Bending Analysis of A Cantilever Nanobeam With End Forces By Laplace Transform

In this study, the static behavior of nanobeams subjected to end concentrated loads is theoretically investigated in the Laplace domain. A closed form of solution for the title problem is presented using Euler-Bernoulli beam theory.  Nonlocal elasticity theory proposed by Eringen is used to represent small scale effect. A systems of differential equations containing a small scale parameter is derived for nanobeams. Laplace transformation is applied to this systems of differential equations containing a small scale parameter. The exact static response of the nanobeam with end concentrated loads is obtained by applying inverse Laplace transform. The calculate results are plotted in a series of figures for various combinations of concentrated loads.