Search results for: Sinc Numerical Methods

Authors: V. D. Thi, M. Li, M. Khelifa, M. El Ganaoui, Y. Rogaume

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This paper presents a two-dimensional model to study the heat and moisture transfer through porous building materials. Dynamic and static coupled models of heat and moisture transfer in porous material under low temperature are presented and the coupled models together with variable initial and boundary conditions have been considered in an analytical way and using the finite element method. The resulting coupled model is converted to two nonlinear partial differential equations, which is then numerically solved by an implicit iterative scheme. The numerical results of temperature and moisture potential changes are compared with the experimental measurements available in the literature. Predicted results demonstrate validation of the theoretical model and effectiveness of the developed numerical algorithms. It is expected to provide useful information for the porous building material design based on heat and moisture transfer model.

Keywords: Finite element method, heat transfer, moisture transfer, porous materials, wood.

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Authors: C. Rajan, K. Geetha, S. Geetha

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The motivation of image compression technique is to reduce the irrelevance and redundancy of the image data in order to store or pass data in an efficient way from one place to another place. There are several types of compression methods available. Without the help of compression technique, the file size is knowingly larger, usually several megabytes, but by doing the compression technique, it is possible to reduce file size up to 10% as of the original without noticeable loss in quality. Image compression can be lossless or lossy. The compression technique can be applied to images, audio, video and text data. This research work mainly concentrates on methods of encoding, DCT, compression methods, security, etc. Different methodologies and network simulations have been analyzed here. Various methods of compression methodologies and its performance metrics has been investigated and presented in a table manner.

Keywords: Image compression techniques, encoding, DCT, lossy compression, lossless compression, JPEG.

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Authors: Evgeniy Burlutskiy

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The paper presents a one-dimensional transient mathematical model of compressible thermal multi-component gas mixture flows in pipes. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved. Thermo-physical properties of multi-component gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas mixture viscosity is calculated on the basis of the Lee-Gonzales-Eakin (LGE) correlation. Numerical analysis on rapid decompression in conventional dry gases is performed by using the proposed mathematical model. The model is validated on measured values of the decompression wave speed in dry natural gas mixtures. All predictions show excellent agreement with the experimental data at high and low pressure. The presented model predicts the decompression in dry natural gas mixtures much better than GASDECOM and OLGA codes, which are the most frequently-used codes in oil and gas pipeline transport service.

Keywords: Mathematical model, Rapid Gas Decompression

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Authors: Md. Fazlul Karim, Ahmad Izani Ismail, Mohammed Ashaque Meah

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This paper focuses on the development of a 2-D boundary fitted and nested grid (BFNG) model to compute the tsunami propagation of Indonesian tsunami 2004 along the coastal region of Penang in Peninsular Malaysia.

In the presence of a curvilinear coastline, boundary fitted grids are suitable to represent the model boundaries accurately. On the other hand, when large gradient of velocity within a confined area is expected, the use of a nested grid system is appropriate to improve the numerical accuracy with the least grid numbers.

This paper constructs a shallow water nested and orthogonal boundary fitted grid model and presents computational results of the tsunami impact on the Penang coast due to the Indonesian tsunami of 2004. The results of the numerical simulations are compared with available data.

Keywords: Boundary Fitted Nested Model, Tsunami, Penang Island, 2004 Indonesian Tsunami.

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Authors: A. Yanik, U. Aldemir

Abstract:

This study investigates the benefits of implementing the semi-active devices in relation to passive viscous damping in the context of seismically isolated bridge structures. Since the intrinsically nonlinear nature of semi-active devices prevents the direct evaluation of Laplace transforms, frequency response functions are compiled from the computed time history response to sinusoidal and pulse-like seismic excitation. A simple semi-active control policy is used in regard to passive linear viscous damping and an optimal non-causal semi-active control strategy. The control strategy requires optimization. Euler-Lagrange equations are solved numerically during this procedure. The optimal closed-loop performance is evaluated for an idealized controllable dash-pot. A simplified single-degree-of-freedom model of an isolated bridge is used as numerical example. Two bridge cases are investigated. These cases are; bridge deck without the isolation bearing and bridge deck with the isolation bearing. To compare the performances of the passive and semi-active control cases, frequency dependent acceleration, velocity and displacement response transmissibility ratios T_a(w), T_v(w), and T_d(w) are defined. To fully investigate the behavior of the structure subjected to the sinusoidal and pulse type excitations, different damping levels are considered. Numerical results showed that, under the effect of external excitation, bridge deck with semi-active control showed better structural performance than the passive bridge deck case.

