• Steel and Composite Structures
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• 제38권1호
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• pp.1-15
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• 2021

In this paper, a higher order shear deformation theory for bending analysis of functionally graded plates resting on Pasternak foundation and under various boundary conditions is exposed. The proposed theory is based on the assumption that porosities can be produced within functionally graded plate which may lead to decline in strength of materials. In this research a novel distribution of porosity according to the thickness of FG plate are supposing. Governing equations of the present theory are derived by employing the virtual work principle, and the closed-form solutions of functionally graded plates have been obtained using Navier solution. Numerical results for deflections and stresses of several types of boundary conditions are presented. The exactitude of the present study is confirmed by comparing the obtained results with those available in the literature. The effects of porosity parameter, slenderness ratio, foundation parameters, power law index and boundary condition types on the deflections and stresses are presented.

• Coupled systems mechanics
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• 제13권1호
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• pp.43-60
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• 2024

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature.The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.

• 한국세라믹학회지
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• 제22권3호
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• pp.60-66
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• 1985

The formation mechanism of unstable alkali and its existing states in the clinker were studied. The relation of unstable alkali content vs. other water-soluble components porosity and the distributionof potassium were investigated. The results are as follows :1) Two states of unstable alkali seem to exist in clinker ie compounds of $K_2O-Al_2O_3$ system and free $K_2O$ 2) The content of water-soluble $Al_2O_3$ tends to increase with increase of unstable alkali content, 3) Most of alkalies in clinker are concentrated in liquid phase at high temperature. Therefore it is possible to make various $K_2O-Al_2O_3$ system compounds according to the content of $K_2O$ in the liquid phase of clinker. In this experiment we found out a $K_2O-Al_2O_3$ compound of high $Al_2O_3$ content (34%) and high $K_2O$ content (33%) in clinker with 1.09% unstable alkali. 4) The porosity of clinker tends to increase with increase of unstable alkali content. 5) The amount of trapped alkali vapor may increase in closed pore in the clinker with high alkali and low $SO_3$ condecent. Therefore free $K_2O$ is the condensed alkali on the wall of closed pore in the clinker.

• 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.

• Advances in materials Research
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• 제8권3호
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• pp.155-177
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• 2019

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.

• Steel and Composite Structures
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• 제39권3호
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• pp.275-290
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• 2021

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

• Smart Structures and Systems
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• 제18권5호
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• pp.911-930
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• 2016

The main purpose of this paper is to study the effects of initial stress, gravity, anisotropy and porosity on the propagation of shear wave (SH-waves) in a fiber-reinforced layer placed over a porous media. The frequency equations in a closed form have been derived for SH-waves by applying suitable boundary conditions. The frequency equations have been expanded and approximated up to $2^{nd}$ order of Whittaker's function. It has been observed that the SH-wave velocity decreases as width of fiber-reinforced layer increases. However, with the increase of initial stress, gravity parameter and porosity, the phase velocity increases. The results obtained are in perfect agreement with the standard results investigated by other relevant researchers.

• 한국세라믹학회지
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• 제48권5호
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• pp.463-466
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• 2011

Wet foams formed through direct foaming were stabilized using various concentrations of amiphiphilic particles that could control pore size and porosity. These porous materials showed moderate strength upon compression with high porosity. Bubble size and wet foam stability were tailored by amphiphile concentration, particle concentration, contact angle, and pH of the suspension to obtain crack-free porous solid after sintering. Closed and open pores were obtained with sizes of 30~300 ${\mu}m$ and porosities of over 80%.

• 소성∙가공
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• 제12권5호
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• pp.449-456
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• 2003

Multi-step induction heating process was applied to the powder compact melting technique as a new heating process to achieve pinpoint accuracy, faster cycle time, repeatability, non-contact and energy-efficient heat in a minimal amount of time. The objective of this study is the establishment of the input data diagram of multi step induction heating process for automation of the fabrication process of 6061 Al foams with desired density. At first, proper induction coil was designed to obtain a uniform temperature distribution over the entire cross sectional area of specimen. By using this coil, foaming experiments were performed to investigate the multi-step induction heating conditions such as capacity, temperature and time conditions of each heating and holding step. On the basis of the obtained multi-step induction heating conditions, relationship between final heating temperature and fraction of porosity was investigated.

• 자원리싸이클링
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• 제19권1호
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• pp.33-39
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• 2010

화력발전소에서 배출되는 바닥재와 준설토를 70:30(wt%)로 혼합하고 이를 $6{\pm}2mm$ 크기 구형으로 성형 및 로터리 킬른에서 $1125^{\circ}C$/15 min으로 소성한 뒤, 그 물리적 특성을 평가함으로써 오염 토양을 복원하는데 사용되는 흡착제로의 적용 가능성을 분석하였다. 제조된 소결체(BD)는 100 ${\mu}m$ 이상의 거대 기공 및 10 ${\mu}m$ 이하의 미세기공을 모두 가지고 있었으며, 비표면적, 기공율 그리고 공극율은 각각 $12.0m^2/g$, 30.1%그리고 38.2%이었다. BD 소결체를 한번 분쇄한 시편(BD-C)은 종횡비$\fallingdotseq$2의 부정형이었으나, 부피비중 및 기공크기 분포는 BD와 비슷한 값을 나타내었다. 한편 BD-C 시편의 비표면적, 기공율 그리고 공극율은 BD에 비해 더 우수한 값을 나타내었는데 이는 내부에 존재하던 폐기공(closed pores)이 분쇄과정에서 개기공(open pores)으로 변환되면서 겉보기 부피가 감소했기 때문이다. 제조된 소결체의 영 전하점(IEP)는 약 pH=5이었고 따라서 미생물을 소결체에 결합시킬 때 반응용액의 최적 pH를 알 수 있었다. 본 연구에서 제조된 소결체는 오염 토양 복원에 사용되는 흡착제로의 적용이 가능하며, 더구나 측정된 데이터를 이용하여 BD와 BD-C를 적절한 비율로 혼합하면 적용 상황에 따라 다른 공극율, 기공율 등의 요구 조건을 최적으로 맞출 수 있을 것으로 기대된다.