The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis

2021 ◽  
pp. 239779142110298
Author(s):  
Abusaleh Naderi
Keyword(s):  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Three Dimensional ◽  
Nonlocal Elasticity Theory ◽  
Graphene Sheets ◽  
Two Dimensional ◽  
Dynamic Simulations ◽  
Buckling Stress ◽  
Simplifying Assumptions ◽  
Comparison Of The Results

This paper studies buckling problem of square nano-plates under uniform biaxial pressure through using three-dimensional nonlocal elasticity theory. Equations of stability are solved analytically for square nano-plates with simple supports using a Navier-type method. Critical buckling stress is presented for nano square plates with different thickness-length and nonlocal parameter-length ratios. The critical buckling stress is also reported using different local (classical) and nonlocal two-dimensional plate theories constructed essentially based on some simplifying assumptions. Comparison of the results of two-dimensional and three-dimensional theories for both local and nonlocal cases shows that the nonlocal two-dimensional plate theories are not as accurate as the local two-dimensional ones. This issue however reveals importance of the nonlocal three-dimensional solutions. Finally, through comparison of the numerical results with those obtained from molecular dynamic simulations, the value of the nonlocal parameter is calibrated for square graphene sheets. This parameter can be also used for the other nonlocal three-dimensional mechanical analyses of square graphene sheets to find accurate solutions.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

scholarly journals Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlinear Oscillations ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Largest Lyapunov Exponent ◽  
Graphene Sheets ◽  
Parametric Vibrations

AbstractParametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant alteration in the character of oscillations, including the appearance of chaotic attractors.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

Impact Dynamics of Single-Layered Graphene Sheets in Multibody Framework Using Nonlocal-Based-ANCF Modeling

2019 ◽  
Vol 19 (09) ◽  
pp. 1950099
Author(s):  
Qingtao Wang ◽  
Yang Zhang ◽  
Qixin Zhu ◽  
Zhaojun Pang
Keyword(s):  
Pair Potential ◽  
Gold Atom ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Impact Dynamics ◽  
Graphene Sheets ◽  
Dynamic Simulations ◽  
Definition Of ◽  
Vdw Force ◽  
The Impact

A new nonlinear model based on the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory is proposed to investigate the single-layered graphene sheets (SLGSs) impacted by nanoparticles. The geometrical definition of SLGSs is described by using the ANCF thin plate element, and the strain energy is expressed by using the nonlocal theory. The Lennard–Jones pair potential is adopted to model the van der Waals (vdW) force between SLGSs and nanoparticles. The impact dynamics of the system is simulated in multibody framework by using the generalized-alpha numerical integration method. The impact response of the gold atom–SLGSs system is simulated to validate the performance of the proposed model. Three impact dynamic simulations are conducted to investigate the influence of nanoparticles on the impact dynamics of SLGSs. The results show that the coupling of SLGSs vibration and vdW force led to the amplitude inconsistence of [Formula: see text]-position for nanoparticles.

Thermo-Electro-Mechanical Vibration Characteristics of Graphene/Piezoelectric/Graphene Sandwich Nanobeams

2017 ◽  
Vol 35 (1) ◽  
pp. 65-79 ◽  
Author(s):  
N. Kammoun ◽  
H. Jrad ◽  
S. Bouaziz ◽  
M. B. Amar ◽  
M. Soula ◽  
...  
Keyword(s):  
Nonlocal Elasticity ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Mechanical Vibration ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Mode Shapes ◽  
Governing Equations ◽  
Numerical Examples ◽  
Generalized Differential

AbstractThis paper reports an investigation on thermo-electro-mechanical vibration of graphene/piezoelectric graphene/piezoelectric/graphene sandwich nanobeams. Based on the nonlocal elasticity theory, Timoshenko beam theory and Hamilton's principles, the governing equations are developed and solved using generalized differential quadrature (GDQ) method. The effects of the nonlocal parameter, external electrical voltage, temperature change and axial force on vibration of graphene/piezoelectric/graphene sandwich nanobeams are examined. The performance and the accuracy of the presented model are highlighted through numerical examples with different boundary conditions. This study reports that the nonlocal parameter and thermo-electro-mechanical loadings have important effect on the natural frequencies and the deflection mode shapes of the graphene/piezoelectric/graphene sandwich nanobeam. The present work can serve as guideline for the design of a nanoscale graphene/piezoelectric/graphene beams based electromechanical resonator sensors.

