•Journal•ISSN: 2353-7396

# Curved and Layered Structures

About: Curved and Layered Structures is an academic journal. The journal publishes majorly in the area(s): Finite element method & Boundary value problem. It has an ISSN identifier of 2353-7396. It is also open access. Over the lifetime, 155 publication(s) have been published receiving 1143 citation(s).

Topics: Finite element method, Boundary value problem, Shell (structure), Timoshenko beam theory, Bending

##### Papers

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TL;DR: In this article, a comparison between classical 2D finite elements and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders is made.

Abstract: Abstract The paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.

43 citations

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TL;DR: In this article, a comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly varying thickness is developed using static equilibrium equations and the quasi-static approximation of Maxwell's equations.

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.

43 citations

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TL;DR: In this paper, a complete and homogeneous presentation of plane stress and plane strain problems using the Strong Formulation Finite Element Method (SFEM) is presented, in particular, a greater emphasis is given to the numerical implementation of the governing and boundary conditions of the partial differential system of equations.

Abstract: Abstract This present paper has a complete and homogeneous presentation of plane stress and plane strain problems using the Strong Formulation Finite Element Method (SFEM). In particular, a greater emphasis is given to the numerical implementation of the governing and boundary conditions of the partial differential system of equations. The paper’s focus is on numerical stability and accuracy related to elastostatic and elastodynamic problems. In the engineering literature, results are mainly reported for isotropic and homogeneous structures. In this paper, a composite structure is investigated. The SFEM solution is compared to the ones obtained using commercial finite element codes. Generally, the SFEM observes fast accuracy and all the results are in very good agreement with the ones presented in literature.

41 citations

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TL;DR: In this article, a model for the analysis of a smart composite piezo-magneto-thermo-elastic thin plate with rapidly-varying thickness is presented.

Abstract: A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermo- elastic thin plate with rapidly-varying thickness is devel- oped in the present paper. A rigorous three-dimensional formulation is used as the basis of multiscale asymptotic homogenization. The asymptotic homogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell's equations. The work culminates in the derivation of a set of differential equations and associated boundary conditions. These sys- tems of equations are called unit cell problems and their solution yields such coefficients as the effective elastic, piezoelectric, piezomagnetic, dielectric permittivity and others. Among these coefficients, the so-called product co- efficients are also determined which are present in the be- havior of the macroscopic composite as a result of the in- teractions and strain transfer between the various phases but can be absent from the constitutive behavior of some individual phases of the composite material. The model is comprehensive enough to allow calculation of such lo- cal fields as mechanical stress, electric displacement and magnetic induction. In part II of this work, the theory is illustrated by means of examples pertaining to thin lam- inated magnetoelectric plates of uniform thickness and wafer-type smart composite plates with piezoelectric and piezomagnetic constituents. The practical importance of the model lies in the fact that it can be successfully em- ployed to tailor the effective properties of a smart compos- ite plate to the requirements of a particular engineering application by changing certain geometric or material pa- rameters. The results of the model constitute an important refinement over previously established work. Finally, it is shown that in the limiting case of a thin elastic plate of uni- form thickness the derived model converges to the familiar classical plate model.

41 citations

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TL;DR: In this paper, the free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated and the method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylinders.

Abstract: Abstract In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

40 citations