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Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem
Author(s) -
Steinboeck A.,
Jia X.,
Hoefinger G.,
Rubin H.,
Mang H. A.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2317
Subject(s) - buckling , eigenvalues and eigenvectors , linearization , truss , mathematics , bifurcation , tangent , sensitivity (control systems) , stiffness , nonlinear system , stability (learning theory) , mathematical analysis , normal mode , vibration , structural engineering , geometry , engineering , computer science , physics , quantum mechanics , electronic engineering , machine learning
In addition to the determination of load levels at critical points of stability problems, frequently the postbuckling behavior is of interest. For non‐linear problems, the so‐called consistently linearized eigenvalue problem is a suitable tangent linearization method, which facilitates determination of stability limits. The solution process of the eigenproblem is significantly simplified by appropriate coordinate transformations. Within this process, characteristic shapes of eigenvalue curves allow identification of bifurcation buckling modes, snap‐through modes, and hilltop buckling modes. Mathematical properties of the eigenvalue curves are addressed and conclusions regarding the shape of postbuckling paths are drawn. Considerations also touch upon the conversion from imperfection sensitivity into insensitivity. The theoretical findings are corroborated by examples dealing with a von Mises truss and a similar discrete system, showing a remarkable postbuckling behavior such as a zero‐stiffness equilibrium path. For both systems, the same approach of stiffness increase allows conversion from imperfection sensitivity into insensitivity. Copyright © 2008 John Wiley & Sons, Ltd.