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.

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.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

1998 ◽  
Vol 120 (3) ◽  
pp. 392-400 ◽  
Author(s):  
A. Saxena ◽  
S. N. Kramer
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
Beam Equation ◽  
Large Deflections ◽  
Euler Beam ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

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.

Behavior and Design of Web-Slotted Cold-Formed Channels Experiencing Local-Distortional-Global Interactive Buckling

2013 ◽  
Vol 351-352 ◽  
pp. 747-752
Author(s):  
Shuai Liu ◽  
Qi Jie Ma ◽  
Pei Jun Wang
Keyword(s):  
Effective Width ◽  
The Finite Element Method ◽  
Distortional Buckling ◽  
Buckling Mode ◽  
Geometric Imperfection ◽  
Interactive Behavior ◽  
Buckling Behavior ◽  
Initial Geometric Imperfection ◽  
Interactive Buckling ◽  
Shed Light

This article aims to shed light on the nonlinear local-distortional-global interactive behavior of web-slotted channel columns by use of the finite element method. The effects of three kinds of initial geometric imperfection based on different distortional buckling mode were evaluated. It indicates that different distortional buckling mode does little difference on the nonlinear interactive buckling behavior of web-slotted channels. Based on the extensive parametric study, some modifications were made to the traditional Effective Width Method for the practical design of web-slotted channel columns undergoing local-distortional-global interactive buckling.

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.

Post-buckling Behavior of Stiffened Cross-Ply Cylindrical Shells

1994 ◽  
Vol 61 (4) ◽  
pp. 998-1000 ◽  
Author(s):  
M. Savoia ◽  
J. N. Reddy
Keyword(s):  
Axial Compression ◽  
Carrying Capacity ◽  
Shell Theory ◽  
Load Carrying Capacity ◽  
Imperfection Sensitivity ◽  
Buckling Modes ◽  
Geometric Imperfection ◽  
Buckling Behavior ◽  
Load Carrying ◽  
Post Buckling

The post-buckling of stiffened, cross-ply laminated, circular determine the effects of shell lamination scheme and stiffeners on the reduced load-carrying capacity. The effect of geometric imperfection is also included. The analysis is based on the layerwise shell theory of Reddy, and the “smeared stiffener” technique is used to account for the stiffener stiffness. Nu cylinders under uniform axial compression is investigated to merical results for stiffened and unstiffened cylinders are presented, showing that imperfection-sensitivity is strictly related to the number of nearly simultaneous buckling modes.

Effects of Aspect Ratio and Side Constraints on Elastic Buckling of Multi Wall Structures and Tubes

2011 ◽  
Author(s):  
Arka P. Chattopadhyay ◽  
Elizabeth Frink ◽  
Kevin Lease ◽  
X. J. Xin
Keyword(s):  
Aspect Ratio ◽  
Structural Safety ◽  
Buckling Mode ◽  
Aspect Ratios ◽  
Side Constraint ◽  
Wall Structures ◽  
Buckling Behavior ◽  
Side Constraints ◽  
Theoretical Predictions ◽  
Research Findings

Buckling of plates and tubes plays an important role in structural safety and energy absorption. Although buckling of plates and tubes has been studied theoretically and experimentally in the past, the effects of aspect ratio and side constraint on buckling of multi-wall structures and tubes has not been investigated systematically. In this work, finite element simulations have been carried out to investigate the buckling behavior of multi-wall structures and tubes. A series of one- to three-panel walls and square tubes with various aspect ratios were simulated. The critical aspect ratios causing buckling mode transition were obtained and compared with theoretical predictions available in the literature. Effects of wall angle and side constraint on buckling behavior were investigated. The relevance of research findings to honeycomb-like structures was discussed.

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.

Design and Testing of a Thin-Flexure Bistable Mechanism Suitable for Stamping From Metal Sheets

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Benjamin Todd ◽  
Brian D. Jensen ◽  
Stephen M. Schultz ◽  
Aaron R. Hawkins
Keyword(s):  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Plane Motion ◽  
Acceleration Threshold ◽  
Metal Sheets ◽  
Out Of Plane ◽  
A New Technique ◽  
Bistable Mechanism ◽  
Force Displacement ◽  
Design And Testing

We present a new technique for fabricating compliant mechanisms from stamped metal sheets. The concept works by providing thinned segments to allow rotation of flexural beams 90 deg about their long axis, effectively providing a flexure as wide as the sheet’s thickness. The method is demonstrated with the design and fabrication of a metal bistable mechanism for use as a threshold accelerometer. A new model based on elliptic integral solutions is presented for bistable mechanisms incorporating long, thin flexures. The resulting metal bistable mechanisms are tested for acceleration threshold sensing using a drop test and a vibration test. The mechanisms demonstrate very little variation due to stress relaxation or temperature effects. The force-displacement behavior of a mechanism is also measured. The mechanisms’ switching force is less than the designed value because of out-of-plane motion and dynamic effects.

LOCAL/DISTORTIONAL/GLOBAL MODE INTERACTION IN SIMPLY SUPPORTED COLD-FORMED STEEL LIPPED CHANNEL COLUMNS

2011 ◽  
Vol 11 (05) ◽  
pp. 877-902 ◽  
Author(s):  
P. B. DINIS ◽  
D. CAMOTIM
Keyword(s):  
Shell Element ◽  
Mode Interaction ◽  
Buckling Mode ◽  
Global Mode ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Buckling Behavior ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Cold Formed Steel

This paper reports the results of a numerical investigation concerning the elastic and elastic-plastic post-buckling behavior of cold-formed steel-lipped channel columns affected by local/distortional/global (flexural-torsional) buckling mode interaction. The results presented and discussed are obtained by means of analyses performed in the code ABAQUS and adopting column discretizations into fine four-node isoparametric shell element meshes. The columns analysed (i) are simply supported (locally/globally pinned end sections with free warping), (ii) have cross-section dimensions and lengths ensuring equal local, distortional, and global (flexural-torsional) critical buckling loads, thus maximizing the mode interaction phenomenon under scrutiny, and (iii) contain critical-mode initial geometrical imperfections exhibiting different configurations, all corresponding to linear combination of the three "competing" critical buckling modes. After briefly addressing the lipped channel column "pure" global post-buckling behavior, one presents and discusses in detail numerical results concerning the post-buckling behavior of similar columns experiencing strong local/distortional/global mode interaction effects. These results consist of (i) elastic (mostly) and elastic-plastic equilibrium paths, (ii) curves and figures providing the evolution of the deformed configurations of several columns (expressed as linear combinations of their local, distortional, and global components) and, for the elastic-plastic columns, (iii) figures enabling a clear visualization of (iii1) the location and growth of the plastic strains, and (iii2) the characteristics of the failure mechanisms more often detected in this work.

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