scholarly journals Buckling Mode Jump at Very Close Load Values in Unattached Flat-End Columns: Theory and Experiment

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
H. Kalathur ◽  
T. M. Hoang ◽  
R. S. Lakes ◽  
W. J. Drugan
Keyword(s):  
Critical Load ◽  
Mode Shape ◽  
Structural Damping ◽  
Load Drop ◽  
Displacement Control ◽  
Buckling Mode ◽  
Buckling Instability ◽  
Structural Support ◽  
Full Contact ◽  
Large Hysteresis

Buckling of compressed flat-end columns loaded by unattached flat platens is shown, theoretically and experimentally, to occur first at the critical load and associated mode shape of a built-in column, followed extremely closely by a second critical load and different mode shape characterized by column end tilt. The theoretical critical load for secondary or end tilt buckling for a column geometry tested is shown to be only 0.13% greater than the critical load for primary buckling, in which the ends are in full contact with the compression platens. The experimental value is consistent with this theoretical one. Interestingly, under displacement control, the first buckling instability is characterized by a smoothly increasing applied load, whereas the closely following second instability causes an abrupt and large load drop (and hence exhibits incremental negative stiffness). The end tilt buckling gives rise to large hysteresis that can be useful in structural damping but that is nonconservative and potentially catastrophic in the context of design of structural support columns.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

scholarly journals Numerical Simulation of Buckling and Post-Buckling Behavior of a Central Notched Thin Aluminum Foil with Nonlinearity in Consideration

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 582 ◽  
Author(s):  
Mahdieh Shahmardani ◽  
Per Ståhle ◽  
Md Shafiqul Islam ◽  
Sharon Kao-Walter
Keyword(s):  
Mode Shape ◽  
Tensile Loading ◽  
Width Ratio ◽  
Plastic Behavior ◽  
Yield Limit ◽  
Buckling Mode ◽  
Buckling Stress ◽  
Buckling Behavior ◽  
Sheet Width ◽  
Post Buckling

In thin notched sheets under tensile loading, wrinkling appears on the sheet surface, specifically around the cracked area. This is due to local buckling and compression stresses near the crack surfaces. This study aims to numerically study the buckling behavior of a thin sheet with a central crack under tension. A numerical model of a notched sheet under tensile loading is developed using the finite element method, which considers both material and geometrical nonlinearity. To overcome the convergence problem caused by the small thickness-to-length/width ratio and to stimulate the buckling, an imperfection is defined as a small perturbation in the numerical model. Both elastic and elasto-plastic behavior are applied, and the influence of them is studied on the critical buckling stress and the post-buckling behavior of the notched sheet. Numerical results for both elastic and elasto-plastic behavior reflect that very small perturbations need more energy for the activation of buckling mode, and a higher buckling mode is predominant. The influences of different parameters, including Poisson’s ratio, yield limit, crack length-to-sheet-width ratio, and the sheet aspect ratio are also evaluated with a focus on the critical buckling stress and the buckling mode shape. With increase in Poisson’s ratio. First, the critical buckling stress reduces and then remains constant. A higher yield limit results in increases in the critical buckling stress, and no change in the buckling mode shape while adopting various crack length-to-sheet-width ratios, and the sheet aspect ratio changes the buckling mode shape.

Buckling of a spherical shell embedded in an elastic medium loaded by a far-field hydrostatic pressure

2001 ◽  
Vol 36 (6) ◽  
pp. 535-544 ◽  
Author(s):  
S-L Fok ◽  
D. J Allwright
Keyword(s):  
Hydrostatic Pressure ◽  
Spherical Shell ◽  
Critical Load ◽  
Elastic Medium ◽  
Upper Bound ◽  
Mode Number ◽  
Elastic Buckling ◽  
Far Field ◽  
Buckling Mode ◽  
Geometric Constants

Elastic buckling of a spherical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure is analysed using the energy method together with a Rayleigh—Ritz trial function. For simplicity, only axisymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be small for the linear theory to be applicable. An expression is derived relating the pressure load to the buckling mode number, from which the upper-bound critical load can be determined. It is found that the presence of the surrounding elastic medium increases the critical load of the shell and the corresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typical values of material and geometric constants.

scholarly journals Stability analysis of steel frames according to Eurocode 3

2019 ◽  
Vol 68 (2) ◽  
pp. 145-163
Author(s):  
Sylwia Pogonowska-Płatek ◽  
Wojciech Dornowski
Keyword(s):  
Global Stability ◽  
Critical Load ◽  
Steel Frames ◽  
Quantitative Comparison ◽  
Order Effects ◽  
The Finite Element Method ◽  
Buckling Mode ◽  
Qualitative And Quantitative ◽  
Portal Frame ◽  
Eurocode 3

In the paper, the qualitative and quantitative comparison of EC3 methods to verify the global stability of the structure is presented. The steel portal frame subjected to varied loads is considered. The initial global sway imperfection and the initial local bow imperfections of member frame are taken into account. The sensitivity of a structure to the 2nd order effects is assessed indirectly using the elastic critical load. The elastic critical load of a frame is calculated according to the buckling mode. The 2nd order effects are taken into account using the finite element method. Keywords: second order effects, steel frame, global stability, critical load.

EFFECT OF SUPPORT STIFFNESS ON STABILITY OF SHALLOW ARCHES

2010 ◽  
Vol 10 (05) ◽  
pp. 1099-1110 ◽  
Author(s):  
JIANGUO CAI ◽  
JIAN FENG
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
Virtual Work ◽  
Stiffness Coefficient ◽  
Rotational Stiffness ◽  
Initial Stiffness ◽  
Buckling Mode ◽  
Concentrated Load ◽  
Shallow Arches ◽  
Bifurcation Buckling

The nonlinear behavior and in-plane stability of parabolic shallow arches with elastic rotational supports are investigated. A central concentrated load is applied to create the compression in the supports. Nonlinear buckling analysis based on the virtual work formulation is carried out to obtain the critical load for both symmetric snap-through buckling and anti-symmetric bifurcation buckling. It is found that the effect of rotational stiffness of the elastic supports on the critical loads is significant. The critical load increases as either the initial stiffness coefficient α or the stiffening rate β increases. The effect of the stiffening rate β on the critical loads decreases, as the initial stiffness coefficient α increases. In addition, the influence of rotational stiffness on the bifurcation buckling is larger than that on the snap-through buckling. The limit of the geometric parameter λ between the bifurcation and snap-through buckling modes also increases with the increase in the stiffening rate β. In addition, the snap-through buckling mode governs the buckling of the arch with larger stiffening rates.

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