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 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.

Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory

2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Axial Compression ◽  
Buckling Load ◽  
Small Scale ◽  
Beam Model ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Nonlocal Continuum Theory ◽  
Walled Carbon Nanotubes

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

scholarly journals Stability of nanobeams and nanoplates with defects

2021 ◽  
Vol 25 (2) ◽  
pp. 221-238
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Critical Stress ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Physical Parameters ◽  
Axial Loads ◽  
Critical Buckling Load ◽  
Support Conditions ◽  
The Impact

The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.

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 Design Buckling Curves for Clamped Orthotropic Laminated Plates

2004 ◽  
Vol 13 (5) ◽  
pp. 096369350401300 ◽  
Author(s):  
Nicholas G. Tsouvalis ◽  
Vassilios J. Papazoglou
Keyword(s):  
Uniaxial Compression ◽  
Pure Shear ◽  
Ritz Method ◽  
Laminated Plates ◽  
Buckling Load ◽  
Orthotropic Plates ◽  
Critical Buckling Load ◽  
Lamination Theory ◽  
Plane Bending

Non-dimensional design buckling curves for clamped rectangular orthotropic plates are presented in this study. These curves provide the critical buckling load of thin, symmetric, cross-ply laminated plates as a function of the laminate's rigidities and aspect ratio for the following seven configurations of the applied in-plane loads: uniform uniaxial compression, triangular uniaxial compression, uniaxial in-plane bending, pure shear, uniform uniaxial compression combined with shear, triangular uniaxial compression combined with shear, and uniaxial in-plane bending combined with shear. Approximate mathematical formulae are also provided. The Classical Lamination Theory, in conjunction with the Rayleigh-Ritz method, has been used for the determination of the critical buckling load. The validity of the study is confirmed by comparing its results with other both theoretical and numerical ones.

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.

Buckling analysis of orthotropic smart laminated nanoplates based on the nonlocal continuum mechanics using third-order shear and normal deformation theory

2018 ◽  
Vol 32 (5) ◽  
pp. 593-618
Author(s):  
Morteza Ghasemi ◽  
Abdolrahman Jaamialahmadi
Keyword(s):  
Boundary Condition ◽  
Deformation Theory ◽  
Open Circuit ◽  
Buckling Load ◽  
Closed Circuit ◽  
Third Order ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Normal Deformation ◽  
Piezoelectric Layers

In this article, the nonlocal buckling behavior of biaxially loaded graphene sheet with piezoelectric layers based on an orthotropic intelligent laminated nanoplate model is studied. The nonlocal elasticity theory is used in the buckling analysis to show the size scale effects on the critical buckling loads. The electric potential in piezoelectric layers satisfies Maxwell’s equation for either open- or closed-circuit boundary conditions. Based on the third-order shear and normal deformation theory, the nonlinear equilibrium equations are obtained. In order to obtain the linear nonlocal stability equations, the adjacent equilibrium criterion is used. The linear nonlocal governing stability equations are solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling loads are compared with those of molecular dynamics simulations. Finally, the effects of different parameters on the critical buckling loads are studied in detail. The results show that by increasing the nonlocal parameter, the critical buckling load decreases. The piezoelectric effect increases the critical buckling load for both open- and closed-circuit boundary conditions. For open-circuit boundary condition, the variation in the critical buckling load is due to the stiffness and piezoelectric effects, but for closed circuit, it is due to the stiffness effect only. Also, the critical buckling load for open circuit is bigger than that of closed one.

Shear in Structural Stability: On the Engesser–Haringx Discord

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Johan Blaauwendraad
Keyword(s):  
Structural Engineering ◽  
Flexural Rigidity ◽  
Thought Experiment ◽  
Quantitative Information ◽  
Buckling Load ◽  
Structural Members ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Helical Springs ◽  
Wide Range

Since Haringx introduced his stability hypothesis for the buckling prediction of helical springs over 60 years ago, discussion is on whether or not the older hypothesis of Engesser should be replaced in structural engineering for stability studies of shear-weak members. The accuracy and applicability of both theories for structures has been subject of study in the past by others, but quantitative information about the accuracy for structural members is not provided. This is the main subject of this paper. The second goal is to explain the experimental evidence that the critical buckling load of a sandwich beam-column surpasses the shear buckling load GAs, which is commonly not expected on basis of the Engesser hypothesis. The key difference between the two theories regards the relationship, which is adopted in the deformed state between the shear force in the beam and the compressive load. It is shown for a wide range of the ratio of shear and flexural rigidity to which extent the two theories agree and/or conflict with each other. The Haringx theory predicts critical buckling loads which are exceeding the value GAs, which is not possible in the Engesser approach. That sandwich columns have critical buckling loads larger than GAs does, however, not imply the preference of the Haringx hypothesis. This is illustrated by the introduction of the thought experiment of a compressed cable along the central axis of a beam-column in deriving governing differential equations and finding a solution for three different cases of increasing complexity: (i) a compressed member of either flexural or shear deformation, (ii) a compressed member of both flexural and shear deformations, and (iii) a compressed sandwich column. It appears that the Engesser hypothesis leads to a critical buckling load larger than GAs for layered cross section shapes and predicts the sandwich behavior very satisfactory, whereas the Haringx hypothesis then seriously overestimates the critical buckling load. The fact that the latter hypothesis is perfectly confirmed for helical springs (and elastomeric bearings) has no meaning for shear-weak members in structural engineering. Then, the Haringx hypothesis should be avoided. It is strongly recommended to investigate the stability of the structural members on the basis of the Engesser hypothesis.

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