scholarly journals On the buckling of an elastic holey column

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170477 ◽  
Author(s):  
C. G. Johnson ◽  
U. Jain ◽  
A. L. Hazel ◽  
D. Pihler-Puzović ◽  
T. Mullin
Keyword(s):  
Critical Strain ◽  
Theoretical Study ◽  
Regular Array ◽  
Buckling Mode ◽  
Buckling Modes ◽  
Euler Buckling ◽  
Circular Holes ◽  
Regular Line ◽  
Slender Columns ◽  
Fitting Parameters

We report the results of a numerical and theoretical study of buckling in elastic columns containing a line of holes. Buckling is a common failure mode of elastic columns under compression, found over scales ranging from metres in buildings and aircraft to tens of nanometers in DNA. This failure usually occurs through lateral buckling, described for slender columns by Euler’s theory. When the column is perforated with a regular line of holes, a new buckling mode arises, in which adjacent holes collapse in orthogonal directions. In this paper, we firstly elucidate how this alternate hole buckling mode coexists and interacts with classical Euler buckling modes, using finite-element numerical calculations with bifurcation tracking. We show how the preferred buckling mode is selected by the geometry, and discuss the roles of localized (hole-scale) and global (column-scale) buckling. Secondly, we develop a novel predictive model for the buckling of columns perforated with large holes. This model is derived without arbitrary fitting parameters, and quantitatively predicts the critical strain for buckling. We extend the model to sheets perforated with a regular array of circular holes and use it to provide quantitative predictions of their buckling.

scholarly journals Effects of plies orientations and initial geometric imperfections on buckling strength of a composite stiffened panel

2018 ◽  
Vol 191 ◽  
pp. 00008
Author(s):  
Ikram Feddal ◽  
Abdellatif Khamlichi ◽  
Koutaiba Ameziane
Keyword(s):  
Stiffened Panel ◽  
Buckling Mode ◽  
Element Analysis ◽  
Geometric Imperfections ◽  
Stiffened Panels ◽  
Specific Strength ◽  
Euler Buckling ◽  
Buckling Behavior ◽  
Composite Stiffened Panel ◽  
Strength And Stiffness

The use of composite stiffened panels is common in several activities such as aerospace, marine and civil engineering. The biggest advantage of the composite materials is their high specific strength and stiffness ratios, coupled with weight reduction compared to conventional materials. However, any structural system may reach its limit and buckle under extreme circumstances by a progressive local failure of components. Moreover, stiffened panels are usually assembled from elementary parts. This affects the geometric as well as the material properties resulting in a considerable sensitivity to buckling phenomenon. In this work, the buckling behavior of a composite stiffened panel made from carbon Epoxy Prepregs is studied by using the finite element analysis under Abaqus software package. Different plies orientations sets were considered. The initial distributed geometric imperfections were modeled by means of the first Euler buckling mode. The nonlinear Riks method of analysis provided by Abaqus was applied. This method enables to predict more consistently unstable geometrically nonlinear induced collapse of a structure by detecting potential limit points during the loading history. It was found that plies orientations of the composite and the presence of geometric imperfections have huge influence on the strength resistance.

The Role of Adhesive in the Load Response of Adhesively Bonded Aluminum Hat Sections Under Axial Compression

2001 ◽  
Author(s):  
Jianping Lu ◽  
Golam M. Newaz ◽  
Ronald F. Gibson
Keyword(s):  
Compressive Strength ◽  
Plastic Collapse ◽  
Adhesively Bonded ◽  
Buckling Mode ◽  
Buckling Loads ◽  
Buckling Modes ◽  
Load Response ◽  
Peak Loads ◽  
Post Buckling

Abstract Aluminum hat section, either adhesively bonded or unbonded, experiences buckling, post buckling and plastic collapse when axially compressed. However, there exist obvious differences in the load response between the bonded and unbonded hat sections. Finite element eigenvalue buckling analysis is carried out to predict the buckling load and mode. Experiments show that when adhesively bonded hat sections begin to buckle there is a transformation from the first buckling mode to the higher ones, while the unbonded hat sections develop the post buckling based on the lowest buckling mode. The different buckling modes result in not only different buckling loads but different peak loads of the hat sections as well. Finally, the ultimate compressive strength formulae are proposed for the hat sections.