Keywords: Bridge structures, passive control, seismic, semi-active control, viscous damping.

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Authors: Dalvir Singh, Somnath Chattopadhyaya

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During welding or flame cutting of metals, the prediction of heat affected zone (HAZ) is critical. There is need to develop a simple mathematical model to calculate the temperature variation in HAZ and derivative analysis can be used for this purpose. This study presents analytical solution for heat transfer through conduction in mild steel plate. The homogeneous and nonhomogeneous boundary conditions are single variables. The full field analytical solutions of temperature measurement, subjected to local heating source, are derived first by method of separation of variables followed with the experimental visualization using infrared imaging. Based on the present work, it is suggested that appropriate heat input characteristics controls the temperature distribution in and around HAZ.

Keywords: Conduction Heat Transfer, Heat Affected Zone (HAZ), Infra-Red Imaging, Numerical Method, Orthogonal Function, Plasma Arc Cutting, Separation of Variables, Temperature Measurement.

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Authors: Laith Jaafer Habeeb

Abstract:

The present study is concerned with the free convective two dimensional flow and heat transfer, within the framework of Boussinesq approximation, in anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Lattice Boltzmann method fornon-Darcy flow model. Effects of the moving lid direction (top, bottom, left, and right wall moving in the negative and positive x&ydirections), number of moving walls (one or two opposite walls), the sliding wall velocity, and four different constant temperatures opposite walls cases (two surfaces are being insulated and the twoother surfaces areimposed to be at constant hot and cold temperature)have been conducted. The results obtained are discussed in terms of the Nusselt number, vectors, contours, and isotherms.

Keywords: Numerical simulation, lid-driven cavity flow, saturated porous medium, different velocity and heated walls.

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm- Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solution of classical Sturm–Liouville problem is presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems.

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Authors: Rabah Haoui

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The aim of this work is to analyze a viscous flow in the axisymmetric nozzle taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier- Stokes equations is realized by using the finite volume method to determine the supersonic flow parameters at the exit of convergingdiverging nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, along with CFL coefficient and mesh size level is selected to ensure numerical convergence. The effect of the boundary layer thickness is significant at the exit of the nozzle. The best solution is obtained with using a very fine grid, especially near the wall, where we have a strong variation of velocity, temperature and shear stress. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: Supersonic flow, viscous flow, finite volume, nozzle

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Authors: L. Dahmani, M.Kouane

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In this paper are illustrated the principal aspects connected with the numerical evaluation of thermal stress induced by high gradient temperature in the concrete beam. The reinforced concrete beam has many advantages over steel beam, such as high resistance to high temperature, high resistance to thermal shock, Better resistance to fatigue and buckling, strong resistance against, fire, explosion, etc. The main drawback of the reinforced concrete beam is its poor resistance to tensile stresses. In order to investigate the thermal induced tensile stresses, a numerical model of a transient thermal analysis is presented for the evaluation of thermo-mechanical response of concrete beam to the high temperature, taking into account the temperature dependence of the thermo physical properties of the concrete like thermal conductivity and specific heat.

Keywords: Cracking, Gradient Temperature, Reinforced Concrete beam, Thermo-mechanical analysis.

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Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

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This paper presents the effect of stiffeners on the behavior of slender steel I-beams. Nonlinear three dimensional finite element models are developed to represent the stiffened steel I-beams. The well established finite element (ANSYS 13.0) program is used to simulate the geometric and material nonlinear nature of the problem. Verification is achieved by comparing the obtained numerical results with the results of previous published experimental work. The parameters considered in the analysis are the horizontal stiffener's position and the horizontal stiffener's dimensions as well as the number of vertical stiffeners. The studied dimensions of the horizontal stiffeners include the stiffener width, the stiffener thickness and the stiffener length. The results of the achieved numerical parametric study for slender steel I-beams show the significant effect of stiffeners on the beam behavior and its failure load.

Keywords: Steel I-beams, local buckling, slender, stiffener, thin walled section.

