scholarly journals Cellular buckling from mode interaction in I-beams under uniform bending

2011 ◽  
Vol 468 (2137) ◽  
pp. 245-268 ◽  
Author(s):  
M. Ahmer Wadee ◽  
Leroy Gardner
Keyword(s):  
Variational Principles ◽  
Structural Strength ◽  
Local Buckling ◽  
Numerical Continuation ◽  
Mode Interaction ◽  
Lateral Torsional Buckling ◽  
Post Buckling ◽  
Strength And Stiffness ◽  
First Time ◽  
Differential And Integral Equations

Beams made from thin-walled elements, while very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on variational principles for the ubiquitous I-beam with thin flanges under uniform bending is presented. The resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post-buckling range can be portrayed. The interaction between global lateral-torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling (snaking) being predicted theoretically for the first time. Solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling.

scholarly journals Cellular buckling in stiffened plates

2014 ◽  
Vol 470 (2168) ◽  
pp. 20140094 ◽  
Author(s):  
M. Ahmer Wadee ◽  
Maryam Farsi
Keyword(s):  
Analytical Model ◽  
Analytical Approach ◽  
Laboratory Experiments ◽  
Variational Principles ◽  
Numerical Continuation ◽  
Mode Interaction ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Global Mode ◽  
Differential And Integral Equations

An analytical model based on variational principles for a thin-walled stiffened plate subjected to axial compression is presented. A system of nonlinear differential and integral equations is derived and solved using numerical continuation. The results show that the system is susceptible to highly unstable local–global mode interaction after an initial instability is triggered. Moreover, snap-backs in the response showing sequential destabilization and restabilization, known as cellular buckling or snaking, arise. The analytical model is compared with static finite element (FE) models for joint conditions between the stiffener and the main plate that have significant rotational restraint. However, it is known from previous studies that the behaviour, where the same joint is insignificantly restrained rotationally, is captured better by an analytical approach than by standard FE methods; the latter being unable to capture cellular buckling behaviour even though the phenomenon is clearly observed in laboratory experiments.

scholarly journals STRAIN-STRESS EXPERIMENTAL BEHAVIOUR OF TAPERED COLUMNS IN SINGLE-SPAN FRAMES/TRAPECINIŲ KOLONŲ VIENANAVIUOSE RĖMUOSE DEFORMACIJŲ-ĮTEMPIŲ BŪVIS

2000 ◽  
Vol 6 (2) ◽  
pp. 82-86 ◽  
Author(s):  
Vaidotas Šapalas
Keyword(s):  
Local Buckling ◽  
Longitudinal Axis ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Perpendicular Plane ◽  
Strain Stress ◽  
Tapered Columns ◽  
The Stability ◽  
Experimental Behaviour ◽  
Tapered Column

Two single-span frame tests were carried out. The width of frame is 6m, column's height 4.17m. Frame supports are pinned. Connection between column and beam is rigid. Beam of the frame was loaded with two vertical and one horizontal loads. The stability of tappered columns was analysed in frame plane and in perpendicular plane, according to [1] and [2] methods. All deflections were calculated taking into account support movements. During the first frame test R1-1 the tapered column collapsed at the load 2V=400kN and H=200 kN (vertical and horizontal loads). During the second test R1-2 the tapered column collapsed at the load 2V=390 kN and H=175 kN. In both tests columns collapsed in lateral-torsional buckling way. Because the column's web is very thin at the load 2V=300 kN and H=150 kN the column's web achieved local buckling. But the column was still carrying the load. During both tests at the load 2V=300 kN and H=150 kN the column began to twist in the middle of its height about the longitudinal axis and to bend about the weak axis. In test R1-1, the vertical experimental deflection (in point 6, see Fig 1 a) is about 17.5% smaller than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 11.6% smaller than the theoretical one. In test R1-2, vertical experimental deflection (in point 6, see Fig 1 a) is about 21.1% bigger than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 29.6% smaller than the theoretical one. In test R1-1, an experimental compression stresses in section A-A (see Fig 2) are about 11.2% smaller than the theoretical one. Experimental tension stresses in section A-A are about 8.65% smaller than the theoretical one. In test R1-2, an experimental compression stresses in section A-A is about 0.43% bigger than the theoretical one. An experimental tension strain in section A-A is about 1.73% smaller than the theoretical one.