scholarly journals Elastic buckling of thin plate with circular holes in bending

2019 ◽  
Vol 136 ◽  
pp. 04043
Author(s):  
Guo Yanli ◽  
Song Xiaoqing ◽  
Li Xiao ◽  
Yao Xingyou ◽  
Xia Zhifan ◽  
...  
Keyword(s):  
Finite Element ◽  
Perforated Plate ◽  
Thickness Ratio ◽  
Thin Plates ◽  
Elastic Buckling ◽  
Buckling Mode ◽  
Element Analysis ◽  
Short Side ◽  
Finite Element Software ◽  
Circular Holes

Stress redistribution will occur around the hole for the perforated plate under bending, and the buckling mode of bending plate is changed, which makes the design of bending plate more complicated. The finite element software ABAQUS is used to establish the perforated plate under bending model, analyze the degree of influence of the plate aspect ratio, width-thickness ratio, size and position of the holes, meanwhile, the distance between holes is also discussed. The results show that the thickness of the plate size and width-thickness ratio have little influence on the elastic buckling performance of thin plates with holes in bending. As the size of the holes increase, the influence is greater, and there is a certain regularity. The opening position is closer to the short side of the plate, the buckling coefficient of plate will be significantly decreased. The effect is greater with the increase of opening size, the distance between holes have a safe value, the position of the opening is more obvious for the buckling of the bending plate. Finally, based on the data from finite element analysis, the proposed formula of buckling stability coefficient k for the bending perforated plate is given.

An Exploration of Buckling Modes and Deflection of a Fixed-Guided Beam

2010 ◽  
Author(s):  
Gregory L. Holst ◽  
Gregory H. Teichert ◽  
Brian D. Jensen
Keyword(s):  
Elliptic Integral ◽  
Large Deflections ◽  
Buckling Mode ◽  
Beam Shape ◽  
Buckling Modes ◽  
Buckling Behavior ◽  
Reaction Forces ◽  
Combined Models ◽  
Beam Bending ◽  
Bistable Mechanism

This paper explored the deflection and buckling of fixed-guided beams. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. One of the strengths of the model is its ability to accurately predict buckling behavior and the buckled beam shape. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed based on the equations for stress and strain and the buckling profile of the beam calculated with the elliptic integral solution. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force vs. displacement predictions of the model are compared to the experimental force vs. deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force vs. deflection data for each device. The paper’s main contributions include the addition of the axial buckling model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models may incorrectly predict a beam’s buckling mode unless unrealistic constraints are placed on the beam.

Elastic buckling of imperfect circular toroidal shells under external pressure

1998 ◽  
Vol 212 (3) ◽  
pp. 197-209 ◽  
Author(s):  
G D Galletly
Keyword(s):  
External Pressure ◽  
Mode Shapes ◽  
Buckling Mode ◽  
Geometric Imperfections ◽  
Buckling Modes ◽  
The North ◽  
Buckling Resistance ◽  
Maximum Decrease ◽  
Initial Geometric Imperfections ◽  
Toroidal Shells

When perfect, externally pressurized complete circular toroidal shells buckle, the minimum buckling pressure pcr usually occurs in the axisymmetric n = 0 mode, with pcr for n = 2 being only slightly larger. In the present paper, the effects of axisymmetric initial geometric imperfections on reducing pcr for the perfect shell are investigated. Various types of imperfection are studied, i.e. localized flat spots, smooth dimples, sinusoids and buckling mode shapes. The principal geometry investigated was R/b = 10, b/t = 100, although other geometries were also considered. The maximum decrease in buckling resistance, Δ pcr, was found to be about 16 per cent at δ 0/t = 1 and it occurred with smooth dimples at the north (φ = 180°) and south (φ=0°) poles. This value of Δ pcr is not large. Circular toroidal shells thus do not appear to be very sensitive to axisymmetric initial geometric imperfections. The reductions in the buckling pressure of the above shell, arising because of initial imperfections having the shape of the n = 0 and the n = 2 buckling modes, were 12 and 9 per cent respectively for wo/t = 1. These decreases in the buckling resistance are smaller than that for the ‘two smooth dimple’ case mentioned above.

Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Gregory L. Holst ◽  
Gregory H. Teichert ◽  
Brian D. Jensen
Keyword(s):  
Compliant Mechanisms ◽  
Large Deflections ◽  
Buckling Mode ◽  
Buckling Modes ◽  
Reaction Forces ◽  
Combined Models ◽  
Modeling And Experiments ◽  
Beam Bending ◽  
Bending Behavior ◽  
Bistable Mechanism

This paper explores the deflection and buckling of fixed-guided beams used in compliant mechanisms. The paper’s main contributions include the addition of an axial deflection model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models typically incorrectly predict a beam’s buckling mode unless unrealistic constraints are placed on the beam. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force versus displacement predictions of the model are compared to the experimental force versus deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force versus deflection data for each device.

