Continuation methods for tracing the equilibrium path in flexible mechanism analysis

Engineering Computations (Swansea, Wales)

Volumn 15, Issue 2-3, 1998, Pages 190-220

  Cardona, Alberto ^a   Huespe, Alfredo ^a  

^a Instituto de Desarrollo Tecnologico para la Industria Quimica   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); ITERATIVE METHODS; LAGRANGE MULTIPLIERS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS); SET THEORY; SYSTEMS ANALYSIS; DEFORMATION; ELASTICITY; FLEXIBLE STRUCTURES;

CONTINUATION METHODS; JACOBIAN MATRICES; NEWTON ITERATIONS; NONLINEAR ALGEBRAIC FUNCTIONS; JACOBIAN METHOD;

STRUCTURAL ANALYSIS;

EID: 0031655002     PISSN: 02644401     EISSN: None     Source Type: Journal    
DOI: 10.1108/02644409810202602     Document Type: Article

References (24)

1. Bellini, P.X. and Chulya, A. (1987), "An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations",J. Comp. and Struct., Vol. 26, pp. 99-110.
2. Bergan, P.G. (1982), "Automated incremental iterative solution methods in structural mechanics", in Hinton, Owen and Taylor (Eds), Recent Advances in Nonlinear Computational Mechanics, Pineridge Press.
3. Cardona, A. (1989), "An integrated approach to mechanism analysis", PhD thesis, Université de Liège, Belgium, Collection des Publications de la Faculté des Sciences Appliquées, No. 127.
4. Cardona, A. and Géradin, M. (1988), "A beam finite element nonlinear theory with finite rotations", Int. J. Num. Meth. Engng, Vol. 26, pp. 2403-38.
5. Cardona, A., Géradin, M. and Doan, D.B. (1991), "Rigid and flexible joint modeling in multibody dynamics using finite elements", Comput. Methods Appl. Mech. Engrg, Vol. 89, pp. 395-418.
6. Crisfield, M.A. (1981), "A fast incremental/iterative solution procedure that handles snapthrough",J. Comp. and Struct., Vol. 13, pp. 55-62.
7. Eriksson, A. (1993), "On improved predictions for structural equilibrium path evaluations", Int. J. Num. Meth. Engng, Vol. 36, pp. 201-20.
8. Felippa, C.A. (1984), "Dynamic relaxation under general increment control", in Liu, Belytschko and Park (Eds), Innovative Methods for Nonlinear Problems, Pineridge Press.
9. Fried, I. (1984), "Orthogonal trajectory accession to the nonlinear equilibrium curve", Comput. Methods Appl. Mech. Engrg, Vol. 47, pp. 283-97.
10. Keller, H.B. (1978), "Global homotopies and Newton methods", in de Boor and Golub (Eds), Recent Adv. Numerical Analysis, Academic Press, pp. 73-94.
11. Keller, H.B. (1983), "The bordering algorithm and path following near singular points of higher nullity", SIAM J. Sci. Stat. Comput., Vol. 4, pp. 573-82.
12. Le Tallec, P. (1995), "Numerical methods for nonlinear three-dimensional elasticity", preprint.
13. Lee, S.L., Manuel, F.S. and Rossow, E.C. (1968), "Large deflection and stability of elastic frames", ASCE J. Engng. Mech. Div., Vol. 94, pp. 521-33.
14. Park, K.C. (1982), "Family of solution algorithms for nonlinear structural analysis based on relaxation equations", Int. J. Num. Meth. Engng, Vol. 18, pp. 1337-47.
15. Ramm, E. (1982), "The Riks-Wempner approach - an extension of the displacement control method in nonlinear analysis", in Hinton, Owen and Taylor (Eds), Recent Advances in Nonlinear Computational Mechanics, Pineridge Press.
16. Rheinboldt, W.C. (1980), "Solution fields of nonlinear equations and continuation methods", SIAM - J. Numer. Anal., Vol. 17, pp. 221-37.
17. Rheinboldt, W.C. (1986), Numerical Analysis of Parametrized Nonlinear Equations, Volume of Lecture Notes in Math. Sci., Univ. Arkansas, J. Wiley.
18. Riks, E. (1972), "The application of Newton's method to the problem of elastic stability", J. Appl. Mech., Vol. 39, pp. 1060-6.
19. Riks, E. (1979), "An incremental approach to the solution of snapping and buckling problems", Int. J. Solids Structures, Vol. 15, pp. 529-51.
20. Rion, W.L. and van Brunt, V. (1990), "Differential geometry based homotopy continuation", Computers Chem. Engng., Vol. 14, pp. 889-900.
21. SAMCEF - Module d'Analyse de Mécanismes MECANO (Manuel d'Utilisation) 1994.
22. Schweizerhof, K.H. and Wriggers, P. (1986), "Consistent linearization for path following methods in nonlinear finite element analysis", Comput. Methods AppL Mech. Engrg, Vol. 59, pp. 261-79.
23. Simo, J.C. and Vu-Quoc, L. (1986), "A three-dimensional finite strain rod model, part {II}: computer aspects", Comput. Methods Appl. Mech. Engrg., Vol. 58, pp. 79-116.
24. Wriggers, P. and Simo, J.C. (1990), "A general procedure for the direct computation of turning and bifurcation points", Int. J. Num. Meth. Engng, Vol. 30, pp. 155-76.