Analysis on Secondary Effect of Corrugated Webs in Steel-Concrete Composite Beams

2011 ◽  
Vol 255-260 ◽  
pp. 596-601 ◽  
Author(s):  
Ke Bin Jiang ◽  
Yong Ding ◽  
Ya Wen Liu ◽  
Feng Zheng
Keyword(s):  
Local Buckling ◽  
Secondary Effect ◽  
Shape Parameters ◽  
Corrugated Webs ◽  
Analytical Work ◽  
Corrugated Web ◽  
Finite Element Package ◽  
First Time ◽  
Numerical And Analytical Methods ◽  
Good Agreement

Some secondary effect introduced by corrugated configuration of corrugated web was studied and formulas were proposed. The deduction for these formulas was resolved into two steps. Step I: to solve the behavior of whole corrugated web by considering it as an orthotropic plate; Step II: to solve the secondary effect according to the shape parameters of corrugation based on the result of Step I. Subsequently, a numerical experiment was designed to validate the analytical work with the help of finite element package ANSYS taking material nonlinearity into consideration. The results obtained from numerical and analytical methods show good agreement. It indicates that the formulas proposed in this paper are convenient and efficient. This research deals with this secondary effect for the first time; more studies are needed for the effect on local buckling of corrugated webs.

Design Sensitivity of Buckled Thin-Walled Composite Structural Elements

1997 ◽  
Vol 50 (11S) ◽  
pp. S3-S10 ◽  
Author(s):  
Leonel I. Alma´nzar ◽  
Luis A. Godoy
Keyword(s):  
Volume Fraction ◽  
Local Buckling ◽  
Design Sensitivity ◽  
Transverse Load ◽  
Design Parameters ◽  
Structural Elements ◽  
Perturbation Expansions ◽  
Cross Sectional ◽  
Buckling Loads ◽  
Post Buckling

This paper presents a theory and applications to account for changes in the fundamental, buckling, and post-buckling states when design parameters of a composite material are modified. The influence of micro-mechanical parameters (the volume fraction and the fiber orientation) and of cross-sectional dimensions is investigated. A numerical example for columns made of composite materials is presented. Sensitivity is studied for local buckling loads. Explicit expressions are obtained for the sensitivities in the form of perturbation expansions. A beam under transverse load is also investigated, and geometric design parameters employed to investigate sensitivity. The information from the sensitivity analysis can be used to improve a design by modification of the buckling load.

Enhancing Broadband Vibration Energy Suppression Using Local Buckling Modes in Constrained Metamaterials

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Ryan L. Harne ◽  
Daniel C. Urbanek
Keyword(s):  
Vibration Suppression ◽  
Local Buckling ◽  
Engineering Systems ◽  
Buckling Modes ◽  
Dynamic Mass ◽  
Stiffness Reduction ◽  
Elastomeric Dampers ◽  
Practical Engineering ◽  
Post Buckling ◽  
Relative Change

Studies on dissipative metamaterials have uncovered means to suppress vibration and wave energy via resonant and bandgap phenomena through such engineered media, while global post-buckling of the infinitely periodic architectures is shown to tailor the attenuation properties and potentially magnify the effective damping effects. Yet, despite the promise suggested, the practical aspects of deploying metamaterials necessitates a focus on finite, periodic architectures, and the potential to therefore only trigger local buckling features when subjected to constraints. In addition, it is likely that metamaterials may be employed as devices within existing engineering systems, so as to motivate investigation on the usefulness of metamaterials when embedded within excited distributed or multidimensional structures. To illuminate these issues, this research undertakes complementary computational and experimental efforts. An elastomeric metamaterial, ideal for embedding into a practical engineering structure for vibration control, is introduced and studied for its relative change in broadband damping ability as constraint characteristics are modified. It is found that triggering a greater number of local buckling phenomena provides a valuable balance between stiffness reduction, corresponding to effective damping magnification, and demand for dynamic mass that may otherwise be diminished in globally post-buckled metamaterials. The concept of weakly constrained metamaterials is also shown to be uniformly more effective at broadband vibration suppression of the structure than solid elastomeric dampers of the same dimensions.

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