Showing papers by "Reza Attarnejad published in 2016"

Analysis of Euler-Bernoulli nanobeams: A mechanical-based solution

Abstract: 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.

Tsunami generation and associated waves in the water column and seabed due to an asymmetric earthquake motion within an anisotropic substratum

Abstract: In this paper, closed-form integral expressions are derived to describe how surface gravity waves (tsunamis) are generated when general asymmetric ground displacement (due to earthquake rupturing), involving both horizontal and vertical components of motion, occurs at arbitrary depth within the interior of an anisotropic sub-sea solid beneath the ocean. In addition, we compute the resultant hydrodynamic pressure within the seawater and the elastic wavefield within the seabed at any position. The method of potential functions and an integral transform approach, accompanied by a special contour integration scheme, are adopted to handle the equations of motion and produce the numerical results. The formulation accounts for any number of possible acoustic-gravity modes and is valid for both shallow and deep water situations as well as for any focal depth of the earthquake source. Phase and group velocity dispersion curves are developed for surface gravity (tsunami mode), acoustic-gravity, Rayleigh, and Scholte waves. Several asymptotic cases which arise from the general analysis are discussed and compared to existing solutions. The role of effective parameters such as hypocenter location and frequency of excitation are examined and illustrated through several figures which show the propagation pattern in the vertical and horizontal directions. Attention is directed to the unexpected contribution from the horizontal ground motion. The results have important application in several fields such as tsunami hazard prediction, marine seismology and offshore and coastal engineering. In a companion paper we examine the effect of ocean stratification on the appearance and character of internal and surface gravity waves. This article is protected by copyright. All rights reserved.

On the Analysis of FGM Beams: FEM with Innovative Element

Abstract: This paper aims at presenting a new efficient element for free vibration and instability analysis of Axially Functionally Graded Materials (FGMs) non-prismatic beams using Finite Element Method (FEM). Using concept of Basic Displacement Functions (BDFs), two- node element extends to three-node element for obtaining much more exact results using FEM. First, BDFs are introduced and computed using energy method such as unit-dummy load method. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions; free vibration and instability analysis of the FGM beam are studied using finite element method for all types of AFGM beams and the convergence of FEM has been studied. The results from both free vibration and instability analysis are in perfect agreement with those of previously published.