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1
Content available Natural frequencies of FG plates with two new distribution of porosity
Merdaci Slimane, Mostefa Adda Hadj, Khayal Osama M. E. S.
International Journal of Applied Mechanics and Engineering
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2021
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Vol. 26, no. 2
128--142
EN
The functionally graded plates (FGP) with two new porosity distributions are examined in this paper. In this work the plate is modeled using the higher-order shear deformation plate principle. The shear correction variables are neglected. To evaluate the equations of motion, the Hamilton method will be used herein. Therefore, the free vibration analysis of FG plate is developed in this work. For porous smart plates with simply-supported sides, natural frequencies are obtained and verified with the established findings in the literature. The impact of the porosity coefficient on the normal frequencies of the plate for various thickness ratios, geometric ratios, and material properties was investigated in a thorough numerical analysis.
2
Content available Static behaviour of functionally graded plates resting on elastic foundations using neutral surface concept
Van-Loi Nguyen, Minh-Tu Tran, Van-Long Nguyen, Quang-Huy Le
Archive of Mechanical Engineering
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2021
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LXVIII, nr 1
5--22
EN
In this study, static behaviors of functionally graded plates resting on Winkler-Pasternak elastic foundation using the four-variable refined theory and the physical neutral surface concept is reported. The four-variable refined theory assumes that the transverse shear strain has a parabolic distribution across the plate’s thickness, thus, there is no need to use the shear correction factor. The material properties of the plate vary continuously and smoothly according to the thickness direction by a power-law distribution. The geometrical middle surface of the functionally graded plate selected in computations is very popular in the existing literature. By contrast, in this study, the physical neutral surface of the plate is used. Based on the four-variable refined plate theory and the principle of virtual work, the governing equations of the plate are derived. Next, an analytical solution for the functionally graded plate resting on the Winkler-Pasternak elastic foundation is solved using the Navier’s procedure. In numerical investigations, a comparison of the static behaviors of the functionally graded plate between several models of displacement field using the physical neutral surface is given, and parametric studies are also presented.
3
Content available Study on harmonic analysis of functionally graded plates using FEM
Sharma A. K., Sharma P., Chauhan P. S., Bhadoria S. S.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 4
941--961
EN
This paper presents the harmonic and vibration analysis of functionally graded plates using the finite element method. Initially, the plates are assumed isotropic and the material properties of it are assumed to vary continuously through their thickness direction according to a power-law distribution of the volume fractions of the plate constituents. The four noded shell element is used to analyse the functionally graded plates. Four functionally graded plates-Al/Al2O3, Al/ZrO2, Ti–6Al–4V/Aluminium oxide, and SUS304/Si3N4 are considered in the study, and their results are obtained so that the right choice can be made in applications in high temperature environment and in reducing the vibration amplitudes in applications such as aircrafts, rockets, missiles, etc. Numerical results for the natural frequency and harmonic response amplitude are presented. Results are compared and validated with available results in the literature. Effects of boundary conditions, material and damping on natural frequency and harmonic response of the functionally graded plates are also investigated.
4
Content available A study on low velocity impact response of FGM rectangular plates with 3D elasticity based graded finite element modeling
Asemi K., Jedari Salami S.
Journal of Theoretical and Applied Mechanics
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2015
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Vol. 53 nr 4
859—872
EN
Low velocity impact behavior of rectangular plates made of functionally graded materials (FGMs) based on three-dimensional theory of elasticity is studied in this paper. The modified Hertz contact law, which is appropriate for graded materials, is employed. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the graded finite element modeling is applied. Solution of the nonlinear resulted system of equations in the time domain is accomplished via an iterative numerical procedure based each time on Newmark’s integration method. The effects of various involved parameters, such as the graded property profile, projectile velocity and projectile density on time histories of contact force, lateral deflection and normal stresses are investigated in detail. To present efficiency of the present work, several numerical examples are included. The main novelty of the present research, which has not been reported in literature, is considering the difference of lateral deflection through the thickness of the FGM plate due to analyzing three-dimensional elasticity of the plate.
5
Content available remote Static analysis of functionally graded thin rectangular plates with various boundary supports
Pradhan K. K., Chakraverty S.
Archives of Civil and Mechanical Engineering
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2015
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Vol. 15, no. 3
721--734
EN
Present study deals with static analysis of functionally graded (FG) rectangular plates subjected to various possible boundary conditions within the framework of classical plate theory. Material properties of the FG plate are assumed to vary continuously in the thickness direction according to power-law form. The trial functions denoting the transverse deflection of the plate are expressed as simple algebraic polynomials. Uniformly distributed load (UDL) and hydrostatic pressure are considered to be the external mechanical loads. Rayleigh–Ritz method along with mechanical kinematic relations and non-dimensionalization technique are employed in the numerical modeling to obtain the system of linear equations for the pure bending. Here the main objective is to study the effect of aspect ratio and volume fraction of the constituents on numerical factors associated with centroidal deflection, bending moments and normal stresses. New results for these factors are presented after checking the convergence pattern and validation has been done with the available results in special cases.
6
Content available remote Static and Dynamic Thermomechanical Buckling Loads of Functionally Graded Plates
Kowal-Michalska K., Mania R. J.
Mechanics and Mechanical Engineering
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2013
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Vol. 17, nr 1
99--112
EN
In the paper the buckling phenomenon for static and dynamic loading (pulse of finite duration) of FGM plates subjected to simultaneous action of one directional compression and thermal field is presented. Thin, rectangular plates simply supported along all edges are considered. The investigations are conducted for different values of volume fraction exponent and uniform temperature rise in conjunction with mechanical dynamic pulse loading of finite duration.
7
Content available remote Vibrations of microstructured functionally graded plates
Jędrysiak J.
Vibrations in Physical Systems
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2012
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Vol. 25
193--198
EN
Functionally graded plates with a microstructure are considered. The size of the microstructure is assumed to be of an order of the plate thickness. To take into account the effect of the microstructure on vibrations of these plates the tolerance modelling method is applied. Using this method we obtain model equations with smooth functional coefficients involving terms dependent of the microstructure size.
8
Content available remote Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories
Cheng Z., Batra R.
Archives of Mechanics
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2000
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Vol. 52, nr 1
143-158
EN
We derive field equations for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order shear-deformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Kirchhoff plate. This relationship is used to explicitly express the displacements of a plate particle according to the first-order shear deformation theory in terms of the deflection of a homogeneous Kirchhoff plate. These relationships can readily be used to obtain similar correspondences between the deflections of a transversely isotropic laminated plate and a homogeneous Kirchhoff plate.
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