MODE JUMPING AND ATTRACTIVE PATHS IN MULTIMODE ELASTIC BUCKLING

This paper summarizes a part of the first author's Ph.D. Thesis completely devoted to multimode elastic buckling within an FEM strategy. The theoretical arguments unfold among critical points on radial paths (the unique post-critical paths variationally defined), algebraic characterizations, proposition demonstrations and so on, by aiming to prove that the complexity of the phenomenon of multimode buckling (secondary bifurcations, post-critical attractive paths) can be theoretically explained. © 1997 by John Wiley & Sons, Ltd.

[1]  Ahmed K. Noor,et al.  Recent advances in reduction methods for instability analysis of structures , 1983 .

[2]  Kenneth C. Johns.  Imperfection sensitivity of coincident buckling systems , 1974 .

[3]  J. M. T. Thompson,et al.  Discrete branching points in the general theory of elastic stability , 1965 .

[4]  A. Di Carlo,et al.  On nonlinear beam models from the point of view of computational post-buckling analysis , 1982 .

[5]  Raffaele Casciaro,et al.  Asymptotic post-buckling analysis of rectangular plates by HC finite elements , 1995 .

[6]  W. T. Koiter.  Current Trends in the Theory of Buckling , 1976 .

[7]  Franco Brezzi,et al.  How to get around a simple quadratic fold , 1986 .

[8]  Ginevra Salerno,et al.  HOW TO RECOGNIZE THE ORDER OF INFINITESIMAL MECHANISMS - A NUMERICAL APPROACH , 1992 .

[9]  D. Ho.  Higher order approximations in the calculation of elastic buckling loads of imperfect systems , 1971 .

[10]  Ginevra Salerno,et al.  Finite element asymptotic analysis of slender elastic structures: A simple approach , 1992 .

[11]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[12]  D. Ho,et al.  The influence of imperfections on systems with coincident buckling loads , 1972 .

[13]  D. Ho,et al.  Buckling load of non-linear systems with multiple eigenvalues , 1974 .

[14]  A. H. Chilver.  Coupled modes of elastic buckling , 1967 .

[15]  Hans H. Bleich,et al.  Buckling strength of metal structures , 1952 .

[16]  K. Bathe,et al.  An accelerated subspace iteration method , 1980 .

[17]  A. Noor.  Recent advances in reduction methods for nonlinear problems. [in structural mechanics , 1981 .

[18]  A. van der Neut,et al.  The interaction of local buckling and column failure of thin-walled compression members , 1969 .