• 한국재료학회:학술대회논문집
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• 한국재료학회 2007년도 추계학술발표대회 및
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• pp.117.1-117.1
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• 2007

• Steel and Composite Structures
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• 제39권5호
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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.

• 한국전기전자재료학회논문지
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• 제33권3호
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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.

• Structural Engineering and Mechanics
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• 제69권4호
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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.

• Structural Engineering and Mechanics
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• 제88권4호
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• Nuclear Engineering and Technology
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• 제54권12호
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• pp.4491-4498
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• 2022

The thermal stress between W plasma-facing material (PFM) and Cu heat sink in fusion reactors can be significantly reduced by using a W-Cu functionally graded material (W-Cu FGM) interlayer. However, there is still considerable stress at the joining interface between W and W-Cu FGM in the W/W-Cu FGM/Cu portions. In this work, we fabricate W skeletons with continuous gradients in porosity by a modified sedimentation method. Sintering densification behavior and pore characteristics of the sedimented W skeletons at different sintering temperatures were investigated. After Cu infiltration, the final W-Cu FGM was obtained. The results indicate that the pore size and porosity in the W skeleton decrease gradually with the increase of sintering temperature, but the increase of skeleton sintering temperature does not reduce the gradient range of composition distribution of the final prepared W-Cu FGM. And W-Cu FGM with composition distribution from pure W to W-20.5wt.% Cu layer across the section was successfully obtained. The thickness of the pure W layer is about one-fifth of the whole sample thickness. In addition, the prepared W-Cu FGM has a relative density of 94.5 % and thermal conductivity of 185 W/(m·K). The W-Cu FGM prepared in this work may provide a good solution to alleviate the thermal stress between W PFM and Cu heat sink in the fusion reactors.

• Structural Engineering and Mechanics
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• 제85권5호
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• pp.621-633
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• 2023

The major objective of this paper is to study the receding contact problem between two functional graded layers under a flat indenter. The gravity is assumed negligible, and the shear moduli of both layers are assumed to vary exponentially along the thickness direction. In the absence of body forces, the problem is reduced to a system of Fredholm singular integral equations with the contact pressure and contact size as unknowns via Fourier integral transform, which is transformed into an algebraic one by the Gauss-Chebyshev quadratures and polynomials of both the first and second kinds. Then, an iterative speediest descending algorithm is proposed to numerically solve the system of algebraic equations. Both semi-analytical and finite element method, FEM solutions for the presented problem validate each other. To improve the accuracy of the numerical result of FEM, a graded FEM solution is performed to simulate the FGM mechanical characteristics. The results reveal the potential links between the contact stress/size and the indenter size, the thickness, as well as some other material properties of FGM.

• Steel and Composite Structures
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• 제49권6호
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• pp.633-643
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• 2023

In this study, the natural frequencies of Functional Graded Materials (FGM) plates are predicted using Artificial Neural Network (ANN). A model based on Third-order Shear Deformation Theory (TSDT) and FEM is used to train the ANN model. Different training methods are tested to simulate input and output dependency. As this is a parametric model, several architectures and optimization algorithms were tested. The proposed model allows us to minimize the CPU time to evaluate candidate material properties for FGM plate material selection and demonstrate their influence on dynamic behavior. Consequently, the time required for the FGM design process (candidate materials for material selection) and the geometric optimization of the FGM structure would remain reasonable. The ANN model can help industries to produce FGM plates with good mechanical properties of the selected materials. I addition, this model can be used to directly predict vibration behavior by testing a large number of FGM plates, representing all possible combinations of metals and ceramics in today's industry, without having to solve any eigenvalue problems.

• Steel and Composite Structures
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• 제28권6호
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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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• 제48권4호
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.