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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Authors: Zerarka Hizia, Akchiche Mustapha, Prunier Florent

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The landslide of Ain El Hammam (AEH) is characterized by a complex geology and a high hydrogeology hazard. AEH's perpetual reactivation compels us to look closely at its triggers and to better understand the mechanisms of its evolution in mass and in depth. This study builds a numerical model to simulate the influencing factors such as precipitation, non-saturation, and pore pressure fluctuations, using Plaxis software. For a finer analysis of instabilities, we use Hill's criterion, based on the sign of the second order work, which is the most appropriate material stability criterion for non-associated elastoplastic materials. The results of this type of calculation allow us, in theory, to predict the shape and position of the slip surface(s) which are liable to ground movements of the slope, before reaching the rupture given by the plastic limit of Mohr Coulomb. To validate the numerical model, an analysis of inclinometer measures is performed to confirm the direction of movement and kinematic of the sliding mechanism of AEH’s slope.

Keywords: Landslide, second order work, precipitation, inclinometers.

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Authors: Yunus Doğan, Ahmet Durap

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Coastal regions are the one of the most commonly used places by the natural balance and the growing population. In coastal engineering, the most valuable data is wave behaviors. The amount of this data becomes very big because of observations that take place for periods of hours, days and months. In this study, some statistical methods such as the wave spectrum analysis methods and the standard statistical methods have been used. The goal of this study is the discovery profiles of the different coast areas by using these statistical methods, and thus, obtaining an instance based data set from the big data to analysis by using data mining algorithms. In the experimental studies, the six sample data sets about the wave behaviors obtained by 20 minutes of observations from Mersin Bay in Turkey and converted to an instance based form, while different clustering techniques in data mining algorithms were used to discover similar coastal places. Moreover, this study discusses that this summarization approach can be used in other branches collecting big data such as medicine.

Keywords: Clustering algorithms, coastal engineering, data mining, data summarization, statistical methods.

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Authors: M. Yoneda

Abstract:

In this paper, a lateral walking design force per person is proposed and compared with Imperial College test results. Numerical simulations considering the proposed walking design force which is incorporated into the neural-oscillator model are carried out placing much emphasis on the synchronization (the lock-in phenomenon) for a pedestrian bridge model with the span length of 50 m. Numerical analyses are also conducted for an existing pedestrian suspension bridge. As compared with full scale measurements for this suspension bridge, it is confirmed that the analytical method based on the neural-oscillator model might be one of the useful ways to explain the synchronization (the lock-in phenomenon) of pedestrians being on the bridge.

Keywords: Pedestrian bridge, human-induced lateral vibration, neural-oscillator, full scale measurement, dynamic response analysis.

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Authors: R. Ziaie Moayed , S. Tamassoki , E. Izadi

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Investigation of sandy clay behavior is important since urban development demands mean that sandy clay areas are increasingly encountered, especially for transportation infrastructures. This paper presents the results of the finite element analysis of the direct shear test (under three vertical loading 44, 96 and 192 kPa) and discusses the effects of different parameters such as cohesion, friction angle and Young's modulus on the shear strength of sandy clay. The numerical model was calibrated against the experimental results of large-scale direct shear tests. The results have shown that the shear strength was increased with increase in friction angle and cohesion. However, the shear strength was not influenced by raising the friction angle at normal stress of 44 kPa. Also, the effect of different young's modulus factors on stress-strain curve was investigated.

Keywords: Shear strength, Finite element analysis, Large direct shear test, Sandy clay.

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Authors: A. Chaudhuri, C. Guha, T. K. Dutta

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Pressure driven microscale gas flow-separation has been investigated by solving the compressible Navier-Stokes (NS) system of equations. A two dimensional explicit finite volume (FV) compressible flow solver has been developed using modified advection upwind splitting methods (AUSM+) with no-slip/first order Maxwell-s velocity slip conditions to predict the flowseparation behavior in microdimensions. The effects of scale-factor of the flow geometry and gas species on the microscale gas flowseparation have been studied in this work. The intensity of flowseparation gets reduced with the decrease in scale of the flow geometry. In reduced dimension, flow-separation may not at all be present under similar flow conditions compared to the larger flow geometry. The flow-separation patterns greatly depend on the properties of the medium under similar flow conditions.

Keywords: AUSM+, FVM, Flow-separation, Microflow.

