In this article, a novel method, namely full modified nonlocal (FMNL) theory, for bending and buckling analysis of simply supported rectangular nano plates has been proposed. In this theory, a complete representation of strong-form 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 and critical buckling load, the truncation errors will be eliminated. A radius of convergence for the computed series is calculated to make sure the analyses are valid and reliable. 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 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 theory that considers only two terms of the series of the modified nonlocal constitutive equation in predicting critical buckling loads and maximum bending deflections.
Meccanica – Springer Journals
Published: Jan 9, 2017
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