• Earthquakes and Structures
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• v.14 no.2
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• pp.103-115
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• 2018

In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1582-1589
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• 2004

The dynamic response of an eccentric Griffith crack in functionally graded piezoelectric ceramic strip under anti-plane shear impact loading is ana lysed using integral transform method. Laplace transform and Fourier transform are used to reduce the problem to two pairs of dual integral equations, which are then expressed to Fredholm integral equations of the second kind. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. The impermeable crack boundary condition is adopted. Numerical values on the dynamic stress intensity factors are presented for the functionally graded piezoelectric material to show the dependence of the gradient of material properties and electric loadings.

• Structural Engineering and Mechanics
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• v.89 no.6
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• pp.601-615
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• 2024

Effect of ring and straight stiffeners in the buckling as well as vibration characteristics of metal-ceramic functionally graded plates with cutout subjected to various uniaxial and localized in-plane compressive edge loadings was explored in the present work. In the current work, the distinguishing characteristics of metal and ceramic are merged in a single volume, and power law was used for estimating the material composition throughout thickness. Buckling and free vibration characteristics were studied initially for unstiffened Al/SiC functionally graded plates with cutout. Subsequently, the influence of cutout ratio on buckling load as well as natural frequency for different power law indices was discussed. The functionally graded plate was stiffened by three different stiffener patterns, namely; ring stiffener, straight stiffener, as well as a combination of the ring and the straight stiffener, to enhance the buckling as well as vibration characteristics. The effect of stiffener depth ratio for different stiffener patterns was also presented for functionally graded plates having different cutout sizes under various loading conditions. Such studies on functionally graded material have potential applications in a variety of technological fields including the aerospace and defense sectors.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.1067-1089
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• 2014

In this paper, three dimensional static and dynamic analyses of two dimensional functionally graded annular sector plates have been investigated. The material properties vary through both the radial and axial directions continuously. Graded finite element and Newmark direct integration methods have been used to solve the 3D-elasticity equations in time and space domains. The effects of power law exponents and different boundary conditions on the behavior of FGM annular sector plate have been investigated. Results show that using 2D-FGMs and graded elements have superiority over the homogenous elements and 1D-FGMs. The model has been compared with the result of a 1D-FGM annular sector plate and it shows good agreement.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.285-287
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• 2014

Equations of motion for the vibration analysis of rotating pre-twisted beams with functionally graded material properties are derived in this paper. Based on Timoshenko beam theory, the effects of shear and rotary inertia are considered. The pre-twisted beam has a rectangular cross-section and is mounted on a rotating rigid hub with a setting angle. Functionally graded material (FGM) properties are considered along the height direction of the beam. The equations of stretching and bending motion are derived by Kane's method employing hybrid deformation variables. To validate the derived equations, natural frequencies of a rotating FGM pre-twisted beam are compared to those obtained by a commercial software ANSYS. The effects of the pre-twisted angle, slenderness ratio, hub radius, volume fraction exponent, and angular speed on the modal characteristics of the system are investigated with the proposed model.

• Steel and Composite Structures
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• v.21 no.1
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• pp.123-136
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• 2016

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Advances in nano research
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• v.6 no.3
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• pp.219-242
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• 2018

In this study, static bending of an edge cracked cantilever nanobeam composed of functionally graded material (FGM) subjected to transversal point load at the free end of the beam is investigated based on modified couple stress theory. Material properties of the beam change in the height direction according to exponential distributions. The cracked nanobeam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-nanobeams connected through a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the static deflections of the edge cracked FGM nanobeams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and different material distributions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked FGM nanobeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Steel and Composite Structures
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• v.32 no.5
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• pp.611-632
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• 2019

In this work, a four-variable refined plate model is applied to study the thermomechanical bending of two kinds of functionally graded material (FGM) sandwich plates. The sandwich core of one kind is isotropic with the FGM face sheets whereas in the second kind, the sandwich core is FGM with the isotropic and homogeneous face sheets. By considering only four unknown variables, the governing equations are written based on the principle of virtual work and then Navier method is employed to solve these equations. Deflections and stresses of two kinds of FGM sandwich structures are analyzed and discussed. The validity and efficiency of the proposed model is checked by comparing it with various available solutions in the literature. The effects of volume fraction distribution, geometric ratio and thermal load on thermomechanical bending properties of FGM sandwich plate are investigated in detail.

• Steel and Composite Structures
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• v.15 no.2
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• pp.221-245
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• 2013

This paper presents an analytical solution to the thermomechanical bending analysis of functionally graded sandwich plates by using a new hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are investigated.

• Structural Engineering and Mechanics
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• v.61 no.4
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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.