Abstract
Newton’s method or its modification is undoubtedly one of the most popular method for the solution of problems of nonlinear structural analysis. However, in spite of its high efficiency, because of unsuccessful convergence or — at times — even divergence, researchers are increasingly recognizing the need for making these algorithms robust and globally convergent. But even so, globally convergent quasi-Newton algorithm, in the absence of highly specialized response parameter incrementation features, are ineffective in the neighborhood of limit points, where the Jacobian of the nonlinear equations ceases to be positive definite.
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References
P. Abbott, “Computing solution arcs of nonlinear equation with a parameter”, The Computer Journal, 23, (1980) 85–89.
F. Coleman and A. Hulbert, “A direct active set algorithm for large sparse quadratic programs with simple bounds”, Mathematical Programming, 45, (1989) 373–406.
W. Dinkelbach, “On nonlinear fractional programming”, Management Science, 13, (1967) 492–498.
N. I. M. Gould, “On practical conditions for the existence and uniqueness of solution to the general equality quadratic programming problem”, Mathematical Programming, 32, (1985) 90–99.
R. Jagannathan, “On some properties of programing problems in parametric form pertaining to fractional programming”, Management Science, 12, (1966) 609–615.
Kamat and L.T. Watson, “A quasi-Newton versus a homotopy method for nonlinear structural analysis”, Computers & Structures, 17, (1983) 579–585.
B. Noble, Applied linear algebra, ( Prentice-Hall, New Jersey, 1969 ).
E. Riks, “An incremental approach to the solution of snapping and buckling problems”, Int. J. Solids Structures, 15, (1979) 529–551.
S. Schaible, “Fractional programming. II. On Dinkelbach’s Algorithm.”, Management Science, 22, (1976) 868–873.
I. Shavitt, C. F. Bender, A. Pipano and R. P. Hosteny, “The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvectors of very large matrices”, J. Comp. Phys., 11, (1973) 90–108.
L. T. Watson, M. P. Kamat and M. H. Reaser, “A robust hybrid algorithm for computing multiple equilibrium solutions”, Engineering Computation, 2, (1985) 30–34.
G. A. Wempner, “Discrete approximations related to nonlinear theories of solids”, Int. J. Solid Structures, 7, (1971) 1581–1599.
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© 1994 Springer-Verlag Berlin Heidelberg
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Csébfalvi, A., Csébfalvi, G. (1994). Post-buckling analysis of frames by a hybrid path-following method. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_24
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DOI: https://doi.org/10.1007/978-3-642-46802-5_24
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