A New Method for Bending Analysis of Nano Beam and Rectangular Nano Plate: Full Modified Nonlocal Theory

In this article, a novel method, namely full modified nonlocal (FMNL) theory, for analysis of nano structures under different case loading. Also bending analysis of rectangular nano plates and nano beams are investigated in order to demonstrate the effectiveness of the presented theory. For this purpose, a complete representation of governing equation and boundary conditions are derived based on the infinite series of modified nonlocal constitutive equations by applying the variational principle. It is shown that by rearranging and then computing the sum of the infinite series which appears in the maximum bending deflection, the truncation errors will be eliminated. In addition, the results of the presented method are compared with MD simulations to confirm the validity of FMNL theory. One of the advantages of the FMNL theory is that the defect of nonlocal (NL) theory in vanishing of small scale effect for some problems can be resolved. Furthermore, the FMNL theory will be a criterion for accuracy of the primary modified nonlocal (PMNL) theory that considers only two terms of the series of the modified nonlocal constitutive equation in predicting maximum bending deflections.