Efficient implicit finite element analysis of sheet forming processes

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The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time-savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton-Raphson iterations. This also applies to quasi-static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10.
Original languageUndefined
Pages (from-to)1083-1107
Number of pages24
JournalInternational journal for numerical methods in engineering
Issue number8
Publication statusPublished - 2003


  • shell elements
  • sheet forming
  • iterative solvers
  • IR-59428
  • METIS-216384
  • Implicit dynamic finite element analysis

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