The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads

1969 ◽  
Vol 36 (4) ◽  
pp. 775-783 ◽  
Author(s):  
A. D. Kerr ◽  
M. T. Soifer
Keyword(s):  
Exact Solution ◽  
Perturbation Analysis ◽  
Degrees Of Freedom ◽  
Elastic System ◽  
Buckling Load ◽  
Nonlinear Formulation ◽  
Shallow Arch ◽  
Buckling Loads ◽  
State Of Stress

The effect of the linearization of the prebuckled state upon the determined buckling loads is studied first on an elastic system of two degrees of freedom and then on a shallow arch subjected to a uniform lateral load; structures that exhibit a nontrivial state of stress, an upper buckling load, a lower buckling load, and a bifurcation load. For each case the exact solution of the nonlinear formulation is discussed first. Then, using the perturbation analysis, the instability loads are determined again using the exact and the linearized prebuckled state, respectively. The paper concludes with a comparison of the obtained buckling loads and a discussion of relevant problems. It was found that the usual “adjacent equilibrium” argument presented in the literature, according to which only the displacements are perturbed, is not applicable for the determination of the bifurcation pressures of the shallow arch. A proper argument is presented and then used to determine the bifurcation and limit points.

scholarly journals Buckling of nanobeams and nanorods with cracks

2019 ◽  
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Piecewise Constant ◽  
Cracklike Defects ◽  
General Method

Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

scholarly journals DETERMINATION OF THE CRITICAL BUCKLING LOADS OF EULER COLUMNS USING STODOLA-VIANELLO ITERATION METHOD

2018 ◽  
Vol 30 (3) ◽  
Author(s):  
Ofondu I.O. ◽  
Ikwueze E.U. ◽  
Ike C.C.
Keyword(s):  
Iteration Method ◽  
Longitudinal Axis ◽  
Rayleigh Quotient ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Relative Errors ◽  
Fixed End

The Stodola-Vianello iteration method was implemented in this work to determine the critical buckling load of an Euler column of length l with fixed end (x = 0) and pinned end (x = l), where the longitudinal axis is the x-direction.The critical buckling loads were found to be variable, depending on the x-coordinate. Integration and the Rayleigh quotients were used to find average buckling coefficients. First iteration gave relative errors of 4% using integration and 2.5% using Rayleigh quotient.Second iteration gave average relative errorsless than 1% for both the integration and the Rayleigh quotients. Better estimates of the critical buckling loads were obtained using the Rayleigh quotient in the Stodola-Vianello’s iteration.

scholarly journals Buckling Load Predictions of Panel and Shell using Vibration Correlation Technique

2019 ◽  
Vol 9 (2) ◽  
pp. 1842-1845
Keyword(s):  
Shell Element ◽  
Thermal Buckling ◽  
Buckling Load ◽  
Correlation Technique ◽  
Buckling Loads ◽  
Surface Conditions ◽  
Marine Industry ◽  
Hull Structure ◽  
Submarine Hull

Prediction of buckling loads is a very important phenomenon for aerospace and marine industry. In this paper buckling predictions of a submarine hull is considered by using a shell element and a rectangular panel is considered by using a plate element. The buckling load of a submarine hull can be predicted by using vibration correlation technique. Determination of these buckling loads can be carried out based on the boundary conditions of the submarine hull structure. The technique will be carried by considering both surface conditions and to determine the crippling load of a hull. This paper aims to use VCT for a submarine hull structure used in marine, ocean and can compare the results to aerospace industry by considering a rectangular panel for which buckling is predicted using vibration correlation technique . VCT is not very extensively used in case of thermal buckling. However in this paper, VCT is applied to verify the thermal buckling of a simple thin rectangular panel subjected to parabolic loading.

Flexural-Torsional Buckling of Pultruded Fiber-Reinforced Polymer Angle Beams under Eccentric Loading

2020 ◽  
Vol 982 ◽  
pp. 201-206
Author(s):  
Jaksada Thumrongvut ◽  
Natthawat Pakwan ◽  
Samaporn Krathumklang
Keyword(s):  
Buckling Load ◽  
Fiber Reinforced Polymer ◽  
Width Ratio ◽  
Fiber Reinforced ◽  
Torsional Buckling ◽  
Eccentric Load ◽  
Buckling Loads ◽  
Reinforced Polymer ◽  
Cross Sectional Dimension ◽  
Flexural Torsional Buckling

In this paper, the experimental study on the pultruded fiber-reinforced polymer (pultruded FRP) angle beams subjected to transversely eccentric load are presented. A summary of critical buckling load and buckling behavior for full-scale flexure tests with various span-to-width ratios (L/b) and eccentricities are investigated, and typical failure mode are identified. Three-point flexure tests of 50 pultruded FRP angle beams are performed. The E-glass fibre/polyester resin angle specimens are tested to examine the effect of span-to-width ratio of the beams on the buckling responses and critical buckling loads. The angle specimens have the cross-sectional dimension of 76x6.4 mm with span-to-width ratios, ranging from 20 to 40. Also, four different eccentricities are investigated, ranging from 0 to ±2e. Eccentric loads are applied below the horizontal flange in increments until beam buckling occurred. Based upon the results of this study, it is found that the load and mid-span vertical deflection relationships of the angle beams are linear up to the failure. In contrast, the load and mid-span lateral deflection relationships are geometrically nonlinear. The general mode of failure is the flexural-torsional buckling. The eccentrically loaded specimens are failed at critical buckling loads lower than their concentric counterparts. Also, the quantity of eccentricity increases as buckling load decreases. In addition, it is noticed that span-to-width ratio increases, the buckling load is decreased. The eccentric location proved to have considerable influence over the buckling load of the pultruded FRP angle beams.

scholarly journals CFRP Origami Metamaterial with Tunable Buckling Loads: A Numerical Study

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 917
Author(s):  
Houyao Zhu ◽  
Shouyan Chen ◽  
Teng Shen ◽  
Ruikun Wang ◽  
Jie Liu
Keyword(s):  
Numerical Study ◽  
Buckling Load ◽  
Fe Modelling ◽  
Buckling Loads ◽  
Folding Angle ◽  
Mechanical Responses ◽  
Reinforced Plastic ◽  
Rate Of Increase ◽  
Practical Engineering ◽  
Identical Rate

Origami has played an increasingly central role in designing a broad range of novel structures due to its simple concept and its lightweight and extraordinary mechanical properties. Nonetheless, most of the research focuses on mechanical responses by using homogeneous materials and limited studies involving buckling loads. In this study, we have designed a carbon fiber reinforced plastic (CFRP) origami metamaterial based on the classical Miura sheet and composite material. The finite element (FE) modelling process’s accuracy is first proved by utilizing a CFRP plate that has an analytical solution of the buckling load. Based on the validated FE modelling process, we then thoroughly study the buckling resistance ability of the proposed CFRP origami metamaterial numerically by varying the folding angle, layer order, and material properties, finding that the buckling loads can be tuned to as large as approximately 2.5 times for mode 5 by altering the folding angle from 10° to 130°. With the identical rate of increase, the shear modulus has a more significant influence on the buckling load than Young’s modulus. Outcomes reported reveal that tunable buckling loads can be achieved in two ways, i.e., origami technique and the CFRP material with fruitful design freedoms. This study provides an easy way of merely adjusting and controlling the buckling load of lightweight structures for practical engineering.

Determination of buckling loads for wooden beams using the elastic models

2019 ◽  
Vol 89 (8) ◽  
pp. 1501-1512 ◽  
Author(s):  
Stanislav Kotšmíd ◽  
Pavel Beňo
Keyword(s):  
Buckling Loads

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

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