Inextensibility and Its Effect on the Number of Equilibria of Shallow Buckled Beams

2020 ◽  
Vol 87 (12) ◽  
Author(s):  
Philip S. Harvey ◽  
Richard Wiebe ◽  
Thomas M. N. Cain
Keyword(s):  
Numerical Model ◽  
Energy Minimization ◽  
Buckling Mode ◽  
Euler Buckling ◽  
Buckled Beams ◽  
Buckled Beam ◽  
Initial Rise ◽  
Lateral Constraint ◽  
Number Of Equilibria ◽  
Mode A

Abstract A buckled beam with shallow rise under lateral constraint is considered. The initial rise results from a prescribed end displacement. The beam is modeled as inextensible, and analytical solutions of the equilibria are obtained from a constrained energy minimization problem. For simplicity, the results are derived for the archetypal beam with pinned ends. It is found that there are an infinite number of zero lateral-load equilibria, each corresponding to an Euler buckling mode. A numerical model is used to verify the accuracy of the model and also to explore the effects of extensibility.

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.

Investigation on Free Vibration of Buckled Beams

2012 ◽  
Vol 433-440 ◽  
pp. 41-44 ◽  
Author(s):  
Ming Hsu Tsai ◽  
Wen Yi Lin ◽  
Kuo Mo Hsiao ◽  
Fu Mio Fujii
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Beam Theory ◽  
Taylor Series Expansion ◽  
Element Formulation ◽  
Governing Equations ◽  
Nonlinear Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
D’Alembert Principle

The objective of this study is to investigate the deformed configuration and free vibration around the deformed configuration of clamped buckled beams by co-rotational finite element formulation. The principle of virtual work, d'Alembert principle and the consistent second order linearization of the nonlinear beam theory are used to derive the element equations in current element coordinates. The governing equations for linear vibration are obtained by the first order Taylor series expansion of the equation of motion at the static equilibrium position of the buckled beam. Numerical examples are studied to investigate the natural frequencies of clamped buckled beams with different slenderness ratios under different axial compression.

Modeling and Experimental Validation of Actuating a Bistable Buckled Beam Via Moment Input

2015 ◽  
Vol 82 (5) ◽  
Author(s):  
Jonathon Cleary ◽  
Hai-Jun Su
Keyword(s):  
Theoretical Model ◽  
Experimental Test ◽  
Experimental Validation ◽  
Stable Equilibrium ◽  
Compliant Mechanisms ◽  
Computational Tool ◽  
Specific Mechanism ◽  
Test Setup ◽  
Buckled Beams ◽  
Buckled Beam

Bistable mechanisms have two stable equilibrium positions separated by a higher energy unstable equilibrium position. They are well suited for microswitches, microrelays, and many other macro- and micro-applications. This paper discusses a bistable buckled beam actuated by a moment input. A theoretical model is developed for predicting the necessary input moment. A novel experimental test setup was created for experimental verification of the model. The results show that the theoretical model is able to predict the maximum necessary input moment within 2.53%. This theoretical model provides a guideline to design bistable compliant mechanisms and actuators. It is also a computational tool to size the dimensions of buckled beams for actuating a specific mechanism.

Relationship between Euler buckling and unstable equilibria of buckled beams

2017 ◽  
Vol 95 ◽  
pp. 151-161 ◽  
Author(s):  
Mihaela Nistor ◽  
Richard Wiebe ◽  
Ilinca Stanciulescu
Keyword(s):  
Euler Buckling ◽  
Buckled Beams

Bistable Buckled Beam: Modelling and Piezoelectric Actuation

2008 ◽  
Vol 54 ◽  
pp. 281-286 ◽  
Author(s):  
C. Maurini ◽  
Joel Pouget ◽  
Stefano Vidoli
Keyword(s):  
Piezoelectric Actuation ◽  
Nonlinear Properties ◽  
Buckled Beams ◽  
System A ◽  
Buckled Beam ◽  
Piezoelectric Beam ◽  
Transversal Motion ◽  
Bistable Structures ◽  
Two Parameter ◽  
Two Equilibria