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Authors: Ayad A. Abdalla, Elhadi I. Elhadi, Hisham A. Elfergani

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Developing mixed convection in circular and annular sector ducts is investigated numerically for steady laminar flow of an incompressible Newtonian fluid with Pr = 0.7 and a wide range of Grashof number (0 £ Gr £ 10⁷). Investigation is limited to the case of heating in circular and annular sector ducts with apex angle of 2ϕ = π/4 for the thermal boundary condition of uniform wall temperature axially and peripherally. A numerical, finite control volume approach based on the SIMPLER algorithm is employed to solve the 3D governing equations. Numerical analysis is conducted using marching technique in the axial direction with axial conduction, axial mass diffusion, and viscous dissipation within the fluid are assumed negligible. The results include developing secondary flow patterns, developing temperature and axial velocity fields, local Nusselt number, local friction factor, and local apparent friction factor. Comparisons are made with the literature and satisfactory agreement is obtained. It is found that free convection enhances the local heat transfer in some cases by up to 2.5 times from predictions which account for forced convection only and the enhancement increases as Grashof number increases. Duct geometry and Grashof number strongly influence the heat transfer and pressure drop characteristics.

Keywords: Mixed convection, annular and circular sector ducts, heat transfer enhancement, pressure drop.

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Authors: Guangbin Wang, Fuping Tan

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In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results.

Keywords: Nonsingular H-matrix, parallel alternating method, convergence.

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Authors: Haode Huo, Jingjing He, Rui Kang, Xuefei Guan

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This paper presents a study of Lamb wave damage diagnosis of composite delamination using instantaneous phase data. Numerical experiments are performed using the finite element method. Different sizes of delamination damages are modeled using finite element package ABAQUS. Lamb wave excitation and responses data are obtained using a pitch-catch configuration. Empirical mode decomposition is employed to extract the intrinsic mode functions (IMF). Hilbert–Huang Transform is applied to each of the resulting IMFs to obtain the instantaneous phase information. The baseline data for healthy plates are also generated using the same procedure. The size of delamination is correlated with the instantaneous phase change for damage diagnosis. It is observed that the unwrapped instantaneous phase of shows a consistent behavior with the increasing delamination size.

Keywords: Delamination, lamb wave, finite element method, EMD, instantaneous phase.

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Authors: Morteza Kazemi Torbaghan, Seyed Mehran Kazemi, Rahele Zhiani, Fakhriye Hamed

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Truss optimization problem has been vastly studied during the past 30 years and many different methods have been proposed for this problem. Even though most of these methods assume that the design variables are continuously valued, in reality, the design variables of optimization problems such as cross-sectional areas are discretely valued. In this paper, an improved hill climbing and an improved simulated annealing algorithm have been proposed to solve the truss optimization problem with discrete values for crosssectional areas. Obtained results have been compared to other methods in the literature and the comparison represents that the proposed methods can be used more efficiently than other proposed methods

Keywords: Size Optimization of Trusses, Hill Climbing, Simulated Annealing.

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Authors: N. Samarinas, C. Evangelides, C. Vrekos

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The aim of this paper is the comparison of three different methods, in order to produce fuzzy tolerance relations for rainfall data classification. More specifically, the three methods are correlation coefficient, cosine amplitude and max-min method. The data were obtained from seven rainfall stations in the region of central Greece and refers to 20-year time series of monthly rainfall height average. Three methods were used to express these data as a fuzzy relation. This specific fuzzy tolerance relation is reformed into an equivalence relation with max-min composition for all three methods. From the equivalence relation, the rainfall stations were categorized and classified according to the degree of confidence. The classification shows the similarities among the rainfall stations. Stations with high similarity can be utilized in water resource management scenarios interchangeably or to augment data from one to another. Due to the complexity of calculations, it is important to find out which of the methods is computationally simpler and needs fewer compositions in order to give reliable results.

Keywords: Classification, fuzzy logic, tolerance relations, rainfall data.

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Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

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This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: Distributed model, flexible manipulator, observer, robot control.

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Authors: N. Nacereddine, L. Hamami, M. Tridi, N. Oucief

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In non destructive testing by radiography, a perfect knowledge of the weld defect shape is an essential step to appreciate the quality of the weld and make decision on its acceptability or rejection. Because of the complex nature of the considered images, and in order that the detected defect region represents the most accurately possible the real defect, the choice of thresholding methods must be done judiciously. In this paper, performance criteria are used to conduct a comparative study of four non parametric histogram thresholding methods for automatic extraction of weld defect in radiographic images.

Keywords: Radiographic images, non parametric methods, histogram thresholding, performance criteria.

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Authors: Iwona Nowak, Jacek Smolka, Andrzej J. Nowak

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The paper discusses a 3D numerical solution of the inverse boundary problem for a continuous casting process of alloy. The main goal of the analysis presented within the paper was to estimate heat fluxes along the external surface of the ingot. The verified information on these fluxes was crucial for a good design of a mould, effective cooling system and generally the whole caster. In the study an enthalpy-porosity technique implemented in Fluent package was used for modeling the solidification process. In this method, the phase change interface was determined on the basis of the liquid fraction approach. In inverse procedure the sensitivity analysis was applied for retrieving boundary conditions. A comparison of the measured and retrieved values showed a high accuracy of the computations. Additionally, the influence of the accuracy of measurements on the estimated heat fluxes was also investigated.

