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Equilibrium subsets for multi-parametric structural analysis
1997 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 140, no 3-4, 305-327 p.Article in journal (Refereed) Published
Abstract [en]

The paper discusses multi-parametric formulations for structural equilibrium problems. By seeking subsets of equilibrium states, which also fulfil extra conditions, more detailed information on structural behaviour can be obtained. These conditions can be related to analyses of, e.g. critical behaviour, imperfections or optimisation. The paper shows a general problem setting and some interesting augmentations. A solution method for the special case of one-dimensional equilibrium subsets is described. The algorithm is a generalisation of a path-following algorithm, where new methods are developed for the evaluation of the path tangent, and for the isolation of special solution points. Examples are used to show the properties and the possibilities of the ideas.

Place, publisher, year, edition, pages
1997. Vol. 140, no 3-4, 305-327 p.
Keyword [en]
Algorithms, Mathematical models, Problem solving, Set theory, Equilibrium subsets, Path following algorithm, Structural analysis
National Category
Applied Mechanics
URN: urn:nbn:se:kth:diva-117946OAI: diva2:603969

References: Pacoste, C., Eriksson, A., Element behaviour in post-critical plane frame analysis (1995) Comput. Methods Appl. Mech. Engrg., 125, pp. 319-343; Crisfield, M.A., New solution procedures for linear and non-linear finite element analysis (1986) The Mathematics of Finite Elements and Applications V, , J. Whitman ed., Academic Press, London; Rheinboldt, W.C., Riks, E., Solution techniques for nonlinear finite element equations (1983) State-of-the-Art Surveys on Finite Element Technology, , A. K. Noor and W. D. Pilkey, eds., ASME; Rheinboldt, W.C., (1986) Numerical Analysis of Parameterized Nonlinear Equations, , Wiley, New York; Allgower, E.L., Georg, K., (1990) Numerical Continuation Methods. An Introduction, , Springer, Berlin; Riks, E., The application of Newton's method to the problem of elastic stability (1972) J. Appl. Mech. Trans. ASME, 39, pp. 1060-1065; Crisfield, M.A., A fast incremental/iterative solution procedure that handles snap-through (1981) Comput. Struct., 13, pp. 55-62; Eriksson, A., On linear constraints for Newton-Raphson corrections and critical point searches in structural F.E. problems (1989) Int. J. Numer. Methods Engrg., 28, pp. 1317-1334; Chan, T.F., Resasco, D.C., Generalized deflated block-elimination (1986) SIAM J. Numer. Anal., 23, pp. 913-924; Thompson, J.M.T., Hunt, G.W., (1984) Elastic Instability Phenomena, , John Wiley, London; Sewell, M.J., On the connexion between stability and the shape of the equilibrium surface (1966) J. Mech. Phys. Solids, 14, pp. 203-230; Rheinboldt, W.C., On the computation of multi-dimensional solution manifolds of parameterized equations (1988) Numer. Math., 53, pp. 165-181; Rammerstorfer, F.G., Fischer, D.F., Parameter sensitivity of nonlinear structures concerning stability limit (1981) Non-linear Finite Element Analysis in Structural Mechanics, , Wunderlich et. al., eds., Springer, Berlin; Jepson, A., Spence, A., Folds in solutions of two parameter systems and their calculation, Part I (1985) SIAM J. Numer. Anal., 22, pp. 347-368; Eriksson, A., Fold lines for sensitivity analyses in structural instability (1994) Comput. Methods Appl. Mech. Engrg., 114, pp. 77-101; Huitfeldt, J., Prediction of critical boundaries in two-parameter nonlinear eigenvalue problems (1992) Numerical Analysis Group, Report 20, , Chalmers University, Göteborg; Huitfeldt, J., Nonlinear eigenvalue problems - Prediction of bifurcation points and branch switching (1991) Numerical Analysis Group, Report 17, , Chalmers University, Göteborg; Eriksson, A., (1994) Generalized Path-following for Structural Criticality, , K. Bell, ed., NSCM VII, Abstracts, Dept. Struct. Engrg., The Norwegian Inst. Techn., Trondheim; Rheinboldt, W.C., Computation of critical boundaries on equilibrium manifolds (1982) SIAM J. Numer. Anal., 19, pp. 653-669; Thom, R., (1988) Structural Stability and Morphogenesis, , Addison-Wesley, Redwood City; Pacoste, C., (1993) On the Application of Catastrophe Theory to Stability Analyses of Elastic Structures, , (Dr. Thesis), Dept. Struct. Engrg., Royal Inst. Techn., Stockholm; Wriggers, P., Wagner, W., Miehe, C., A quadratically convergent procedure for the calculation of stability points in finite element analyses (1988) Comput. Methods Appl. Mech. Engrg., 70, pp. 329-347; Wriggers, P., Simo, J.C., A general procedure for the direct computation of turning and bifurcation points (1990) Int. J. Numer. Methods Engrg., 30, pp. 155-176; Griewank, A., Reddien, G.W., Characterization and computation of generalized turning points (1984) SIAM. J. Numer. Anal., 21, pp. 176-185; Dai, R.-X., Rheinboldt, W.C., On the computation of manifolds of foldpoints for parameter-dependent problems (1990) SIAM. J. Numer. Anal., 27, pp. 437-446; Rabier, P.J., Reddien, G.W., Characterization and computation of singular points with maximum rank deficiency (1986) SIAM. J. Numer. Anal., 23, pp. 1040-1051; Dai, R.-X., (1988) Characterization and Computation of Foldsets for Parameter-dependent Equations, , Ph.D. Thesis, University of Pittsburgh; Littbrand, G., Lidström, T., (1995) Implementation of an Algorithm for Generalized Structural Path Following, , Techn. Rep. 1995:10, Dept. Struct. Engrg., Royal Inst. Techn., Stockholm; Eriksson, A., Kouhia, R., On step size adjustments in structural continuation problems (1995) Comput. Struct., 55, pp. 495-506; Kouhia, R., Mikkola, M., Tracing the equilibrium path beyond simple critical points (1989) Int. J. Numer. Methods Engrg., 28, pp. 2923-2941; Olhoff, N., Rasmussen, J., Lund, E., Method of exact numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analyses (1993) Mech. Struct. Mach., 28, pp. 1-66; Eriksson, A., Pacoste, C., On parameter investigations of instabilities in reticulated space frames (1993) Proc. 4th Int. Conf. on Space Structures, , Guildford, UK; Bergan, P.G., Solution algorithms for nonlinear structural problems (1980) Comput. Struct., 12, pp. 497-509; Pietrzak, J., Vector optimization of structures prone to instability (1992) Comput. Struct., 45, pp. 813-816; Eriksson, A., Derivatives of the tangential stiffness matrices for equilibrium path descriptions (1991) Int. J. Numer. Methods Engrg., 32, pp. 1093-1113; Lidström, T., (1996) Computational Methods for Finite Element Instability Analyses, , (Dr. Thesis), Dept. Struct. Engrg., Royal Inst. Techn., Stockholm

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