• Title, Summary, Keyword: Functionally Graded Material

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Nonlinear static analysis of functionally graded porous beams under thermal effect

  • Akbas, Seref D.
    • Coupled systems mechanics
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    • v.6 no.4
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    • pp.399-415
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    • 2017
  • This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.

A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates

  • Benbakhti, Abdeldjalil;Bouiadjra, Mohamed Bachir;Retiel, Noureddine;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • v.22 no.5
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    • pp.975-999
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    • 2016
  • This work investigates a thermomechanical bending analysis of functionally graded sandwich plates by proposing a novel quasi-3D type higher order shear deformation theory (HSDT). The mathematical model introduces only 5 variables as the first order shear deformation theory (FSDT). Unlike the conventional HSDT, the present one presents a novel displacement field which includes undetermined integral variables. The mechanical properties of functionally graded layers of the plate are supposed to change in the thickness direction according to a power law distribution. The core layer is still homogeneous and made of an isotropic ceramic material. The governing equations for the thermomechanical bending investigation are obtained through the principle of virtual work and solved via Navier-type method. Interesting results are determined and compared with quasi-3D and 2D HSDTs. The influences of functionally graded material (FGM) layer thickness, power law index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are discussed.

Thermal effect on axisymmetric bending of functionally graded circular and annular plates using DQM

  • Hamzehkolaei, N. Safaeian;Malekzadeh, P.;Vaseghi, J.
    • Steel and Composite Structures
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    • v.11 no.4
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    • pp.341-358
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    • 2011
  • This paper presents the effects of thermal environment and temperature-dependence of the material properties on axisymmetric bending of functionally graded (FG) circular and annular plates. The material properties are assumed to be temperature-dependent and graded in the thickness direction. In order to accurately evaluate the effect of thermal environment, the initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Governing equations and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the virtual work principle based on the elasticity theory. The differential quadrature method (DQM) as an efficient and robust numerical tool is used to obtain the initial thermal stresses and response of the plate. Comparison studies with some available results for FG plates are performed. The influences of temperature rise, temperature-dependence of material properties, material graded index and different geometrical parameters are carried out.

Dynamic Propagation of a Interface Crack in Functionally Graded Layers under Anti-plane Shear (면외전단하중이 작용하는 기능경사재료 접합면 균열의 동적전파에 관한 연구)

  • Shin, Jeong-Woo;Lee, Young-Shin;Kim, Sung-Chan
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.459-464
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    • 2010
  • The dynamic propagation of an interface crack between two dissimilar functionally graded layers under anti-plane shear is analyzed using the integral transform method. The properties of the functionally graded layers vary continuously along the thickness. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to a dual integral equation, which is then expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented. Followings are helpful to increase of the resistance of the interface crack propagation of FGM: a) increase of the gradient of material properties; b) increase of the material properties from the interface to the upper and lower free surface; c) increase of the thickness of FGM layer. The DERR increases or decreases with increase of the crack moving velocity.

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Bending analysis of thick functionally graded piezoelectric rectangular plates using higher-order shear and normal deformable plate theory

  • Dehsaraji, M. Lori;Saidi, A.R.;Mohammadi, M.
    • Structural Engineering and Mechanics
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    • v.73 no.3
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    • pp.259-269
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    • 2020
  • In this paper, bending-stretching analysis of thick functionally graded piezoelectric rectangular plates is studied using the higher-order shear and normal deformable plate theory. On the basis of this theory, Legendre polynomials are used for approximating the components of displacement field. Also, the effects of both normal and shear deformations are encountered in the theory. The governing equations are derived using the principle of virtual work and variational approach. It is assumed that plate is made of piezoelectric materials with functionally graded distribution of material properties. Hence, exponential function is used to modify mechanical and electrical properties through the thickness of the plate. Finally, the effect of material properties, electrical boundary conditions and dimensions are investigated on the static response of plate. Also, it is shown that results of the presented model are close to the three dimensional elasticity solutions.

Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading

  • Kocaturk, Turgut;Akbas, Seref Doguscan
    • Structural Engineering and Mechanics
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    • v.41 no.6
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    • pp.775-789
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    • 2012
  • This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

Comparative Numerical Analysis of Homogenized and Discrete-Micromechanics Models for Functionally Graded Materials (기능경사재를 위한 균질화와 이산화-미시역학 모델에 대한 비교 수치해석)

  • Ha, Dae-Yul;Lee, Hong-Woo;Cho, Jin-Rae
    • Proceedings of the KSME Conference
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    • pp.399-404
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    • 2000
  • Functionally graded materials(FGMs) involve dual-phase graded layers in which two different constituents are mixed continuously and functionally according to a given volume fraction. For the analysis of their thermo-mechanical response, conventional homogenized methods have been widely employed in order to estimate equivalent material properties of the graded layer. However, such overall estimations are insufficient to accurately predict the local behavior. In this paper, we compare the thermo-elastic behaviors predicted by several overall material-property estimation techniques with those obtained by discrete analysis models utilizing the finite element method, for various volume fractions and loading conditions.

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Radial vibration behaviors of cylindrical composite piezoelectric transducers integrated with functionally graded elastic layer

  • Wang, H.M.;Wei, Y.K.;Xu, Z.X.
    • Structural Engineering and Mechanics
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    • v.38 no.6
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    • pp.753-765
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    • 2011
  • The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid

  • Shafiee, Ali A.;Daneshmand, Farhang;Askari, Ehsan;Mahzoon, Mojtaba
    • Structural Engineering and Mechanics
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    • v.50 no.1
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    • pp.53-71
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    • 2014
  • A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.

Large deformation bending analysis of functionally graded spherical shell using FEM

  • Kar, Vishesh Ranjan;Panda, Subrata Kumar
    • Structural Engineering and Mechanics
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    • v.53 no.4
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    • pp.661-679
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    • 2015
  • In this article, nonlinear finite element solutions of bending responses of functionally graded spherical panels are presented. The material properties of functionally graded material are graded in thickness direction according to a power-law distribution of volume fractions. A general nonlinear mathematical shallow shell model has been developed based on higher order shear deformation theory by taking the geometric nonlinearity in Green-Lagrange sense. The model is discretised using finite element steps and the governing equations are obtained through variational principle. The nonlinear responses are evaluated through a direct iterative method. The model is validated by comparing the responses with the available published literatures. The efficacy of present model has also been established by demonstrating a simulation based nonlinear model developed in ANSYS environment. The effects of power-law indices, support conditions and different geometrical parameters on bending behaviour of functionally graded shells are obtained and discussed in detail.