Marcello Pignataro

Asymmetric interactive buckling of thin-walled columns with initial imperfections

Abstract In this paper the effect of the interaction between two or more simultaneous buckling modes on the postbuckling behaviour of uniformly compressed thin-walled members (TWM) is analysed by means of the general theory of elastic stability. The analysis is restricted to third-order terms of the energy expansion and therefore can be fruitfully applied to the investigation of structures with asymmetric postbuckling behaviour only. Initial imperfection effect is taken into account. A simplified procedure is suggested for solving the nonlinear equations relative to the evaluation of the bifurcated paths. By using the finite strip method an extensive parametric analysis is performed. It is found that when the flexural-torsional (FT) buckling interacts with a local symmetric and antisymmetric mode, sensitivity to initial inperfections is remarkable and is comparable to the one arising from the interaction between the Euler (E) and any local buckling.

On the effect of the local overall interaction on the postbuckling of uniformly compressed channels

Abstract On the basis of the general theory of elastic stability due to Koiter, postbuckling analysis of simply supported channels under uniform compression is performed. Attention is essentially focused on local/eularian and local/flexural-torsional simultaneous bucklin modes interaction. The column is treated as a plate assemblage. Linearized expressions for the displacement field are employed while assuming strain-displacements relationships that are linear for the curvatures and up to second order terms for the in-plane strains. The total potential energy is hence written up to third order terms in order to investigate asymmetric buckling phenomena. A discrete model is developed through an automatic procedure of algebraic manipulation, and an extensive parametric analysis is performed. After determining the range of geometric parameters which characterize different types of interaction, it is found that in the postbuckling range the local/eulerian interaction is more dangerous than the local/flexural-torsional one, due to the column higher imperfection sensitivity.

Three-dimensional vibrations of tethered satellite systems

The three-dimensional free vibrations of an orbiter-towed tethered satellite system with nominally vertical tether during stationkeeping phase are studied analytically. The tether is modeled as an elastic continuum with mass and the orbiter and the subsatellite as two concentrated masses. The linearized equations of motion with variable coefficients are solved by means of a perturbation technique. An analysis of the order of magnitude of the different terms involved permits evaluation of the coupling between longitudinal and transversal in-plane vibrations coming to an approximate closed-form solution of the eigenvalue problem.

On nonlinear beam models from the point of view of computational post-buckling analysis

Abstract The buckling and post-buckling analysis of elastic planar frames is considered and the use of geometrically exact beam models is thereby advocated. It is shown that usual technical beam models fail to predict correctly the curvature of the post-buckling curve at bifurcation even for standard problems of elastic stability theory. It is also argued that versatile and efficient computational procedures for bifurcation analysis of general planar frames are to be based on unconstrained beam models. Some remarks on finite element representation of nonlinear beam models are passed in conclusion.

Post-buckling analysis of corrugated panels in the presence of multiple interacting modes

In this paper, the effect of the interaction between one overall buckling mode and many local modes on the post-buckling behaviour of uniformly compressed corrugated sheets is analysed by means of the general theory of elastic stability. The analysis is restricted to third order terms of the energy expansion and, therefore, it can be fruitfully applied to the investigation of structures with asymmetric post-buckling behaviour only. Initial imperfection effect is taken into account. By using the finite strip method, an extensive parametric analysis is performed.

A Parametric Postbuckling Analysis of an Asymmetric Two-Bar Frame

ABSTRACT ABSTRACT The modified potential energy approach of flexurally elastic, axially, and shear undeformable beams is employed to investigate the buckling and (asymmetric) postbuckling behavior of the two-bar frame which was experimentally tested by Roorda in 1965. Following a Koiter-type energy approach, a suitable perturbation formulation is, derived from a hybrid functional which is obtained by adding to the potential energy certain extra terms which account for the energy associated with the internal joint forces acting on the beam. In this way the nonlinear constraints expressing continuity of displacement across the joints are accommodated by introducing joint forces acting as Lagrangian multipliers. The inherent simplicity of the model herein proposed allows a thorough parametric analysis to be performed without undue complications up to and including fourth-order terms. The general trend compares favorably with the experimental results. Previous analytical results limited to a third-order analy...

Bifurcation analysis of a circular arch under hydrostatic pressure

SommarioNel presente lavoro si studia la biforcazione di un arco circolare soggetto a pressione idrostatica nel campo elastico facendo uso di un modello di trave cinematicamente esatto. Le corrispondenti equazioni di campo nonlineari vengono risolte utilizzando una tecnica perturbativa. Vengono riportati in diagramma una serie di risultati numerici riguardanti la dipendenza del carico critico e del parametro di carico del secondo ordine dai parametri geometrici e meccanici.SummaryIn this paper the bifurcation analysis of a circular arch under hydrostatic pressure in the elastic postbuckling range is performed by means of a geometrically exact beam model. The relevant nonlinear field equations are solved by utilizing a perturbation technique. A number of numerical results regarding the dependence of the critical load and the second order load parameter on the geometric and mechanical parameters are plotted in diagrams.

On the proper treatment of axial and shear undeformability constraints in post-buckling analysis of beams

Zusammenfassung Das Modell des nichtausdehnbaren und unter Schub nichtverformbaren Tragers wird betrachtet um das Verhalten schlanker Bauwerke nach der Knickung zu untersuchen. Innerhalb des Rahmens einer Koiterschen Energiemethode wird eine best geeignete Perturbationsformulierung von einem gemischten Funktional hergeleitet. Letzteres erhalt man indem zur potentiellen Energie einige besondere Glieder addiert werden, die der von den inneren Kraften an den Tragerenden herruhrenden nichtlinearen Energie Rechnung tragen. Die Losung eines einfachen Tragerproblems wird zur Illustration angegeben.

Symmetric Bifurcation of Plane Frames through a Modified Potential Energy Approach

Abstract The modified potential energy approach to the nonlinear analysis of slender elastic beams is employed to investigate the buckling and postbuckling behavior of two symmetric plane frames, namely a hinged portal frame and a hinged two-bar frame, The beams are assumed to be inextensible and shear undeformable. The “hybrid” functional on which the present analysis is based according to a Koiter-type energy approach is obtained from the total potential energy functional by adding extra terms which account for the nonlinear energy associated with the internal forces applied at the beam ends. Thus the nonlinear constraints on the potential energy (expressed in terms of the cross-section rotation φ only), which are associated with the continuity condition relative to the axial and lateral displacement across the joints, are accounted for by introducing the corresponding joint forces as Lagrangian multipliers. The inherent simplicity of the proposed beam model facilitates the postbuckling analysis of the ...

Coupled instabilities in thin-walled beams: a qualitative approach

A direct one-dimensional beam model is adopted. Kinematics is described by axis displacement, rigid rotation of the cross-section and an average measure of warping. Mechanical power is introduced as a linear functional of the kinematic descriptors and their first derivatives, hence mechanical actions naturally result as their duals. In particular, the bi-shear and bi-moment turn out to be quantities spending power on the warping and on its first derivative, respectively. Assuming as basic postulate the balance between external and internal power, local equilibrium equations for the mechanical actions are obtained. In addition to the standard inner constraint of shear indeformability, a linear relationship between twist and warping is assumed. To obtain field equations in terms of displacements, non-linear hyperelastic constitutive relations are formulated. Two coupled bifurcations for axially loaded beams are examined: in the first case no coupling occurs, in the second the beam can be sensitive to initial imperfections.