University of Tehran Press Journal of Computational Applied Mechanics 2423-6713 47 2 2016 12 01 Analysis of Euler-Bernoulli nanobeams: A mechanical-based solution 159 180 60708 10.22059/jcamech.2017.140165.97 EN Mohammad Zakeri School of Civil Engineering, College of Engineering, University of Tehran, Tehran P.O. Box 11365-4563, Iran. Reza Attarnejad School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran Amir Mohsen Ershadbakhsh School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran Journal Article 2016 01 10 The accuracy and efficiency of the elements proposed by finite element method (FEM) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. In the present study, novel functions, namely basic displacements functions (BDFs), are introduced and exploited for structural analysis of nanobeams using finite element method based on Eringen’s nonlocal elasticity and EulerBernoulli beam theory. BDFs are obtained through solving the governing differential equation of motion of nanobeams using the power series method. Unlike the conventional methods which are almost categorized as displacement-based methods, the flexibility basis of the method ensures true satisfaction of equilibrium equations at any interior point of the element. Accordingly, shape functions and structural matrices are achieved in terms of BDFs by application of merely mechanical principles. In order to evaluate the competency and accuracy of the proposed method with different boundary conditions, several numerical examples with various boundary conditions are scrutinized. Carrying out several numerical examples, the results in stability analysis, free longitudinal vibration and free transverse vibration show a complete accordance with those in literature. https://jcamech.ut.ac.ir/article_60708_41737af207ed25f5023a869b9add6f81.pdf