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A truncated Newton-Lanczos method for overcoming limit and bifurcation points. (English) Zbl 0704.73100

Summary: In this study procedures for overcoming limit and bifurcation points in large-scale structural analysis problems are described and evaluated. The methods are based on Newton’s method for the outer iterations, while for the linearized problem in each iteration the preconditioned truncated Lanczos method is employed. Special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method. The proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
65F30 Other matrix algorithms (MSC2010)
74G60 Bifurcation and buckling
74H45 Vibrations in dynamical problems in solid mechanics
65K10 Numerical optimization and variational techniques
74P10 Optimization of other properties in solid mechanics
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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[1] ’Incremental/iterative solution procedures for nonlinear structural problems’, in et al. (eds.), Numerical Methods for Non-linear Problems, Pineridge Press, Swansea, U.K., 1980, pp. 261-290.
[2] and , ’Combining quasi-Newton and arc-length methods for the analysis of nonlinear problems in the post limit range’, Proc. First World Congress on Computational Mechanics, Austin, Texas, Sept. 1986.
[3] Crisfield, Comp. Struct. 13 pp 55– (1981)
[4] and , ’A work control method for geometrically nonlinear analysis’, Proc. NUMETA’ 85 Conference, Swansea, U.K., 1985, pp. 913-921.
[5] Papadrakakis, Int. j. numer. methods eng. 29 pp 141– (1990)
[6] Papadrakakis, Comp. Struct. 30 pp 705– (1988)
[7] and , ’Conjugate gradient algorithms in nonlinear structural analysis problems’, Comp. Methods Appl. Mech. Eng., 11-27 (1986).
[8] Papadrakakis, Int.j. numer. methods. eng. 28 pp 1299– (1989)
[9] Nash, SIAM J. Sci. Stat. Comp. 6 pp 599– (1985)
[10] O’Leary, Math. Program. 23 pp 20– (1982)
[11] Crisfield, Int. j. numer. methods eng. 19 pp 1269– (1983)
[12] ’Variable step lengths for non-linear structural analysis’, TRRL Laboratory Report 1049, 1982.
[13] The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N.J., 1980, p. 10. · Zbl 0431.65017
[14] Bergan, Comp. Struct. 12 pp 497– (1980)
[15] Kani, J. Struct. Div. ASCE 112 pp 1806– (1987)
[16] Papadrakakis, Comp. Struct. 14 pp 393– (1981)
[17] Dembo, Math. Program. 26 pp 190– (1983)
[18] ’A truncated Newton-Lanczos method for overcoming limit and bifurcation points’, ISAAR Report 88-3, NTUA, 1989.
[19] Papadrakakis, J. Appl. Mech. ASME 53 pp 291– (1986)
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