• Geomechanics and Engineering
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• 제24권6호
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• pp.545-557
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• 2021

Since the functionally graded materials (FGMs) are used extensively as thermal barriers in many of applications. Therefore, the current article focuses on studying and presenting dynamic responses of multilayer functionally graded (FG) deep beams placed in a thermal environment that is not addressed elsewhere. The material properties of each layer are proposed to be temperature-dependent and vary continuously through the height direction based on the Power-Law function. The deep layered beam is exposed to harmonic sinusoidal load and temperature rising. In the modelling of the multilayered FG deep beam, the two-dimensional (2D) plane stress continuum model is used. Equations of motion of deep composite beam with the associated boundary conditions are presented. In the frame of finite element method (FEM), the 2D twelve-node plane element is exploited to discretize the space domain through the length-thickness plane of the beam. In the solution of the dynamic problem, Newmark average acceleration method is used to solve the time domain incrementally. The developed procedure is verified and compared, and an excellent agreement is observed. In numerical examples, effects of graduation parameter, geometrical dimension and stacking sequence of layers on the time response of deep multilayer FG beams are investigated with temperature effects.

• Advances in nano research
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• 제7권2호
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• pp.135-143
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• 2019

The important effect of porosity on the mechanical behaviors of a continua makes it necessary to account for such an effect while analyzing a structure. motivated by this fact, a new two-step porosity dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) porous nanobeams. In the introduced homogenization method, which is a modified form of the power-law model, the effects of porosity distributions are considered. Based on Hamilton's principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adapted to put emphasis on the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

• 대한기계학회논문집A
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• 제35권12호
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• pp.1647-1653
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• 2011

일반적으로 사출금형의 사출주기는 플라스틱 제품의 냉각 시간에 크게 좌우되는 데, 냉각회로를 적용하여 조절할 수 있다. 금형의 냉각회로는 전통적으로 기계가공을 통하여, 직선형상만을 생성할 수 있었지만, 최근 적층조형 방법의 개발로 코어 형상을 따라가는 형상적응형 냉각회로를 생성할 수 있게 되었다. 한편 금형의 다이 재질로 열저항력이 크고, 치수변화가 적은 H13 스틸이 널리 사용되고 있지만, 열전도율이 낮기 때문에 냉각효율은 높지 않다. 이러한 점에서 열전달 효율을 극대화 시킬 수 있는 방법으로 H13 스틸과 구리(Cu)를 기능적으로 혼합한 기능성 경사 복합재(FGM)를 적층조형을 이용하여 냉각회로에 적용하는 방안이 검토되고 있다. 이러한 시도로서 본 논문에서는 H13 스틸과 Cu 간의 FGM을 이용한 형상적응형 냉각회로의 모델링 방법을 제안하고자 한다.

• Smart Structures and Systems
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• 제26권2호
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• pp.253-262
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• 2020

In this paper, a new higher order shear deformation model is developed for static analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. The model account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG beam. Based on the present higher-order shear deformation model, the equations of motion are derived by the principle of virtual works. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, and geometry on the bending of imperfect FG beams. It can be concluded that the proposed model is simple and precise for the resolution of the behavior of flexural FGM beams while taking into account the shape of distribution of the porosity.

• Steel and Composite Structures
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• 제30권6호
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• pp.603-615
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• 2019

In the present work, free vibration of beams made of imperfect functionally graded materials (FGMs) including porosities is investigated. Because of faults during process of manufacture, micro voids or porosities may arise in the FGMs, and this situation causes imperfection in the structure. Therefore, material properties of the beams are assumed to vary continuously through the thickness direction according to the volume fraction of constituents described with the modified rule of mixture including porosity volume fraction which covers two types of porosity distribution over the cross section, i.e., even and uneven distributions. The governing equations of power law FGM (P-FGM) and sigmoid law FGM (S-FGM) beams are derived within the frame works of classical beam theory (CBT) and first order shear deformation beam theory (FSDBT). The resulting equations are solved using separation of variables technique and assuming FG beams are simply supported at both ends. To validate the results numerous comparisons are carried out with available results of open literature. The effects of types of volume fraction function, beam theory and porosity volume fraction, as well as the variations of volume fraction index, span to depth ratio and porosity volume fraction, on the first three non-dimensional frequencies are examined in detail.

