• Smart Structures and Systems
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• 제25권2호
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• pp.197-218
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• 2020

In this work, thermomechanical flexural analysis of functionally graded material sandwich plates with P-FGM face sheets and E-FGM and symmetric S-FGM core is performed by employing a nth-order shear deformation theory. A novel type of S-FGM sandwich plates, namely, both P-FGM face sheets and a symmetric S-FGM hard core are considered. By employing only four unknown variables, the governing equations are obtained based on the principle of virtual work and then Navier method is used to solve these equations. Analytical solutions are deduced to compute the stresses and deflections of simply supported S-FGM sandwich plates. The effects of volume fraction variation, geometrical parameters and thermal load on thermomechanical flexural behavior of the symmetric FGM sandwich plates are investigated.

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.551-561
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• 2017

As FGM (functionally graded material) bars which vibrate in axial or longitudinal direction have great potential for applications in diverse engineering fields, developing a reliable mathematical model that provides very reliable vibration and wave characteristics of a FGM axial bar, especially at high frequencies, has been an important research issue during last decades. Thus, as an extension of the previous works (Hong et al. 2014, Hong and Lee 2015) on three-layered FGM axial bars (hereafter called FGM bars), an enhanced spectral element model is proposed for a FGM bar model in which axial and radial displacements in the radial direction are treated more realistic by representing the inner FGM layer by multiple sub-layers. The accuracy and performance of the proposed enhanced spectral element model is evaluated by comparison with the solutions obtained by using the commercial finite element package ANSYS. The proposed enhanced spectral element model is also evaluated by comparison with the author's previous spectral element model. In addition, the effects of Poisson's ratio on the dynamics and wave characteristics in example FGM bars are numerically investigated.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.813-822
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• 2022

In this article, the buckling and free vibration of multi-directional FGM sandwich plates are investigated. The material properties of FGM sandwich plates are assumed to be varying continuously in the in the longitudinal, transverse and thickness directions. The material properties are evaluated based on Voigt's micro-mechanical model considering power law distribution method with arbitrary power index. Equations of motion for the buckling and vibration analysis of multi-directional FGM sandwich plate are obtained based on refined shear deformation theory. Analytical solution for simply supported multidirectional FGM sandwich plate is carried out using Navier's solution technique. The FGM sandwich plate considered in this work has a homogeneous ceramic core and two functionally graded face sheets. Influence of volume fraction index in the longitudinal, transverse and thickness direction, layer thickness, and geometrical parameter over natural frequency and critical buckling load of multi-directional FGM sandwich plate is investigated. The finding shows a multi-directional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters have been identified which will guide researchers in selecting fabrication routes for improving the performance of such structures.

• Journal of the Korean Society of Hazard Mitigation
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• 제7권5호
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• pp.47-60
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• 2007

In this paper, we investigate the natural frequencies and buckling loads of functionally graded material (FGM) plates and shells, using a quasi-conforming shell element that accounts for the transverse shear strains and rotary inertia. The eigenvalue of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but their Poisson's ratios of the FGM plates and shells are assumed to be constant. The expressions of the membrane, bending and shear stiffness of FGM shell element are more complicated combination of material properties than a homogeneous element. In order to validate the finite element numerical solutions, the Navier's solutions of rectangular plates based on the first-order shear deformation theory are presented. The present numerical solutions of composite and sigmoid FGM (S-FGM) plates are proved by the Navier's solutionsand various examples of composite and FGM structures are presented. The present results are in good agreement with the Navier's theoretical solutions.

• Journal of the Korean Crystal Growth and Crystal Technology
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• 제11권3호
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• pp.115-119
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• 2001

Hydroxyapatite-yttria stabilized zirconia bioceramics containing fine zirconia particles were prepared as 3-layered functionally graded materials (FGMs) using a spark plasma sintering (SPS) and hot pressing (HP) apparatuses. The pretreatment of the raw hydroxyapatite promoted the sinterability of hydroxyapatite. The maximum density of pretreated FGM composites could be obtained at lower temperature than that for he untreated FGM samples. No decomposition from hydroxyapatite to three calcium phosphate (TCP) was observed in FGMs of HAp-$ZrO_2$ sintered below $1200^{\circ}C$ for 8 min under 10 MPa by SPS. However, the transformation of the tetragonal zirconia to the cubic modification had occurred in FGMs at this temperature. The presence of zirconia i.e. stress induced transformation of zirconia may be expected to enhance the mechanical properties of HAp-$ZrO_2$ FGM. The SPS is concluded as a better method to fabricated the FGM with dense and high strength compared with HP process.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.83-90
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• 2020