Bistable structures, such as buckled beams, are characterized by a two-well potential. Their nonlinear properties are currently exploited in actuators to produce relatively high displacements and forces with low actuation energies. We investigate the use of distributed multiparameter actuation to control the buckling and postbuckling behaviour of a three-layer piezoelectric beam pinned at either end. A two-parameter bending actuation controls the transversal motion, whilst an axial actuation modulates the tangent bending stiffness. The postbuckling behaviour is studied by reducing to a 2 dof system a nonlinear extensible elastica model. When the bending actuation is spatially symmetric, the postbuckling phenomena are characterized by a snapthrough instability. The use of a two-parameter actuation opens new transition scenarios, where it is possible to get quasi-static transitions between the two equilibria of the buckled beam, without any instability phenomenon.

Analytical and Experimental Investigation of Buckled Beams as Negative Stiffness Elements for Passive Vibration and Shock Isolation Systems

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Benjamin A. Fulcher ◽  
David W. Shahan ◽  
Michael R. Haberman ◽  
Carolyn Conner Seepersad ◽  
Preston S. Wilson
Keyword(s):  
Resonance Frequency ◽  
Vibration Isolation ◽  
Negative Stiffness ◽  
Peak Acceleration ◽  
Single Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
Double Beam ◽  
Shock Isolation ◽  
Isolation Systems

The behavior of a buckled beam mechanism, which exhibits both bistability and negative stiffness, is investigated for the purposes of passive shock and vibration isolation. The vibration and shock isolation systems investigated in this research include linear, positive stiffness springs in parallel with the transverse motion of buckled beams, resulting in quasizero stiffness behavior. For vibration isolation systems, quasizero stiffness lowers the resonance frequency of the system, thereby reducing its transmissibility at frequencies greater than resonance. For shock isolation systems, quasizero stiffness provides constant-force shock isolation at tailored force levels, thereby enabling increased capacity for absorbing shock energy relative to a comparable positive stiffness system. Single- and double-beam configurations that exhibit first-mode buckling are utilized for vibration isolation, and a single beam that exhibits first- and third-mode buckling is used for shock isolation. For all cases, the static and dynamic behavior of each configuration is modeled analytically. The models are then used to design prototype vibration and shock isolation systems that are fabricated using selective laser sintering (SLS). The dynamic behavior of the systems in response to base excitations is determined experimentally, and the results are compared to model-based predictions. The vibration isolation prototypes display isolation levels that are tunable by varying the axial compression of the beams. Double-beam systems are shown to provide greater reductions in resonance frequency than single-beam systems for comparable levels of axial compression. However, low-frequency isolation capabilities are sensitive to the high levels of precision required to obtain low levels of system stiffness. The shock isolation prototype provides isolation at prespecified threshold levels of force or acceleration. In the prototype system, an input shock with a peak acceleration of approximately 7 g is reduced to a peak acceleration of the isolated mass of approximately 1 g. High levels of negative acceleration are observed in models and prototype systems when the buckled beam snaps back to its original position; however, models indicate that large negative accelerations can be mitigated using one-way dampers.

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.

Theoretical Analysis and Experimental Investigation on Buckling of FASTMast Deployable Structures

2015 ◽  
Vol 15 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Yulong Jin ◽  
Tao Liu ◽  
Rongxin Lyu ◽  
Bin Ji ◽  
Qifeng Cui
Keyword(s):  
Theoretical Analysis ◽  
Solar Array ◽  
Joint Movement ◽  
Deployable Structures ◽  
Buckling Mode ◽  
Cross Sectional ◽  
Euler Buckling ◽  
Deployable Structure ◽  
Research Findings ◽  
Stiffness Characteristics

