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 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.

scholarly journals Natural vibrations of nanostrips with cracks

2021 ◽  
Vol 25 (1) ◽  
pp. 87-105
Author(s):  
Mainul Hossain ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Material Behavior ◽  
Rotational Inertia ◽  
Natural Vibrations ◽  
Piecewise Constant ◽  
Theory Of Plates ◽  
Local Compliance

Employing the main equations of the theory of plates accounting for the rotational inertia the transverse vibrations of nanobeams and nanostrips are investigated. The nano strips under consideration have piecewise constant dimensions of cross sections. The nanosheets are weakened by cracks at re-entrant corners of steps. While the material behavior corresponds to the Eringen’s nonlocal theory of elasticity it is assumed that the cracks produce additional local compliance, which can be evaluated with the aid of the stress intensity factor at the cracktip. A numerical algorithm for determination of natural frequencies of nanosheets is developed.

scholarly journals Natural vibrations of stepped nanobeams with defects

2019 ◽  
Vol 23 (1) ◽  
pp. 143-158 ◽  
Author(s):  
Jaan Lellep ◽  
Artur Lenbaum
Keyword(s):  
Stress Intensity Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Vibration ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Natural Vibrations ◽  
Piecewise Constant ◽  
Local Compliance

Exact solutions for the transverse vibration of nanobeams based on the nonlocal theory of elasticity are presented. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with crack-like defects. It is assumed that the stationary cracks occur at the re-entrant corners of steps and that the mechanical behaviour of the nanomaterial can be modelled with the Eringen's nonlocal theory. The influence of cracks on the natural vibration is prescribed with the aid of additional local compliance at the weakened cross section. The local compliance is coupled with the stress intensity factor at the crack tip. A general algorithm for determination of eigenfrequencies is developed. It can be used in the case of an arbitrary finite number of steps and cracks.

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.

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.

A modular modeling approach for investigating wool critical buckling from biologically variable along-fiber microstructure

2020 ◽  
pp. 004051752094461
Author(s):  
Indrakumar Vetharaniam ◽  
Jeffrey E Plowman ◽  
Peter Brorens ◽  
Duane Harland
Keyword(s):  
Cross Sections ◽  
Cortical Cell ◽  
Numerical Approach ◽  
Buckling Load ◽  
Cell Type ◽  
Fiber Morphology ◽  
Arbitrary Length ◽  
Critical Buckling Load ◽  
Modeling Approach ◽  
Fiber Microstructure

Mammalian hair fibers are internally sophisticated. We introduce a modeling approach aimed at use in research that derives value from understanding how microstructural organization generates effects at the macroscopic level in the context of natural biological variation. Critical buckling load is solved using a numerical approach applied to a modular fiber microstructure model where fibers of arbitrary length are made up of snippets composed of serial cross-sections at 25 micrometer intervals. As an example, the model is applied to investigate how much effect changes to single microstructural properties (fiber ellipticity, cortical cell type distribution and cell type proportion) have on critical buckling load in the context of prickle. Potential uses and key weak areas in our knowledge of wool fiber morphology and biophysics are discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document