Several classical and higher order plate theories were used to study the buckling of functionally graded material (FGM) plates. In the great majority of research, a power function is used to represent metal and ceramic material transverse distribution (P-FGM). Therefore, the effect of having other transverse variation of material properties on the buckling behavior of thick rectangular FGM plates was not properly addressed. In the present work, this effect is investigated using the Third order Shear Deformable Theory (TSDT) for the case of simply supported FGM plate. Both a sigmoid function and an exponential functions are used to represent the transverse gradual property variation. The plate governing equations are combined with a Navier type expanded solution of the unknown displacements to derive the buckling equation in terms of the pre-buckling in-plane loads. Finally, the critical in-plane load is calculated for the different buckling modes. The model is verified by a comparison of the calculated buckling loads with available published results of Al-SiC P-FGM plates. The conducted parametric study shows that manufacturing FGM plates with sigmoid variation of properties in the thickness direction increases the buckling load considerably. This improvement is found to be more significant for the case of thick plates than that of thin plates. Results also show that this stiffening-like effect of the sigmoid function profile is more evident for cases where the in-plane loads are applied along the shorter edge of the plate.

• Journal of the Korea Academia-Industrial cooperation Society
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• 제9권4호
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• pp.1043-1049
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• 2008

In this paper, we investigate the static response. natural frequencies and buckling loads of functionally graded material (FGM) plates, using a Navier method. The eigenvalues of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but their Poisson's ratios of the FGM plates and shells are assumed to be constant. The expressions of the membrane. bending and shear stiffness of FGM plates art more complicated combination of material properties than a homogeneous element. In order to validate the present solutions, the reference solutions of rectangular plates based on the classical theory are used. The various examples of composite and FGM structures are presented. The present results are in good agreement with the reference solutions.

• Advances in nano research
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• 제12권5호
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• pp.441-455
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• 2022

This study explores the linear and nonlinear solutions of sigmoid functionally graded material (S-FGM) nanoplate with porous effects. A size-dependent numerical solution is established using the strain gradient theory and isogeometric finite element formulation. The nonlinear nonlocal strain gradient is developed based on the Reissner-Mindlin plate theory and the Von-Karman strain assumption. The sigmoid function is utilized to modify the classical functionally graded material to ensure the constituent volume distribution. Two different patterns of porosity distribution are investigated, viz. pattern A and pattern B, in which the porosities are symmetric and asymmetric varied across the plate's thickness, respectively. The nonlinear finite element governing equations are established for bending analysis of S-FGM nanoplates, and the Newton-Raphson iteration technique is derived from the nonlinear responses. The isogeometric finite element method is the most suitable numerical method because it can satisfy a higher-order derivative requirement of the nonlocal strain gradient theory. Several numerical results are presented to investigate the influences of porosity distributions, power indexes, aspect ratios, nonlocal and strain gradient parameters on the porous S-FGM nanoplate's linear and nonlinear bending responses.

• Geomechanics and Engineering
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• 제33권5호
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• pp.427-437
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• 2023

The objective of this work is to study the wave propagation of an FGM plate via a new integral inverse shear model with temperature-dependent material properties. In this contribution, a new model based on a high-order theory field of displacement is included by introducing indeterminate integral variables and inverse co-tangential functions for the presentation of shear stress. The temperature-dependent properties of the FGM plate are assumed mixture of metal and ceramic, and its properties change by the power functions of the thickness of the plate. By applying Hamilton's principle, general formulas of wave propagation were obtained to plot the phase velocity curves and wave modes of the FGM plate with simply supported edges. The effects of the temperature and volume fraction by distributions on wave propagation of the FGM plate are investigated in detail. The results of the dispersion and the phase velocity curves of the propagation wave in the functionally graded plate are compared with previous research.

• Journal of the Korean Society for Aviation and Aeronautics
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• 제15권2호
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• pp.9-17
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• 2007

A Green's function approach based on the laminate theory is adopted for solving the two-dimensional unsteady temperature field and the associated thermal stresses in an infinite plate made of functionally graded material (FGM). All material properties are assumed to depend only on the coordinate x (perpendicular to the surface). The unsteady heat conduction equation is formulated into an eigenvalue problem by making use of the eigenfunction expansion theory and the laminate theory. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the two-dimensional unsteady temperature. The associated thermoelastic field is analyzed by making use of the thermal stress function. Numerical analysis for a FGM plate is carried out and effects of material properties on unsteady thermoelastic behaviors are discussed.