Relationship between Bending Solutions of FGM and Homogenous Circular Cylindrical Shells

2013 ◽  
Vol 353-356 ◽  
pp. 3236-3242
Author(s):  
Ze Qing Wan ◽  
Shi Rong Li
Keyword(s):  
Cylindrical Shell ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Continuous Functions ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Circular Cylindrical Shells

Based on the Loves shell theory, relationship between bending solutions of functionally graded materials (FGM) and homogenous circular cylindrical shells was studied. By comparing the displacement-type governing equations for axially symmetrically bending of FGM and homogenous circular cylindrical shells, an analogous transform relation between the deflections of FGM circular cylindrical shell and those of homogenous one was obtained. By giving the material properties of FGM circular cylindrical shell changing as continuous functions in the thickness direction, the corresponding transition factor between the solutions of the two kind circular cylindrical shells were derived, which reflect the non-uniform properties of the functionally graded material circular cylindrical shell. Numerical example shows that the numerical solutions of the maximum of non-dimensional deflections are almost in agreement with the transformational solutions whennequals approximately 5, wherenis the volume fraction index. As a result, solutions for axially symmetrically bending of a non-homogenous circular cylindrical shell can be reduced to that of a homogenous one and the calculation of the transformation factors.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is 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 effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

scholarly journals Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Muhmmad Nawaz Naeem ◽  
Shazia Kanwal ◽  
Abdul Ghafar Shah ◽  
Shahid Hussain Arshad ◽  
Tahir Mahmood
Keyword(s):  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Lagrangian Function ◽  
Dynamical Equations ◽  
Graded Materials ◽  
Present Technique ◽  
Circular Cylindrical Shells ◽  
Stiffened Cylindrical Shells

The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.

Asymmetric thermo-elastic analysis of long cylindrical shells of functionally graded materials by differential quadrature method

2011 ◽  
Vol 226 (5) ◽  
pp. 1133-1147 ◽  
Author(s):  
R Akbari Alashti ◽  
M Khorsand ◽  
M H Tarahhomi
Keyword(s):  
Cylindrical Shell ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Temperature Fields ◽  
Elastic Analysis ◽  
Graded Materials ◽  
Graded Material ◽  
Power Law Function

Asymmetric thermo-elastic analysis of a long cylindrical shell made of functionally graded material under the effect of thermo-mechanical loadings is carried out. Material properties of the cylindrical shell are assumed to be graded in the radial direction according to a power law function, while the Poisson's ratio is assumed to be constant. Numerical solutions of displacement, stress, and temperature fields are obtained using the Fourier and polynomial differential quadrature methods. The results are compared with the reported analytical solutions which are found to be in very good agreement. The cylindrical shell is considered to be under the effect of both axisymmetric and asymmetric loading conditions. Effects of grading parameter, temperature difference, and the ratio of the outer to inner radii of the cylindrical shell on stresses, displacement, and temperature fields are presented.

scholarly journals Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Kadir Mercan ◽  
Çiğdem Demir ◽  
Ömer Civalek
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Graded Material ◽  
Circular Cylindrical Shells ◽  
Discrete Singular Convolution ◽  
Power Law Index ◽  
Free Vibration Response

AbstractIn 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.

The Ritz formulation applied to the study of the vibration frequency characteristics of functionally graded circular cylindrical shells

2009 ◽  
Vol 224 (1) ◽  
pp. 43-54 ◽  
Author(s):  
M N Naeem ◽  
S H Arshad ◽  
C B Sharma
Keyword(s):  
Vibration Frequency ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Frequency Spectra ◽  
Closed Form Solutions ◽  
Graded Material ◽  
Circular Cylindrical Shells ◽  
Direct Variational Method ◽  
Thin Shell Theory

In this article vibration frequencies of functionally graded circular cylindrical shells are analysed and studied using the Ritz formulation. Since closed-form solutions are limited to simple cases, an approximate method is employed to solve the shell problem, and numerical evaluation is carried out using a direct variational method. Axial modal dependence is chosen in terms of Ritz polynomials to ascertain a rapid convergence of the method. Sanders and Budiansky's thin shell theory is utilized for strain—displacement and curvature—displacement relations. Functionally graded material characteristics for the constituent materials are distributed in accordance with a volume fraction law. Influence of boundary conditions and volume fraction exponents on the vibration frequency spectra is analysed. The present results are compared with some previous works and excellent agreement is found.

scholarly journals Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method

2012 ◽  
Vol 34 (3) ◽  
pp. 139-156 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Axial Compression ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Method Effects ◽  
Circular Cylindrical Shells

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection.  Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper  [13] which were solved by Ritz energy method.

Creep Analysis of Functionally Graded Material Thick-Walled Cylinder

2013 ◽  
Vol 315 ◽  
pp. 867-871 ◽  
Author(s):  
Saifulnizan Jamian ◽  
Hisashi Sato ◽  
Hideaki Tsukamoto ◽  
Yoshimi Watanabe
Keyword(s):  
Cross Section ◽  
Volume Fraction ◽  
Rectangular Cross Section ◽  
Functionally Graded ◽  
Graded Materials ◽  
Incremental Approach ◽  
Creep Analysis ◽  
Graded Material ◽  
Ring Elements ◽  
Walled Cylinder

In this paper, creep analysis for a thick-walled cylinder made of functionally graded materials (FGMs) subjected to thermal and internal pressure is carried out. The structure is replaced by a system of discrete rectangular cross-section ring elements interconnected along circumferential nodal circles. The property of FGM is assumed to be continuous function of volume fraction of material composition. The creep behavior of the structures is obtained by the use of an incremental approach. The obtained results show that the property of FGM significantly influences the stress distribution along the radial direction of the thick-walled cylinder as a function of time.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

scholarly journals Mechanical Properties of Al 25 wt.% Cu Functionally Graded Material

2019 ◽  
Vol 26 (1) ◽  
pp. 327-337 ◽  
Author(s):  
Aref Mehditabar ◽  
Gholam H. Rahimi ◽  
Seyed Ebrahim Vahdat
Keyword(s):  
Cylindrical Shell ◽  
Wear Rate ◽  
Rate Coefficient ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Compressive Test ◽  
High Entropy ◽  
Graded Material ◽  
Maximum Volume Fraction

AbstractThe present work refers to describe the effects of Al2Cu variations on various properties of thick-walled functionally graded (FG) cylindrical shell. Al-25 wt.% Cu hypo-eutectic alloy ingot is melted and centrifugally casted to obtain high entropy FG composite. A series of microstructure examinations such as FESEM and EDX analysis were carried out to determine the distributions of constituent phases and elements. It is revealed that the maximum volume fraction of Al2Cu particle is reached near the inner surface with 35.7 Vol.% and then reduces gradually to 32.5 Vol.% at the outer surface of FG cylindrical shell. The effects of the variations Al2Cu along radial direction of FG tube are discussed through Vickers hardness, wear rate, coefficient of thermal expansion and compressive test measurements. The experimental results show that the wear and hardness are varied in graded manner which the highest wear resistance with wear rate of 9.1×10−5g/mm2 and hardness with 153HV are found towards Al2Cu enriched zone or inner periphery. Moreover, the studied FG cylindrical shell shows drop 2.5% in yield stress and 4.5% in elastic modulus from intermediate to inner layers due to Al2Cu particles clustering in metal matrix.

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