Vol. 12, No. 5, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 5, 563–722
Issue 4, 353–561
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Subscriptions
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Author Index
To Appear
 
ISSN: 1559-3959
Static analysis of nanobeams using Rayleigh–Ritz method

Laxmi Behera and S. Chakraverty

Vol. 12 (2017), No. 5, 603–616
Abstract

Boundary characteristic orthogonal polynomials have been used as shape functions in the Rayleigh–Ritz method for static analysis of nanobeams. The formulation is based on Euler–Bernoulli and Timoshenko beam theories in conjunction with nonlocal elasticity theory of Eringen. Application of Rayleigh–Ritz method converts the problem into a system of linear equations. Some of the parametric studies have been carried out. The novelty of the method is that it can handle any set of classical boundary conditions (viz., clamped, simply supported and free) with ease. Although the assumed shape functions need to satisfy the geometric boundary condition only, the final solution is for the targeted boundary condition of the problem or domain. Deflection and rotation shapes for some of the boundary conditions have also been illustrated.

Keywords
Rayleigh–Ritz method, boundary characteristic orthogonal polynomial, nonlocal elasticity theory
Milestones
Received: 11 November 2016
Revised: 2 June 2017
Accepted: 13 June 2017
Published: 22 November 2017
Authors
Laxmi Behera
Department of Mathematics
National Institute of Technology
Rourkela
India
S. Chakraverty
Department of Mathematics
National Institute of Technology
Rourkela
India