 2000 Elsevier Sci ence S.A. All rights reserved.