A.L. Kalamkarov

Bio: A.L. Kalamkarov is an academic researcher from Halifax. The author has contributed to research in topics: Magneto & Asymptotic homogenization. The author has an hindex of 1, co-authored 1 publications receiving 43 citations.

Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II – Applications

Abstract: Abstract A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly varying thickness is developed in Part I of thiswork. The asymptotichomogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of general expressions for effective elastic, piezoelectric, piezomagnetic, dielectric permittivity and other coefficients. Among these coefficients, the so-called product coefficients are determined which are present in the behavior of the macroscopic composite as a result of the interactions between the various phases but can be absent from the constitutive behavior of some individual phases of the composite structure. The model is comprehensive enough to also allow for calculation of the local fields of mechanical stresses, electric displacement and magnetic induction. The present paper determines the effective properties of constant thickness laminates comprised of monoclinic materials or orthotropic materials which are rotated with respect to their principal material coordinate system. A further example illustrates the determination of the effective properties of wafer-type magnetoelectric composite plates reinforced with smart ribs or stiffeners oriented along the tangential directions of the plate. For generality, it is assumed that the ribs and the base plate are made of different orthotropic materials. It is shown in this work that for the purely elastic case the results of the derived model converge exactly to previously established models. However, in the more general case where some or all of the phases exhibit piezoelectric and/or piezomagnetic behavior, the expressions for the derived effective coefficients are shown to be dependent on not only the elastic properties but also on the piezoelectric and piezomagnetic parameters of the constituent materials. Thus, the results presented here represent a significant refinement of previously obtained results.

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.

Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates

Abstract: By means of Non-Uniform Rational B-Splines (NURBS) curves, it is possible to describe arbitrary shapes with holes and discontinuities. These peculiar shapes can be taken into account to describe the reference domain of several nanoplates, where a nanoplate refers to a flat structure reinforced with Carbon Nanotubes (CNTs). In the present paper, a micromechanical model based on the agglomeration of these nanoparticles is considered. Indeed, when this kind of reinforcing phase is inserted into a polymeric matrix, CNTs tend to increase their density in some regions. Nevertheless, some nanoparticles can be still scattered within the matrix. The proposed model allows to control the agglomeration by means of two parameters. In this way, several parametric studies are presented to show the influence of this agglomeration on the free vibrations. The considered structures are characterized also by a gradual variation of CNTs along the plate thickness. Thus, the term Functionally Graded Carbon Nanotubes (FG-CNTs) is introduced to specify these plates. Some additional parametric studies are also performed to analyze the effect of a mesh distortion, by considering several geometric and mechanical configurations. The validity of the current methodology is proven through a comparative assessment of our results with those available from the literature or obtained with different numerical approaches, such as the Finite Element Method (FEM). The strong form of the equations governing a plate is solved by means of the Generalized Differential Quadrature (GDQ) method.

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.

Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

Abstract: The aim of this paper is to investigate the dynamic behavior of singly and doubly-curved panels reinforced by curvilinear fibers. The Variable Angle Tow (VAT) technology allows the placement of fibers along curvilinear paths with the purpose of improving dynamic performance of plates and shells. The effect of the variation of constants which define analytically the fiber orientation is also investigated by several parametric studies. The Carrera Unified Formulation (CUF) with different thickness functions along the three orthogonal curvilinear directions is the basis of the present theoretical model. Various doubly-curved laminated panels reinforced by curvilinear fibers are analyzed using several structural theories. The Local Generalized Differential Quadrature (LGDQ) method is employed to solve numerically free vibration problems. Compared to the well-known GDQ method from which it descends, the LGDQ is characterized by banded matrices instead of full ones, since the current technique considers only few points of the whole domain. Therefore, the solution of the equation system needs a lower computational effort.