Remarkable postbuckling paths analyzed by means of the consistently linearized eigenproblem

Abstract

SUMMARYIn 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.

Hilltop Buckling as the a and O in Sensitivity Analysis of the Initial Postbuckling Behavior of Elastic Structures

“…For class I, (76) requires (Steinboeck et al 2008a) , 1 · . , d λ , and 4 λ ) as functions of κ which denotes the stiffness of an elastic spring attached to the structure, details of which will be given in Chapter 7 (Numerical investigation).…”

“…6 shows a planar, static, conservative system with two degrees of freedom. The description of this system closely follows (Steinboeck et al 2008a) where additional details can be found. Both rigid bars, 1 and 2 have the same length L and in the non-buckled state they are in-line.…”

“…6. Pin-jointed two-bar system (Steinboeck et al 2008a) 10 ( /2, /2), u ∈ −π π + µ ∈ R and + κ ∈ R are parameters that can be varied in order to achieve qualitative changes of the system. However, in this work, only κ was modified.…”

“…It can be realized by appropriately tuning a set of design parameters of a structure (Steinboeck et al 2008a).…”

Probabilistic buckling analysis of the beam steel structures subjected to fire by the stochastic finite element method

“…The other works were more focused on computational methods and issues, where geometrical imperfections of the uncertain nature are included (Papadopoulos et al [7]). Also, the very interesting and challenging problems of the post-buckling paths were analyzed (Steinböck et al [8]). However, determination of the higher probabilistic moments of both structural response and buckling modes is still very rare and the classical Monte-Carlo simulation is preferred.…”