A review of functionally graded thick cylindrical and conical shells (original) (raw)
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Composite Structures, 2018
The purpose of the paper is to predict the electromechanical behavior of composite shell structures with embedded piezoelectric layers using 3D-shell model based on a discrete double directors shell element. The implementation is applicable to the analysis of isotropic and functionally graded shells with integrated piezoelectric layers. The third-order shear deformation theory is introduced in the present method to remove the shear correction factor and improve the accuracy of transverse shear stresses. The present results were compared with reference solutions from literature in order to verify the accuracy of the present formulation and excellent agreement was found. A parametric study is carried out to highlight the influence of material composition and curvature radius on the deflection and axial stress along the thickness.
Nonlinear vibration of functionally graded cylindrical shells embedded with a piezoelectric layer
Thin-Walled Structures, 2014
This paper addresses the nonlinear vibration problem of simply supported functionally graded (FG) cylindrical shells with embedded piezoelectric layers. The governing differential equations of motion of the FG cylindrical shell are derived using the Lagrange equations under the assumption of the Donnell's nonlinear shallow-shell theory. A semi analytical approach, wherein the displacement fields are expanded by means of a double mixed series based on linear mode shape functions for the longitudinal, circumferential and radial variables, is proposed to characterize the nonlinear response of the cylindrical shell. The large-amplitude response and amplitude frequency curves of the cylindrical shell are obtained by using the proposed approach. Finally, the effects of excitation force and applied voltage on the vibration behavior of the cylindrical shell are investigated.
Applied Mathematical Modelling, 2012
In this paper, three-dimensional elasticity solution is extended to investigate a FGPM finite length, simply supported shell panel under dynamic pressure excitation. The host panel is assumed to be of some functionally graded piezoelectric material (FGPM). The ordinary differential equations (o.d.e.) are derived from the highly coupled partial differential equations (p.d.e.) using series expansions of mechanical and electrical displacements. The resulting system of ordinary differential equations is solved by means of Galerkin finite element method. At last, numerical examples are presented for a FGPM shell panel. To verify the validity of code and formulation, the results of a FGM panel and a FGM plate are compared with the published results.
Finite Element Modeling and Analysis of Functionally Graded (FG) Composite Shell Structures
Procedia Engineering, 2012
This article deals with the finite element modeling and analysis of functionally graded (FG) shell structures under different loading such as thermal and mechanical. Free vibration analysis of functionally graded (FG) spherical shell structure has also been presented. In order to study the influences of important parameters on the responses of FG shell structures, different types of shells have been considered. The responses obtained for FG shells are compared with the homogeneous shells of pure ceramic (Al 2 O 3) and pure metal (steel) shells and it has been observed that the responses of the FGM shells are in between the responses of the homogeneous shells. Based on the analysis, some important results are presented and discussed for thick as well as thin shells.
In this paper, a study on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are taken into account by studying the frequencies of two FG cylindrical shells. Type I FG cylindrical shell has nickel on its inner surface and stainless steel on its outer surface and Type II FG cylindrical shell has stainless steel on its inner surface and nickel on its outer surface. The study is carried out based on third order shear deformation shell theory (TSDT). The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. The analysis is carried out with strains-displacement relations from Love's shell theory. The governing equations are obtained using energy functional with the Rayleigh-Ritz method. Results are presented on the frequency characteristics and the influences of constituent various volume fractions for Type I and II FG cylindrical shells and simply supported boundary conditions on the frequencies.
Modeling and Fe Analysis of Functionally Graded (FG) Composite Shell Structures
2020
This manuscript comprises with FG (functionally graded) analysis and finite modeling element shell frameworks under divergent loading like mechanical & thermal. The analysis of free vibration of FG spherical shell framework has also been depicted. In respect to research the impact of significant aspects on FG shell frameworks responses, divergent kinds of shells were deliberated. Here, responses were attained for FG shells were compared to pure ceramic homogeneous shells (AI203) and EN 31 Steel (pure metal) and it is perceived that FGM Shells responses were in between homogenous shells responses. Furthermore, static analysis done on FG shell structure is to determine the circumferential and longitudinal stress, strain and deformation. Furthermore, modal analysis is to be determining the natural frequencies.
Scientia Iranica, 2011
The static and dynamic analysis of functionally graded material (FGM) skew plates under mechanical load is studied. The FEM formulation based on a third-order shear deformation (TOSD) theory that does not require any shear correction factor is used in the analysis. The C 1 continuity requirement of the higher-order theory has been overcome in this study by adopting a C 0 continuous isoparametric Lagrangian element with seven degrees of freedom at each node. The Mori-Tanaka homogenization scheme is used to estimate the effective properties of the constituents, and it is assumed that mechanical properties vary according to a power-law distribution of the volume fraction of the constituents. The efficiency of the present model has been validated by comparing the results obtained with those available in the literature. The effects of skew angle, boundary conditions, volume-fraction exponent, loading conditions, aspect ratio, thickness ratio, and other parameters on deflection, natural frequency, and critical buckling load of functionally graded skew plates are reported for the first time based on TOSD that can serve as the benchmark for future research.
An asymptotically exact theory of functionally graded piezoelectric shells
International Journal of Engineering Science, 2017
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.
Materials & Design, 2010
This research investigates the free vibration and buckling of a two-layered cylindrical shell made of inner functionally graded (FG) and outer isotropic elastic layer, subjected to combined static and periodic axial forces. Material properties of functionally graded cylindrical shell are considered as temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Theoretical formulations are presented based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the transverse shear and rotary inertias have considerable effect on the fundamental frequency of the FG cylindrical shell. The results for nondimensional natural frequency are in a close agreement with those in literature. It is inferred from the results that the geometry parameters and material composition of the shell have significant effect on the critical axial force, so that the minimum critical load is obtained for fully metal shell. Good agreement between theoretical and finite element results validates the approach. It is concluded that the presence of an additional elastic layer significantly increases the nondimensional natural frequency, the buckling resistance and hence the elastic stability in axial compression with respect to a FG hollow cylinder.