Ch. Schranz:
"Determination of Stability Limits of Elastic Structures by Means of Nonlinear Finite Element and Accompanying Linear Eigenvalue Analysis based on a Singularity-free Parameterization"; Institute for Strength of Materials, Vienna University of Technology, 1999.
Frequently, loss of stability is the reason for the failure of thin-walled structures. Calculation of stability limits, i.\,e., of bifurcation or snap-through points on nonlinear load-displacement paths of elastic struc For the computation of such stability limits the Finite Element Method is employed.In order to avoid an incremental-iterative analysis for determination of a stability limit, such a limit may be estimated initially, For the purpose of improving the quality of initial estimates of stability limits on nonlinear load-displacement paths, special acco They are based on the consistent linearization of the mathematical formulation of the energetic stability criterion for static, cons
Based on characteristic properties of the consistently linearized eigenvalue problem, higher-order estimation functions (in an asymp
A singularity-free parameterization of the consistently linearized eigenvalue problem enables to overcome or circumvent some problem No distinction between loss of stability by bifurcation buckling or snap-through is needed. Furthermore, it is possible to continue the analyses past the snap-through point.
The behavior of the eigenvalue curves for the singularity-free parameterization was studied by means of examples. The favorable properties of the eigenvalue curves are confirmed. This is the basis for further investigations.
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