Bending Sector Graphene Sheet Based on the Elastic Winkler-Pstrnak with the Help of Nonlocal Elasticity Theory Using Developed Kantorovich Method

Authors

  • M. Jabarzadeh Assistant Prof., Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
  • Sh. Dastjerdi MSc Student, Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Abstract:

In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with regard to nonlocal relationship of stress, shear theory of the first order, and obtained linear strains using developed Kantorovich method. In this method, the obtained partial differential equations are converted into two categories that can be solved using analytical and numerical methods. Developed Kantorovich method is a method with a high rate of convergence, in which the expected convergence is achieved with just three to four repetitions. With regard to the fact that no research has yet been conducted in this regard, the results, considering the nonlocal coefficient equal to zero, have been compared with other articles in order to check the validity. In the end, the effect of nonlocal coefficient variations on the results in terms of thickness, boundary conditions, hardness of elastic base and difference between nonlocal and local elasticity analysis has been studied.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Nonlinear Bending Analysis of Sector Graphene Sheet Embedded in Elastic Matrix Based on Nonlocal Continuum Mechanics

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

full text

Buckling analysis of graphene nanosheets based on nonlocal elasticity theory

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

full text

Buckling analysis of graphene nanosheets based on nonlocal elasticity theory

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

full text

buckling analysis of graphene nanosheets based on nonlocal elasticity theory

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

full text

Study the Surface Effect on the Buckling of Nanowires Embedded in Winkler–Pasternak Elastic Medium Based on a Nonlocal Theory

Nano structures such as nanowires, nanobeams and nanoplates have been investigated widely for their innovative properties. In this paper the buckling of nanowires surrounded in a Winkler - Pasternak elastic medium has been examined based on the nonlocal Euler-Bernoully model with considering the surface effects. In the following a parametric study that explores the influence of numerous physica...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 7  issue 2

pages  49- 35

publication date 2014-12-22

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023