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On the influence of the prebuckling behavior of elastic structures on their initial postbuckling behavior
Author(s) -
Mang Herbert A.,
Höfinger Gerhard,
Jia Xin
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110451
Subject(s) - monotonic function , eigenvalues and eigenvectors , mathematics , context (archaeology) , dimensionless quantity , torsion (gastropod) , tangent , stiffness , mathematical analysis , physics , mechanics , thermodynamics , geometry , medicine , paleontology , surgery , quantum mechanics , biology
Depending on whether or not bending and/or torsion are part of the prebuckling deformation state of elastic structures, the initial postbuckling behavior is either completely general or characterized by specific restrictions [1]. In this context, the term ‘completely general’ means (a) no restriction to monotonic improvement or deterioration of the initial postbuckling behavior in consequence of a monotonic change of a design parameter and (b) the impossibility of ‘zero‐stiffness postbuckling’ characterized by a postbuckling path at a constant load level. The mathematical reason for restrictions of the postbuckling behavior is a constraint condition for the eigenvector ν 1 appearing in the classical static stability condition 1$$\tilde {\bf K}_T \cdot {\bf \nu}_1 = {\bf 0}$$ where $\tilde {\bf K}_T$ denotes the tangent stiffness matrix [2]. This condition contains the first and the second derivative of $\tilde {\bf K}_T$ with respect to the dimensionless load parameter λ. The theoretical findings will be verified numerically. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)