E. Borzabadi Farahani

Bio: E. Borzabadi Farahani is an academic researcher from Otto-von-Guericke University Magdeburg. The author has contributed to research in topics: Boundary value problem & Martensite. The author has an hindex of 4, co-authored 7 publications receiving 89 citations. Previous affiliations of E. Borzabadi Farahani include Razi University.

Natural frequency analysis of continuously graded carbon nanotube-reinforced cylindrical shells based on third-order shear deformation theory

Abstract: Based on the third-order shear deformation theory (TSDT), the investigation of the free vibration response of a continuously graded carbon nanotube-reinforced (CGCNTR) cylindrical shell is presented. The volume fractions of randomly oriented straight single-walled carbon nanotubes are assumed to be graded in the thickness direction. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The Mori–Tanaka scheme as an accurate micromechanics model is used for estimating the homogenized material properties of nanocomposites reinforced with equivalent fibers. The equations of motion and the associated boundary conditions are derived using the Hamilton’s principle based on TSDT. The discretization of the system by means of the Generalized Differential Quadrature Method leads to a standard linear eigenvalue problem. Detailed parametric studies have been carried out to s...

A novel 2-D six-parameter power-law distribution for free vibration and vibrational displacements of two-dimensional functionally graded fiber-reinforced curved panels

Abstract: As a first endeavor, the three-dimensional free vibration and vibrational displacements characteristics of two-dimensional functionally graded fiber-reinforced (2-D FGFR) curved panels with different boundary conditions are presented. This paper presents a novel 2-D six-parameter power-law distribution for fiber volume fractions of 2-D FGFR that gives designers a powerful tool for design flexible of structures under multi-functional requirements. Various material profiles in two radial and axial directions can be illustrated using the six-parameter power-law distribution. The study is carried out based on the three-dimensional, linear and small strain elasticity theory. In this work, orthotropic panel is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for FGM curved panels. Results indicate by using the 2-D six-parameter power-law distribution, it is possible to study the influence of different kinds of two-directional material profiles including symmetric and classic on the natural frequencies and modal displacements of a 2-D FGFR panel. Furthermore, maximum amplitude and uniformity of modal displacements distributions can be modified to a required manner by selecting suitable different parameters of 2-D power-law distribution and several various volume fractions profiles in two directions.

A Continuum Phase Field Model for Fracture

Abstract: A variational free-discontinuity formulation of brittle fracture was given by Francfortand Marigo [1], where the total energy is minimized with respect to the crackgeometry and the displacement field simultaneously. The entire evolution of cracksincluding their initiation and branching is determined by this minimization principlerequiring no further criterion. However, a direct numerical discretization of themodel faces considerable difficulties as the displacement field is discontinuous inthe presence of cracks.

Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells

Abstract: This paper aims at investigating the effect of Carbon Nanotube (CNT) agglomeration on the free vibrations of laminated composite doubly-curved shells and panels reinforced by CNTs. The great performances of doubly-curved structures are joined with the excellent mechanical properties of CNTs. Several laminations schemes and various CNT exponential distributions along the thickness of the structures are considered. Thus, it is evident that the shell dynamic behavior can be affected by many parameters which characterize the reinforcing phase. A widespread parametric study is performed in order to show the natural frequency variation. The general theoretical model for shell structures is based on the so-called Carrera Unified Formulation (CUF) which allows to consider several Higher-order Shear Deformations Theories (HSDTs). In addition, a complete characterization of the mechanical properties of CNTs is presented. The governing equations for the free vibration analysis are solved numerically by means of the well-known Generalized Differential Quadrature (GDQ) method due to its accuracy, stability and reliability features.

Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels

Abstract: In this paper, natural frequencies characteristics of a continuously graded carbon nanotube-reinforced (CGCNTR) cylindrical panels based on the Eshelby–Mori–Tanaka approach is considered. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this research work, an equivalent continuum model based on the Eshelby–Mori–Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The CGCNTR shell is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The novelty of the present work is to exploit Eshelby–Mori–Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various mid radius-to-thickness ratio, shell angle, length-to-mean radius ratio and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR cylindrical panels. The interesting and new results show that continuously graded oriented CNTs volume fractions can be utilized for the management of vibrational behavior of structures so that the frequency parameters of structures made of such material can be considerably improved than that of the nanocomposites reinforced with uniformly distributed CNTs.

Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes

Abstract: The static response of composite plates and shells reinforced by agglomerated nanoparticles made of Carbon Nanotubes (CNTs) is investigated in the present paper. A two-parameter agglomeration model is taken into account to describe the micromechanics of such particles, which show the tendency to agglomerate into spherical regions when scattered in a polymer matrix. From the macro mechanical point of view, the structures under consideration are characterized by a gradual variation of their mechanical properties along the thickness direction, since various distributions are employed to describe the volume fraction of the reinforcing phase. Several Higher-order Shear Deformation Theories (HSDTs) are taken into account and compared. The fundamental equations which govern the static problem in hand are solved numerically by means of the Generalized Differential Quadrature (GDQ) method. The variation of the agglomeration parameters, as well as the through-the-thickness profiles which describe the CNT volume fraction, are investigated to show the effect of the reinforcing phase on the static response of these nanocomposite plates and shells. In particular, a posteriori stress and strain recovery procedure is developed for these purposes. The current approach is validated through the comparison with the results available in the literature or obtained by a three-dimensional finite element model.