Shape Effect on Free Vibration of Functionally Graded Plates

Kurtaran, Hasan

doi:10.24107/ijeas.251237

Cited by 4 publications

(4 citation statements)

References 30 publications

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“…In order to further validate the present approach and also to show its accuracy for the analysis of the FG Tables 6 and 7. In Table 6, the results for the first six frequencies of the FG triangular plates with simply supported and clamped edges are compared with those obtained by Kurtaran [67] using the finite element method. The values of the geometrical parameters and material properties that are used in this example are [67] n=2, h=0.1m, a=15.196m, Table 7, the first six frequency parameters are compared with those of Chen et al [68] for two different values of the material graded index n. They used a meshless local natural neighbor interpolation method to get the results.…”

Section: Convergence and Accuracy Studymentioning

confidence: 98%

“…The values of the geometrical parameters and material properties that are used in this example are [67] n=2, h=0.1m, a=15.196m, Table 7, the first six frequency parameters are compared with those of Chen et al [68] for two different values of the material graded index n. They used a meshless local natural neighbor interpolation method to get the results. The following values of the geometrical parameters and material properties are used in this example [68] , [67] and Chen et al [68] formulated the problem based on the FSDT of plates.…”

Section: Convergence and Accuracy Studymentioning

confidence: 99%

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Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Shenas

Malekzadeh

2016

Mechanics of Advanced Materials and Structures

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The free vibration of the functionally graded (FG) isosceles triangular microplates in thermal environment is investigated. The modified strain gradient theory (MSGT) together with the firstorder shear deformation theory (FSDT) of plates is adopted to formulate the problem. The material properties are assumed to be graded in the thickness direction. The Chebyshev-Ritz method is chosen as the solution procedure. After demonstrating the fast rate of convergence and accuracy of the method, the effects of temperature rise, length scale parameters, material gradient index, different boundary conditions, apex angle and width-to-thickness ratio on the free vibration of triangular microplates are studied.

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Section: Convergence and Accuracy Studymentioning

confidence: 98%

Section: Convergence and Accuracy Studymentioning

confidence: 99%

Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Shenas

Malekzadeh

2016

Mechanics of Advanced Materials and Structures

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“…The bending response of E-FGM is similar to the behavior of P-FGM. Hasan [34] investigated the shape effect on the free vibration behavior of FG plates. Circular, elliptical, annular, rectangular, square, skew, and equilateral triangular plates with the same surface area and thickness are compared for simply supported and clamped boundary conditions.…”

Section: Literature Surveymentioning

confidence: 99%

Functionally Graded Panels: A Review

B¹

2020

IJMTST

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Functionally gradedmaterials (FGMs) are not homogeneous materials. It consists of different(two or more) materials, engineered to have a continuously varying spatial composition profile. FGM is the one that can solve practical problems arising from the production and application of a new type of composite material. This paper describes the overview of FGM basic concepts, classification, properties, and its modeling which may focus on the static and dynamic analysis of functionally graded panels. The effective material properties of functionally graded materials for the panel are graded in the thickness direction from the bottom surface to the top surface according to the power-law distribution of volume fractions of the constituents. The use of structures like beams, plates, and shells, which are made from functionally graded (FG) materials, is increasing because of the smooth variation of material properties along with preferred directions. This variation gives continuous stress distribution in the FG structures. Therefore, an FGM can be effectively used in avoiding corrosion, fatigue, fracture, and stress corrosion cracking. The paper covers the literature study on static, buckling and free vibration, thermo-mechanical analysis of FGM panel. From this literature study it is found that, analysis of these problems is made using the constitutive relations and governing equations associated with the classical laminated theory structural model, the FSDT model, the HSDT model,Reissner and Sander theory,differential quadrature, finite element method and closed form solutions. Results are availableon different geometrical dimensional ratios variations, power-law index value n variationsand simply supported,clamped, free edges boundary conditionswith its combinations for FG panels. Lesser literatures are available for different edge boundary conditions such as SCSC, CSCS,SSSC, SFSF, SSSF, SCSF on curved panelfor free vibration, buckling and thermo-structural analysis.

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“…Rectangular finite elements with linear shape functions were used for static analysis, piezothermoelastic dynamics [8], active deflection/vibration control [9] and free vibrations [10]. Eight-node rectangular elements were applied for nonlinear free flexural vibrations [11] and piezoelectric fiber reinforcement [12].…”

Section: Introductionmentioning

confidence: 99%

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

Gilewski

Pełczyński

2020

Materials

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A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM’s material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed.

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Shape Effect on Free Vibration of Functionally Graded Plates

Abstract: In this article, shape effect on free vibration behavior of functionally graded plates is investigated. Square, rectangular, skew, circular, elliptical, annular and equilateral

Cited by 4 publications

References 30 publications

Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Thermal environmental effects on free vibration of functionally graded isosceles triangular microplates

Functionally Graded Panels: A Review

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

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