• Steel and Composite Structures
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• v.49 no.3
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• pp.281-291
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• 2023

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

• Environmental Engineering Research
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• v.12 no.3
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• pp.109-117
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• 2007

The characteristics of carbonaceous particles collected from the combustion of Vacuum Residue (VR) in a test furnace have been investigated. The physical and chemical characterization includes particle size, scanning electron microscopy of the surface structure, measurement of porosity, surface area and density, EDX/XRD analyses and measurement of chemical composition. The studies show that the carbonaceous VR particles are very porous and spheroidal, and have many blow-holes on the surface. The particles become smaller and more sponge-like as the reaction proceeds. The present porosity of VR particles is similar to that of cenospheres from the combustion of heavy oil, and the majority of pores are distributed in macro-pores above $0.03\;{\mu}m$ in diameter. Measurements of pore distribution and surface area showed that the macro-pores contributed most to total pore volume, whereas the micro-pores contributed to total surface area.

• Nuclear Engineering and Technology
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• v.31 no.6
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• pp.608-617
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• 1999

The powder mixture which has a bimodal size distribution, with a large mode corresponding to AUC-UO$_2$ powder and a small one corresponding to ADU-UO$_2$ powder, was prepared, pressed into compacts, and sintered at 1680t for 4 hours in hydrogen gas. The compact density of the powder mixture increases with increasing ADU-UO$_2$content within a content of 20 wt %, since small ADU-UO$_2$ particles can fill interstices between large AUC-UO$_2$particles. The UO$_2$ pellet made using the powder mixture has a lower open porosity than that made using AUC-UO$_2$ powder alone. The mechanism for the formation of a flake-like pore is proposed, and the decrease in open porosity may be ascribed to the decrease in the number of flake-like pores.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.12
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• pp.1784-1792
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• 2001

Numerical analysis on a parallel flow heat exchanger(PFHE) is performed using 2 dimensional turbulent porous modeling. This modeling can consider three-dimensional configuration of passage (flat tube with micro-channels), and the stability and accuracy of numerical results are improved. The geometrical parameters(e.g., the position of separators, inlet/outlet, and porosity of passages of a PFHE) are varied in order to examine the flow and thermal characteristics and flow distribution of the single phase multiple passages system. The flow non-uniformities along the paths of the PFHE are observed to evaluate the thermal performance of the heat exchanger. The location of inlet affects the heat transfer, and the location of outlet affects the pressure drop. The porosity with the optimum thermal performance is around 0.53.

• Geomechanics and Engineering
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• v.9 no.3
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• pp.361-372
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• 2015

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Advances in materials Research
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• v.12 no.2
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• pp.133-159
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• 2023

In this paper, a size-dependent dynamic investigation of a porous metal foams microbeamsis presented. The novelty of this study is to use a metal foam microbeam that contain porosities based on the refined high order shear deformation beam model, with sinusoidal shear strain function, and the modified strain gradient theory (MSGT) for the first time. The Lagrange's principle combined with differential quadrature hierarchicalfinite element method (DQHFEM) are used to obtain the porous microbeam governing equations. The solutions are presented for the natural frequencies of the porous and homogeneoustype microbeam. The obtained results are validated with the analytical methods found in the literature, in order to confirm the accuracy of the presented resolution method. The influences of the shape of porosity distribution, slenderness ratio, microbeam thickness, and porosity coefficient on the free vibration of the porous microbeams are explored in detail. The results of this paper can be used in various design formetallic foammicro-structuresin engineering.

• Advances in materials Research
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• v.5 no.4
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• pp.279-298
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• 2016

Present disquisition proposes an analytical solution method for exploring the buckling characteristics of porous magneto-electro-elastic functionally graded (MEE-FG) plates with various boundary conditions for the first time. Magneto electro mechanical properties of FGM plate are supposed to change through the thickness direction of plate. The rule of power-law is modified to consider influence of porosity according to two types of distribution namely even and uneven. Pores possibly occur inside FGMs due the result of technical problems that lead to creation of micro-voids in these materials. The variation of pores along the thickness direction influences the mechanical and physical properties. Four-variable tangential-exponential refined theory is employed to derive the governing equations and boundary conditions of porous FGM plate under magneto-electrical field via Hamilton's principle. An analytical solution procedure is exploited to achieve the non-dimensional buckling load of porous FG plate exposed to magneto-electrical field with various boundary condition. A parametric study is led to assess the efficacy of material graduation exponent, coefficient of porosity, porosity distribution, magnetic potential, electric voltage, boundary conditions, aspect ratio and side-to-thickness ratio on the non-dimensional buckling load of the plate made of magneto electro elastic FG materials with porosities. It is concluded that these parameters play remarkable roles on the dynamic behavior of porous MEE-FG plates. The results for simpler states are confirmed with known data in the literature. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

