Using of state-space approach to predict deflection of nanobeams

Modified continuum models have been the essence of much attention in nanomechanics through their computational efficiency and the capability to produce accurate results which are comparable to the atomistic models ones. As the dimensions of a structure approach to the nanoscale, the classical continuum theory has not the capability to predict the behavior of nanostructures due to the size-dependent of their properties which is known as size-effects. In this work, the bending behavior of nanobeams with common sets of boundary conditions is investigated using state-space modeling on the basis of nonlocal beam theories. Both uniform load and point load are considered in this study. To this end, Eringen’s equations of nonlocal elasticity are incorporated into the classical beam theories namely as Euler-Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT). The maximum deflection of nanobeams corresponding to each set of boundary conditions is obtained using state variables and matrix algebra. The results are presented for different geometric parameters, boundary conditions, and the values of nonlocal parameter to show the effects of each distinctly. It is found that the non-dimensional maximum deflection corresponding to all boundary conditions and both loading cases will be increased for higher values of nonlocal parameter which show this fact that with increasing the nonlocal parameter, the stiffness of nanobeam decreases.