Analytical solution for buckling of orthotropic double-layered graphene sheets exposed to unidirectional in-plane magnetic field with various boundary conditions

2018 ◽  
Vol 142 ◽  
pp. 9-23 ◽  
Author(s):  
Nebojša Radić ◽  
Dejan Jeremić
Keyword(s):  
Magnetic Field ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Graphene Sheets ◽  
Various Boundary Conditions

Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

2020 ◽  
Vol 75 (2) ◽  
pp. 175-182
Author(s):  
Magdy E. Amin ◽  
Mohamed Moubark ◽  
Yasmin Amin
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Boundary Conditions ◽  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
The One ◽  
Bulk Case

AbstractThe one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

scholarly journals Ritz Method in Vibration Analysis for Embedded Single-Layered Graphene Sheets Subjected to In-Plane Magnetic Field

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 515
Author(s):  
Olga Mazur ◽  
Jan Awrejcewicz
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Magnetic Parameter ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Graphene Sheets ◽  
Classical Plate Theory ◽  
Foundation Parameters

Vibrations of single-layered graphene sheets subjected to a longitudinal magnetic field are considered. The Winkler-type and Pasternak-type foundation models are employed to reproduce the surrounding elastic medium. The governing equation is based on the modified couple stress theory and Kirchhoff–Love hypotheses. The effect of the magnetic field is taken into account due to the Lorentz force deriving from Maxwell’s equations. The developed approach is based on applying the Ritz method. The proposed method is tested by a comparison with results from the existing literature. The numerical calculations are performed for different boundary conditions, including the mixed ones. The influence of the material length scale parameter, the elastic foundation parameters, the magnetic parameter and the boundary conditions on vibration frequencies is studied. It is observed that an increase of the magnetic parameter, as well as the elastic foundation parameters, brings results closer to the classical plate theory results. Furthermore, the current study can be applied to the design of microplates and nanoplates and their optimal usage.

Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

2014 ◽  
Vol 30 (5) ◽  
pp. 443-453 ◽  
Author(s):  
M. Sobhy
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Graphene Sheets ◽  
Elastic Foundations ◽  
Various Boundary Conditions ◽  
Mechanics Of Composite Materials

AbstractIn this article, the analyses of the natural frequency and buckling of orthotopic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

scholarly journals ANALYTICAL SOLUTION OF THE EQUATION OF CONDUCTIVITY FOR VARIOUS BOUNDARY CONDITIONS

2019 ◽  
Vol 2019 (4) ◽  
pp. 33-37
Author(s):  
Vadim Krys'ko ◽  
Olga Saltykova ◽  
Alexey Tebyakin
Keyword(s):  
Analytical Solution ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Solution Method ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Two Dimensional ◽  
Various Boundary Conditions ◽  
The Finite Difference Method

The aim of the work is to obtain an analytical solution of the heat equation for various boundary conditions in the case of a two-dimensional body. As a solution method, the method of variational iterations is used. In the work, both an analytical and a numerical solution of the problem are obtained for the boundary conditions of various types and taking into account the internal heat source. To obtain a numerical solution, the finite difference method was used. The results are compared and the conclusion is made on the reliability of the decisions.

Sign in / Sign up

Export Citation Format

Share Document