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http://dx.doi.org/10.3795/KSME-A.2003.27.8.1281

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

Koo, Sang-Wan (서강대학교 대학원 기계공학과)
Kim, Nak-Soo (서강대학교 기계공학과)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.27, no.8, 2003 , pp. 1281-1286 More about this Journal
Abstract
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 .
Keywords
Line Search; Backtracking Algorithm; Non-Linear FEM; Convergence Rate;
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  • Reference
1 Domain Decomposition using substructuring Method and Parallel Computation of the Rigid-Plastic Finite Elemint analysis /
[ Park,K.;Yang,D.Y. ] / Transactions of Korean Society for Technology of Plasticity
2 ThreeDimensional Rigid-Plastic finite Element Method Using Diagonal Matrix for Large-Scale; Simulation of Metal-Forming Process /
[ Mork,K.;Yoshimura,H. ] / International Journal of Mechanical Science
3 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
4 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   DOI   ScienceOn
5 Scott, J. A., 1999, 'On Ordering Elements for a Frontal Solver,' Commun. Numer. Meth. Engng, Vol. 15, pp. 309-325   DOI   ScienceOn
6 Crisfield, M. A., 1995, Non-linear Finite Element Analysis of Solids and Structures, Vol. 1, John Wiley, pp. 254-265
7 Chung, K. and Wagoner, R. H., 'Numerical Improvement of Viscoplastic, Non-linear Finite Element Analysis,' Int. J. Mech. Sci., Vol. 29, pp. 45-49   DOI   ScienceOn
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   DOI   ScienceOn
9 Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, pp. 754-761
10 Arora, J. S., 1989, Introduction to Optimum Design, McGraw-Hill, pp. 288-289
11 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   DOI   ScienceOn
12 Dennis, Jr, J. E. and Schnabel, R. B., 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, pp. 126-129
13 Bonet, J. and Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, pp. 186-187
14 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   DOI   ScienceOn
15 Jeremic, B., 2001, 'Line Search Techniques for Elasto-Plastic Finite Element Computations in Geomechanics,' Commun. Numer. Mech. Engng, Vol. 17, pp. 115-125   DOI   ScienceOn