• Advances in nano research
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• 제10권3호
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• pp.281-293
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• 2021

This paper presents a new nonlocal Hyperbolic Shear Deformation Beam Theory (HSDBT) for the free vibration of porous Functionally Graded (FG) nanobeams. A new displacement field containing integrals is proposed which involves only three variables. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect and its account for shear deformation by a hyperbolic variation of all displacements through the thickness without using the shear correction factor. It has been observed that during the manufacture of Functionally Graded Materials (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the free vibration analysis of FG beams taking into account the influence of these imperfections is established. Four different porosity types are considered for FG nanobeam. Material characteristics of the FG beam are supposed to vary continuously within thickness direction according to a power-law scheme which is modified to approximate material characteristics for considering the influence of porosities. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio, and the porosity types on the dynamic responses of the nanobeam are discussed.

• 한국분말야금학회:학술대회논문집
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• 한국분말야금학회 2006년도 Extended Abstracts of 2006 POWDER METALLURGY World Congress Part 1
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• pp.87-88
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• 2006

Ceramic-Metal Functionally Graded Materials (FGM) are of great interest for application as Thermal Barrier Coating (TBC) or Wear Resistant Coating (WRC). Spark Plasma Sintering (SPS) is a promising techniques for time-saving consolidation of laminated/graduated powder systems: SPS is a pressure-assisted electrical sintering method which directly applies a pulsed DC current as heat source. In the present work, production of $Al_2O_3-Ni$ FGMs by means of Spark Plasma Sintering is considered; effect of sintering condition on density, hardness and fracture toughness is studied. Problems correlated to this new processing technology are discussed.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. 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.

• Geomechanics and Engineering
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• 제31권1호
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• pp.99-112
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• 2022

The present study examines the natural frequencies (NFs) of perfect/imperfect functionally graded sandwich beams (P/IP-FGSBs), which are composed of a porous core constructed of functionally graded materials (FGMs) and a homogenous isotropic metal and ceramic face sheets resting on elastic foundations. To accomplish this, the material properties of the FGSBs are assumed to vary continuously along the thickness direction as a function of the volume fraction of constituents expressed by the modified rule of the mixture, which includes porosity volume fraction represented using four distinct types of porosity distribution models. Additionally, to characterize the reaction of the two-parameter elastic foundation to the Perfect/Imperfect (P/IP) FGSBs, the medium is assumed to be linear, homogeneous, and isotropic, and it is described using the Winkler-Pasternak model. Furthermore, the kinematic relationship of the P/IP-FGSBs resting on the Winkler-Pasternak elastic foundations (WPEFs) is described using trigonometric shear deformation theory (TrSDT), and the equations of motion are constructed using Hamilton's principle. A closed-form solution is developed for the free vibration analysis of P/IP-FGSBs resting on the WPEFs under four distinct boundary conditions (BCs). To validate the new formulation, extensive comparisons with existing data are made. A detailed investigation is carried out for the effects of the foundation coefficients, mode numbers (MNs), porosity volume fraction, power-law index, span to depth ratio, porosity distribution patterns (PDPs), skin core skin thickness ratios (SCSTR), and BCs on the values of the NFs of the P/IP-FGSBs.

• 대한기계학회논문집A
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• 제38권2호
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• pp.193-203
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• 2014

터빈의 운전온도와 세라믹 입자크기를 고려한 경사기능재료(FGM)로 만들어진 회전하는 가스터빈 블레이드의 열전달해석 및 응력해석을 수행하였다. 경사기능성 블레이드는 벽 두께에 따라서 연속적인 재료물성 변화를 나타낸다. 이러한 경사기능재료의 특성과 온도에 따른 열전 재료물성 변화를 고려하여 블레이드의 시스템 강성을 얻기 위해 블레이드의 열전달해석을 먼저 수행하였다. 이 열전달해석으로 얻은 시스템 강성으로부터 복합 변형 변수를 사용한 회전하는 가스터빈 블레이드의 운동방정식을 유도하였다. 유도된 운동방정식은 상용 유한요소 모델과 해석결과 비교를 통해 그 정확성을 입증하였으며 회전주파수와 구배 지수에 따른 최대 응력의 변화를 조사하였다. 또한, 열전달해석을 통해 가장 낮은 블레이드 온도를 나타내는 구배 지수를 조사하였다.