scholarly journals Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects

2017 ◽  
Vol 7 ◽  
pp. 184798041771310 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Surface Effects ◽  
Geometrical Parameters ◽  
Various Boundary Conditions ◽  
Buckling Behavior

In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.

scholarly journals Development and Verification of the Capacity Curve for Two Dimensional Reinforced Concrete Moment-Resisting Frames System under Earthquake Loading

2021 ◽  
Vol 27 (6) ◽  
pp. 73-96
Author(s):  
Haider A Abass ◽  
Husain Khalaf Jarallah
Keyword(s):  
Reinforced Concrete ◽  
Plastic Hinge ◽  
Pushover Analysis ◽  
Three Dimensional ◽  
Automatic Identification ◽  
Two Dimensional ◽  
Seismic Evaluation ◽  
Concrete Frames ◽  
Capacity Curves ◽  
Comparison Of The Results

Pushover analysis is an efficient method for the seismic evaluation of buildings under severe earthquakes. This paper aims to develop and verify the pushover analysis methodology for reinforced concrete frames. This technique depends on a nonlinear representation of the structure by using SAP2000 software. The properties of plastic hinges will be defined by generating the moment-curvature analysis for all the frame sections (beams and columns). The verification of the technique above was compared with the previous study for two-dimensional frames (4-and 7-story frames). The former study leaned on automatic identification of positive and negative moments, where the concrete sections and steel reinforcement quantities the source of these moments. The comparison of the results between the two methodologies was carried out in terms of capacity curves. The results of the conducted comparison highlighted essential points. It was included the potential differences between default and user-defined hinge properties in modeling. The effect of the plastic hinge length and the transverse of shear reinforcement on the capacity curves was also observed. Accordingly, it can be considered that the current methodology in this paper more logistic in the representation of two and three-dimensional structures.  

scholarly journals MODELING OF ELASTIC-PLASTIC DEFORMATION OF ELEMENTS OF SPATIAL STRUCTURES DURING PULSE INTERACTION WITH FLUID BASED ON THE GODUNOV'S METHOD OF INCREASED ACCURACY

2019 ◽  
Vol 81 (4) ◽  
pp. 488-499
Author(s):  
Wang Cheng ◽  
Yang Tonghui ◽  
Li Wan ◽  
Tao Li ◽  
M.H. Abuziarov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Shock Waves ◽  
Elastoplastic Deformation ◽  
Three Dimensional ◽  
Numerical Results ◽  
Two Dimensional ◽  
Wave Processes ◽  
Detonation Products ◽  
Comparison Of The Results ◽  
Good Agreement

The spatial problem of internal explosive loading of an elastoplastic cylindrical container filled with water in Eulerian - Lagrangian variables using multigrid algorithms is considered. A defining system of three-dimensional equations of the dynamics of gas, fluid, and elastoplastic medium is presented. For numerical modeling, a modification of S.K. Godunov scheme of the increased accuracy for both detonation products and liquids, and elastoplastic container is used. At the moving contact boundaries “detonation products - liquid”, “liquid - deformable body”, the exact solution of the Riemann's problem is used. A time dependent model is used to describe the propagation of steady-state detonation wave through an explosive from an initiation region. In both cases, the initiation of detonation occurs at the center of the charge. Two problems have been solved: the first task for the aisymmetric position of the charge, the second for the charge shifted relative to the axis of symmetry. In the first task, the processes are two-dimensional axisymmetric in nature, in the second task, the processes are essentially three-dimensional. A comparison is made of the results of calculations of the first problem using a three-dimensional method with a solution using a previously developed two-dimensional axisymmetric method and experimental data. Good agreement is observed between the numerical results for the maximum velocities and circumferential strains obtained by various methods and experimental data. There is good agreement between the numerical results obtained by various methods and the known experimental data. Comparison of the results of solving the first and second problems shows a significant effect of the position of the charge on the wave processes in the liquid, the processes of loading the container and its elastoplastic deformation. The dynamic behavior of a gas bubble with detonation products is analyzed. A significant deviation of the bubble shape from the spherical one, caused by the action of shock waves reflected from the structure, is shown. Comparison of the results of solving the first and second problems showed a significant effect of the charge position on wave processes in a liquid, the processes of loading a container and its elastoplastic deformation. In particular, in the second problem, shock waves of higher amplitude are observed in the liquid when reflected from the walls of the container.

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