Keywords: Boundary inverse problem, sensitivity analysis, continuous casting, numerical simulation.

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Authors: G. F. Guimarães, A. R. de Faria, R. R. Rego, A. L. R. D’Oliveira

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One of the most relevant phenomena in manufacturing is the residual stress state development through the manufacturing chain. In most cases, the residual stresses have their origin in the heterogenous plastification produced by the processes. Although a few manufacturing processes have been successfully approached by numerical modeling, there is still lack of understanding on how these processes' interactions will affect the final stress state. The objective of this work is to analyze the effect of the grinding procedure on the residual stress state generated by a quasi-static indentation. The model consists in a simplified approach of shot peening, modeling four cases with variations in indenter size and force. This model was validated through topography, measured by optical 3D focus-variation. The indentation model configured with two loads was then exposed to two grinding procedures and the result was analyzed. It was observed that the grinding procedure will have a significant effect on the stress state.

Keywords: plasticity, residual stress, finite element method, manufacturing

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Authors: B. S. Sindu, Saptarshi Sasmal, Smitha Gopinath

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Cement, the most widely used construction material is very brittle and characterized by low tensile strength and strain capacity. Macro to nano fibers are added to cement to provide tensile strength and ductility to it. Carbon Nanotube (CNT), one of the nanofibers, has proven to be a promising reinforcing material in the cement composites because of its outstanding mechanical properties and its ability to close cracks at the nano level. The experimental investigations for CNT reinforced cement is costly, time consuming and involves huge number of trials. Mathematical modeling of CNT reinforced cement can be done effectively and efficiently to arrive at the mechanical properties and to reduce the number of trials in the experiments. Hence, an attempt is made to numerically study the effective mechanical properties of CNT reinforced cement numerically using Representative Volume Element (RVE) method. The enhancement in its mechanical properties for different percentage of CNTs is studied in detail.

Keywords: Carbon Nanotubes, Cement composites, Representative Volume Element, Numerical simulation

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Authors: Guray Arslan, Riza S. O. Keskin

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Numerical investigations were conducted to study the influence of flexural reinforcement ratio on the diagonal cracking strength and ultimate shear strength of reinforced concrete (RC) beams without stirrups. Three-dimensional nonlinear finite element analyses (FEAs) of the beams with flexural reinforcement ratios ranging from 0.58% to 2.20% subjected to a mid-span concentrated load were carried out. It is observed that the load-deflection and loadstrain curves obtained from the numerical analyses agree with those obtained from the experiments. It is concluded that flexural reinforcement ratio has a significant effect on the shear strength and deflection capacity of RC beams without stirrups. The predictions of diagonal cracking strength and ultimate shear strength of beams obtained by using the equations defined by a number of codes and researchers are compared with each other and with the experimental values.

Keywords: Finite element, flexural reinforcement, reinforced concrete beam, shear strength.

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Authors: Oliver Mărunţălu, Gheorghe Lăzăroiu, Elena Elisabeta Manea, Dana Andreya Bondrea, Lăcrămioara Diana Robescu

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This paper presents the results obtained by numerical simulation using the software ANSYS CFX-CFD for the air pollutants dispersion in the atmosphere coming from the evacuation of combustion gases resulting from the fuel combustion in an electric thermal power plant. The model uses the Navier-Stokes equation to simulate the dispersion of pollutants in the atmosphere. It is considered as important factors in elaboration of simulation the atmospheric conditions (pressure, temperature, wind speed, wind direction), the exhaust velocity of the combustion gases, chimney height and the obstacles (buildings). Using the air quality monitoring stations it is measured the concentrations of main pollutants (SO2, NOx and PM). The pollutants were monitored over a period of 3 months, after that the average concentration are calculated, which is used by the software. The concentrations are: 8.915 μg/m3 (NOx), 9.587 μg/m3 (SO2) and 42 μg/m3 (PM). A comparison of test data with simulation results demonstrated that CFX was able to describe the dispersion of the pollutant as well the concentration of this pollutants in the atmosphere.

Keywords: Air pollutants, computational fluid dynamics, dispersion, simulation.

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

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The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: Biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory.

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