• Electrical & Electronic Materials
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• v.9 no.6
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• pp.605-615
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• 1996

In this paper, the effect of alkaline oxide addition such as Li$_{2}$O and Na$_{2}$O on the microstructure and humidity sensitivity of V$_{2}$O$_{5}$(2 mol%)-doped TiO$_{2}$(98 mol%) was investigated as a function of amount (0, 1, 2, 5, 10 mol%) of Li$_{2}$O and Na$_{2}$O additives. The pores in the alkaline free sample were distributed mostly in the range between 0.16 and 1.0.mu.m in diameter and its porosity was 23.29%. Li$_{2}$O caused grain overgrowth and reduced the porosity with a narrow distribution of the pore size, leading to poor humidity sensitivity. Na$_{2}$O helped to enlarge the distribution of the pore size through the formation of small soluble phases. The pore sizes of the sample containing Na$_{2}$O 2mol% were distributed mostly in the range between 1.0 and 2.5.mu.m in diameter and its porosity and intrusion volume of mercury were 31.13 % and 0.1155 mL/g respectively, which consequently improved the humidity sensing characteristics such as the sensitivity and temperature-stability. Especially, the addition of 2mol% of Na$_{2}$O improved the humidity-sensing characteristics such as sensitivity and linearity in the whole range between 30 and 90 %RH (Percentage Relative Humidity)y)

• Advances in nano research
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• v.8 no.1
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• pp.83-94
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• 2020

An analytical formulation and solution process for the buckling analysis of porous magneto-electro-elastic functionally graded (MEE-FG) beam via different thermal loadings and various boundary conditions is suggested in this paper. Magneto electro mechanical coupling properties of FGM beam are taken to vary via the thickness direction of beam. The rule of power-law is changed to consider inclusion of porosity according to even and uneven distribution. Pores possibly occur inside FGMs due the result of technical problems that lead to creation of micro-voids in these materials. Change in pores along the thickness direction stimulates the mechanical and physical properties. Four-variable tangential-exponential refined theory is employed to derive the governing equations and boundary conditions of porous FGM beam under magneto-electrical field via Hamilton's principle. An analytical model procedure is adopted to achieve the non-dimensional buckling load of porous FG beam exposed to magneto-electrical field with various boundary conditions. In order to evaluate the influence of thermal loadings, material graduation exponent, coefficient of porosity, porosity distribution, magnetic potential, electric voltage and boundary conditions on the critical buckling temperature of the beam made of magneto electro elastic FG materials with porosities a parametric study is presented. It is concluded that these parameters play remarkable roles on the buckling behavior of porous MEE-FG beam. The results for simpler states are proved for exactness with known data in the literature. The proposed numerical results can serve as benchmarks for future analyses of MEE-FG beam with porosity phases.

• Steel and Composite Structures
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• v.45 no.1
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• pp.67-82
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• 2022

In this paper, buckling and free vibration of imperfect, functionally graded beams, including porosities, are investigated, using a higher order shear strain theory. Due to defects during the manufacturing process, micro porosities may appear in the material, hence the appearance of this imperfection in the structure. The material properties of the beams are assumed to vary regularly, with power and sigmoid law, in the direction of thickness. A novel porosity distribution affecting the functionally graded volume fraction is presented. For the compact formulation used for cementite-based materials and already used in P-FGM, we have adapted it for the distribution of S-FGM. The equations of motion in the FG beam are derived using Hamilton's principle. The boundary conditions for beam FG are assumed to be simply supported. Navier's solution is used to obtain the closed form solutions of the FG beam. The numerical results of this work are compared with those of other published research to verify accuracy and reliability. The comparisons of different shear shape functions, the influence of porosity, thickness and inhomogeneity parameters on buckling and free vibration of the FG beam are all discussed. It is established that the present work is more precise than certain theories developed previously.