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
