• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.663-686
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• 2014

This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

• Advances in aircraft and spacecraft science
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• v.7 no.4
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• pp.353-369
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• 2020

This paper presents the flutter analysis and optimum design of axially functionally graded box beam cantilever wing section by considering various geometric and material parameters. The coupled dynamic equations of the continuous model of wing system in terms of material and cross-sectional properties are formulated based on extended Hamilton's principle. By expressing the lift and pitching moment in terms of plunge and pitch displacements, the resultant two continuous equations are simplified using Galerkin's reduced order model. The flutter velocity is predicted from the solution of resultant damped eigenvalue problem. Parametric studies are conducted to know the effects of geometric factors such as taper ratio, thickness, sweep angle as well as material volume fractions and functional grading index on the flutter velocity. A generalized surrogate model is constructed by training the radial basis function network with the parametric data. The optimized material and geometric parameters of the section are predicted by solving the constrained optimal problem using firefly metaheuristics algorithm that employs the developed surrogate model for the function evaluations. The trapezoidal hollow box beam section design with axial functional grading concept is illustrated with combination of aluminium alloy and aluminium with silicon carbide particulates. A good improvement in flutter velocity is noticed by the optimization.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.33 no.3
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• pp.225-230
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• 2020

Recently, with the miniaturization of GIS, there is a need for the miniaturization of spacers as accessories. Miniaturized spacers make it difficult to secure adequate insulation distances, resulting in a more concentrated electric field at the triple junction of high-voltage (HV) conductor-insulator (spacer)-insulation gas (SF₆), which is a weakness in GIS. Therefore, by introducing a new concept design technology, functionally graded material (FGM), which is recently applied to various materials and parts industries, three-dimensional control of the dielectric constant distribution in a spacer can be expected to alleviate triple-junction electric field occupancy and improve insulation performance. In this study, we propose an optimized model using NSGA-II to optimize the permittivity distribution of FGM applied spacer.

• Steel and Composite Structures
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• v.28 no.6
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• pp.735-748
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• 2018

In this study, the semi-analytical finite strip method is adopted to examine the free vibration of cylindrical shells made up of functionally graded material. The properties of functionally graded shells are assumed to be temperature-dependent and vary continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of ceramic and metal. The material properties of the shells and stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with first-order shear deformation theory which accounts for through thickness shear flexibility are employed. The finite strip method is applied to five different shell theories, namely, Donnell, Reissner, Sanders, Novozhilov, and Teng. The approximate procedure is compared favorably with three-dimensional finite elements. Finally, a detailed numerical study is carried out to bring out the effects of power-law index of the functional graded material, stiffeners, and geometry of the shells on the difference between various shell theories. Finally, the importance of choosing the shell theory in simulating the functionally graded cylindrical shells is addressed.

• Structural Engineering and Mechanics
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• v.50 no.3
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• pp.403-417
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• 2014

The present paper addresses a general formulation for the thermo elastic analysis of a functionally graded cylindrical shell subjected to external loads. The shear deformation theory and energy method is employed for this purpose. This method presents the final relations by using a set of second order differential equations in terms of integral of material properties along the thickness direction. The proposed formulation can be considered for every distribution of material properties, whether functional or non functional. The obtained formulation can be used for manufactured materials or structures with numerical distribution of material properties which are obtained by using the experiments. The governing differential equation is applied for two well-known functionalities and some previous results are corrected with present true results.

• Proceedings of the Materials Research Society of Korea Conference
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• 2007.11a
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• pp.117.1-117.1
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• 2007

• Advances in aircraft and spacecraft science
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• v.10 no.1
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• pp.19-49
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• 2023

The present study proposes a theoretical and numerical investigation on the dynamic response behaviour of a functional graded (FG) ceramic-metal tapered rotor shaft system, by the differential quadrature finite elements method (DQFEM) to identify the natural frequencies for modelling and analysis of the structure with suitable validations. The purpose of this paper is to explore the influence of heat gradients on the natural frequency of rotation of FG shafts via three-dimensional solid elements, as well as a theoretical examination using the Timoshenko beam mode, which took into account the gyroscopic effect and rotational inertia. The functionally graded material's distribution is described by two distribution laws: the power law and the exponential law. To simulate varied thermal conditions, radial temperature distributions are obtained using the nonlinear temperature distribution (NLTD) and exponential temperature distribution (ETD) approaches. This work deals with the results of the effect on the fundamental frequencies of different material's laws gradation and temperature gradients distributions. Attempts are conducted to identify adequate explanations for the behaviours based on material characteristics. The effect of taper angle and material distribution on the dynamic behaviour of the FG conical rotor system is discussed.

• Steel and Composite Structures
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• v.39 no.5
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• pp.493-509
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• 2021

There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gateaux differential derivative operator. Thanks to the Gateaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.427-437
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• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

• Earthquakes and Structures
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• v.14 no.2
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• pp.117-128
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• 2018

In this research work, free vibrations of simply supported functionally graded plate resting on a Winkler-Pasternak elastic foundation are investigated by a new shear deformation theory. The influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on shear-deformation plate theories is examined. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The energy functional of the system is obtained using Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models on natural fundamental frequencies.