Fibre Recruitment and Shape Changes of Knee Ligaments during Motion: As Revealed by a Computer Graphics-Based Model

1996 ◽  
Vol 210 (2) ◽  
pp. 71-79 ◽  
Author(s):  
T-W Lu ◽  
J J O'Connor
Keyword(s):  
Computer Graphics ◽  
Sagittal Plane ◽  
Ligament Injury ◽  
Buckling Mode ◽  
Knee Ligaments ◽  
Euler Buckling ◽  
Injury Mechanisms ◽  
Four Bar Linkage ◽  
External Loads ◽  
Shape Changes

A computer graphics-based model of the knee ligaments in the sagittal plane was developed for the simulation and visualization of the shape changes and fibre recruitment process of the ligaments during motion under unloaded and loaded conditions. The cruciate and collateral ligaments were modelled as ordered arrays of fibres which link attachment areas on the tibia and femur. Fibres slacken and tighten as the ligament attachment areas on the bones rotate and translate relative to each other. A four-bar linkage, composed of the femur, tibia and selected isometric fibres of the two cruciates, was used to determine the motion of the femur relative to the tibia during passive (unloaded) movement. Fibres were assumed to slacken in a Euler buckling mode when the distances between their attachments are less than chosen reference lengths. The ligament shape changes and buckling patterns are demonstrated with computer graphics. When the tibia is translated anteriorly or posteriorly relative to the femur by muscle forces and external loads, some ligament fibres tighten and are recruited progressively to transmit increasing shear forces. The shape changes and fibre recruitment patterns predicted by the model compare well qualitatively with experimental results reported in the literature. The computer graphics approach provides insight into the micro behaviour of the knee ligaments. It may help to explain ligament injury mechanisms and provide useful information to guide the design of ligament replacements.

Thermal Stability of an Axial-Compressed Open-Tip Carbon Nanocone

2014 ◽  
Vol 575 ◽  
pp. 227-230
Author(s):  
Ming Liang Liao
Keyword(s):  
Thermal Stability ◽  
Thermal Instability ◽  
Critical Strain ◽  
Md Simulations ◽  
Apex Angle ◽  
Instability Mode ◽  
Buckling Mode ◽  
Carbon Nanocones ◽  
Compression Strain ◽  
Thermal Stability Of

This paper used molecular dynamics (MD) simulations to investigate thermal stability of an axial compressed open-tip carbon nanocone, which have an apex angle of 19.2°. To study the thermal stability, the carbon nanocone was first compressed axially up to the compression strain near its critical strain for buckling. Temperature of carbon nanocone was then increased gradually and the corresponding axial force in the carbon nanocone was monitored to examine the thermal stability of the carbon nanocone. It was found that the critical temperature for thermal instability grows with the decrease of the initial compressed strain. Comparing with the buckling mode of the carbon nanocone, the thermal instability mode displayed a swelling configuration rather than a deflective configuration of the buckling mode. The interesting finding would be helpful for applications of open-tip carbon nanocones.

scholarly journals Experimental and Numerical Buckling Analysis of Delaminated Hybrid Composite Beam Structures

2010 ◽  
Vol 24-25 ◽  
pp. 393-400 ◽  
Author(s):  
M.M. Nasr Esfahani ◽  
H. Ghasemnejad ◽  
P.E. Barrington
Keyword(s):  
Hybrid Composite ◽  
Laminated Composite ◽  
Composite Beams ◽  
Buckling Load ◽  
Buckling Mode ◽  
Buckling Modes ◽  
Critical Buckling Load ◽  
Finite Element Software ◽  
Numerical Studies ◽  
Laminated Composite Beams

In this paper the effect of delamination position on the critical buckling load and buckling mode of hybrid composite beams is investigated. Experimental and numerical studies are carried out to determine the buckling load of delaminated composite beams. The laminated composite beams with various laminate designs of [G90]6, [C90]8, [C0/G0]4 and [C90/G90]4 were manufactured and tested to find the critical buckling load. Three different defect positions were placed through the thickness to find three main buckling modes. It was found that delamination position and lay-up can affect the buckling mode and also the critical buckling load. By approaching the delamination position to the outer surface of the specimen the buckling load decreases. The buckling process of hybrid and non-hybrid composite beams was also simulated by finite element software ANSYS and the critical buckling loads were verified with the relevant experimental results.

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