Vol. 12, No. 5, 2017

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Static analysis of nanobeams using Rayleigh–Ritz method

Laxmi Behera and S. Chakraverty

Vol. 12 (2017), No. 5, 603–616

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.

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