FASTMast (Folding Articulated Square Truss Mast) deployable structure is the main bracing structure for the flexible solar array of the international space stations. This study investigates the buckling of FASTMast deployable structures. To this end, the buckling modes and the stiffness characteristics of this structure using the flex batten as an elastic bearing member were theoretically analyzed. The analytical results show that (1) the buckling mode of a FASTMast deployable structure is similar to the elbow joint movement failure when the stiffness of the flex batten is below a critical stiffness value. Once this critical stiffness is reached, the buckling mode takes on the form of Euler buckling. (2) The stiffness of the flex batten is proportional to its cross-sectional second moment of area. Furthermore, an experimental study was carried out to validate the accuracy of the theoretical analysis. The results from experimental work agree fairly well with those from theoretical analysis. The research findings herein are expected to be useful for future studies on similar structures.

Improving the Energy Absorption of Cruciform With Large Global Slenderness Ratio by Kirigami Approach and Welding Technology

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Caihua Zhou ◽  
Tong Li ◽  
Shizhao Ming ◽  
Zhibo Song ◽  
Bo Wang
Keyword(s):  
Energy Absorption ◽  
Progressive Collapse ◽  
Slenderness Ratio ◽  
Absorption Capacity ◽  
Buckling Mode ◽  
Euler Buckling ◽  
Thin Walled Structures ◽  
Welding Technology ◽  
Parametric Studies ◽  
Thin Walled

Conventional energy absorber usually employs stubby thin-walled structures. Compared with the limited number of stubby thin-walled structures, an equipment has a large number of slender thin-walled structures that has the potential to be used for energy absorption purpose as well. Therefore, improving the energy absorption capacity of these slender thin-walled structures can significantly benefit the crashworthiness of the equipment. However, these slender structures are inclined to deform in Euler buckling mode, which greatly limits their application for energy absorption. In this paper, kirigami approach combined with welding technology is adopted to avoid the Euler buckling mode of a slender cruciform. Both finite element simulations and experiments demonstrated that the proposed approach can trigger a desirable progressive collapse mode and thus improve the energy absorption by around 155.22%, compared with the conventional cruciform. Furthermore, parametric studies related to the kirigami pattern and global slenderness ratio (GSR) are conducted to investigate the improvement of this proposed approach on the energy absorption and the maximum critical value of GSR.

scholarly journals Mechanical Instabilities in Perfect Crystals: From Dislocation Nucleation to Bucklinglike Modes

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Akanksha Garg ◽  
Craig E. Maloney
Keyword(s):  
Pitchfork Bifurcation ◽  
Dislocation Nucleation ◽  
Radius Of Curvature ◽  
Geometrical Parameters ◽  
Free Standing ◽  
Buckling Mode ◽  
Euler Buckling ◽  
Dislocation Type ◽  
Spatially Extended ◽  
The Stability

We perform atomistic simulations of nanoindentation on Lennard–Jones 2D hexagonal crystals. In this work, we find a new spatially extended buckling-like mode of instability, which competes with the previously known instability governed by dislocation-dipole nucleation. The geometrical parameters governing these instabilities are the lattice constant, a, the radius of curvature of the indenter, R, and the thickness of the indenter layer, Ly. Whereas dislocation nucleation is a saddle-node bifurcation governed by R/a, the buckling-like instability is a pitchfork bifurcation (like classical Euler buckling) governed by R/Ly. The two modes of instability exhibit strikingly different behaviors after the onset of instability. The dislocation nucleation mode results in a stable final configuration containing a surface step and a stable dislocation at some depth beneath the surface, while the buckling modes are always followed immediately by subsequent nucleation of many dislocation dipoles. We show that this subsequent dislocation nucleation is also observed immediately after buckling in free standing rods, but only for rods which are of sufficiently wide aspect ratio, while thinner rods exhibit stable buckling followed only later by dislocation nucleation in the buckled state. Finally, we study the utility of several recently proposed local and quasi-local stability criteria in detecting the buckling mode. We find that the so-called Λ criterion, based on the stability of a representative homogeneously deformed lattice, is surprisingly useful in detecting the transition from dislocation-type instability to buckling-type instability.

Sign in / Sign up

Export Citation Format

Share Document