Elasticity Solution for Nano-Beam Subjected to Uniform Static Pressure Using State Space Method

摘要

In this paper, bending behavior of simply supported nano-beam is investigated employing non-local continuum mechanics. By using the Fourier series and state-space method, the two-dimensional governing differential equations in term of displacement components can be obtained. Closed form solution for the bending behavior of nano-beam is obtained by exerting the surface tractions on state variables. Effect of non-local parameter, thickness to length ratio and half wave numbers on the static behavior of nano-beam are examined. Furthermore, these results may also serve as a benchmark to further results into the Euler-Bernoulli beam model as well as the Timoshenko beam model.