Improvement of Convergence Rate by Line Search Algorithm in Nonlinear Finite Element Method

비선형 유한요소법에서 선탐색 알고리즘의 적용에 의한 수렴속도의 개선

  • 구상완 (서강대학교 대학원 기계공학과) ;
  • 김낙수 (서강대학교 기계공학과)
  • Published : 2003.08.01


A line search algorithm to increase a convergence in Newton's method is developed and applied to nonlinear finite element analysis. The algorithm is based on the slack line search theory which is an efficient algorithm to determine initial acceleration coefficient, variable backtracking algorithm proposed by some researchers, and convergence criterion based on residual norm. Also, it is capable of avoiding exceptional diverging conditions. Developed program is tested in metal forming simulation such as forging and ring rolling. Numerical result shows the validity of the algorithm for a highly nonlinear system .


Line Search;Backtracking Algorithm;Non-Linear FEM;Convergence Rate


  1. Mori, K. and Yoshimura, H., 1982, 'Three-Dimensional Rigid-Plastic Finite Element Method Using Diagonal Matrix for Large-Scale Simulation of Metal-Forming Process,' International Journal of Mechanical Science, pp. 1821-1834
  2. Jeremic, B., 2001, 'Line Search Techniques for Elasto-Plastic Finite Element Computations in Geomechanics,' Commun. Numer. Mech. Engng, Vol. 17, pp. 115-125<115::AID-CNM393>3.0.CO;2-6
  3. Dennis, Jr, J. E. and Schnabel, R. B., 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, pp. 126-129
  4. Bonet, J. and Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, pp. 186-187
  5. Esche, S. K., Kinzel, G. L. and Altan, T., 1997, 'Issues in convergence improvement for non-linear finite element programs,' International Journal for Numerical methods in Engineering, Vol. 40, pp. 4577-4594<4577::AID-NME273>3.0.CO;2-D
  6. Arora, J. S., 1989, Introduction to Optimum Design, McGraw-Hill, pp. 288-289
  7. Crisfield, M. A., 1995, Non-linear Finite Element Analysis of Solids and Structures, Vol. 1, John Wiley, pp. 254-265
  8. Yang, D. Y., Chung, W. J. and Shim, H. B., 1990, 'Rigid-Plastic Finite Element Analysis of Sheet Metal Forming Process with Initial Guess Generation,' Int. J. Mech. Sci., Vol. 32, No. 8, pp. 687-708
  9. Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, pp. 754-761
  10. Chung, K. and Wagoner, R. H., 'Numerical Improvement of Viscoplastic, Non-linear Finite Element Analysis,' Int. J. Mech. Sci., Vol. 29, pp. 45-49
  11. Sloan, S. W. and Randolph, M. F., 1983 'Automatic Element Reordering for Finite Element Analysis with Frontal Solution Schemes,' International Journal for Numerical Methods in Engineering, Vol. 19, pp. 1153-1181
  12. Scott, J. A., 1999, 'On Ordering Elements for a Frontal Solver,' Commun. Numer. Meth. Engng, Vol. 15, pp. 309-325<309::AID-CNM246>3.0.CO;2-F
  13. Park, K. and Yang, D. Y., 1998, 'Domain Decomposition using substructuring Method and Parallel Computation of the Rigid-Plastic Finite Element analysis,' Transactions of Korean Society for Technology of Plasticity, pp. 474-480
  14. International Journal of Mechanical Science ThreeDimensional Rigid-Plastic finite Element Method Using Diagonal Matrix for Large-Scale; Simulation of Metal-Forming Process Mork,K.;Yoshimura,H.
  15. Transactions of Korean Society for Technology of Plasticity Domain Decomposition using substructuring Method and Parallel Computation of the Rigid-Plastic Finite Elemint analysis Park,K.;Yang,D.Y.