• Steel and Composite Structures
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• v.45 no.5
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• pp.621-640
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• 2022

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e. along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.457-466
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• 2019

This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.

• Structural Engineering and Mechanics
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• v.91 no.4
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• pp.383-391
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• 2024

Conical shell is a common engineering structure, which is widely used in machinery, civil and construction fields. Most of them are usually exposed to external environments, temperature is an important factor affecting its performance. If the external temperature is too high, the deformation of the conical shell will occur, leading to a decrease in stability. Therefore, studying the thermal-post buckling behavior of conical shells is of great significance. This article takes graphene platelets reinforced metal foams (GPLRMF) conical shells as the research object, and uses high-order shear deformation theory (HSDT) to study the thermal post-buckling behaviors. Based on general variational principle, the governing equation of a GPLRMF conical shell is deduced, and discretized and solved by Galerkin method to obtain the critical buckling temperature and thermal post-buckling response of conical shells under various influencing factors. Finally, the effects of cone angles, GPLs distribution types, GPLs mass fraction, porosity distribution types and porosity coefficient on the thermal post-buckling behaviors of conical shells are analyzed in detail. The results show that the cone angle has a significant impact on the nonlinear thermal stability of the conical shells.

• Proceedings of the Korean Nuclear Society Conference
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• 1995.05a
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• pp.623-629
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• 1995

To investigate the effects of powder shape on U loading density of fuel meat, two kinds of fuel meats were prepared with atomized and comminuted U$_3$Si$_2$ powders by extrusion or rolling process. Extruded fuel meats with atomized spherical U$_3$Si$_2$ powder appeared to have much less porosity than those with comminuted irregular U$_3$Si$_2$ powder at higher U$_3$Si$_2$ fraction- The U$_3$Si$_2$ particles with spherical shape are less fractured in extrusion than in rolling. Most of atomized particles on the whole maintained to have spherical shapes in the extrusion. It has been shown that atomized spherical particles are expected to approach similar upper loading limits comparing with comminuted particles in rolled plates, but exceed comminuted powder loading limits in extruded rods.

• Steel and Composite Structures
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• v.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. 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.

• Steel and Composite Structures
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• v.45 no.3
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• pp.409-423
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• 2022

Nowadays, there is a high demand for great structural implementation and multifunctionality with excellent mechanical properties. The porous structures reinforced by graphene platelets (GPLs) having valuable properties, such as heat resistance, lightweight, and excellent energy absorption, have been considerably used in different engineering implementations. However, stiffness of porous structures reduces significantly, due to the internal cavities, by adding GPLs into porous medium, effective mechanical properties of the porous structure considerably enhance. This paper is relating to vibration analysis of fluidconveying cantilever porous graphene platelet reinforced (GPLR) pipe with fractional viscoelastic model resting on foundations. A dynamical model of cantilever porous GPLR pipes conveying fluid and resting on a foundation is proposed, and the vibration, natural frequencies and primary resonant of such a system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with the fractional viscoelastic model is used to govern the construction relation of nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied to the pipe and the excitation frequency is close to the first natural frequency. The governing equation for transverse motions of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Earthquakes and Structures
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• v.13 no.3
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Steel and Composite Structures
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• v.50 no.2
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• pp.201-216
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• 2024

This paper is motivated by the lack of studies relating to vibration and nonlinear resonance of fluid-conveying cantilever porous GPLR pipes with fractional viscoelastic model resting on nonlinear foundations. A dynamical model of cantilever porous Graphene Platelet Reinforced (GPLR) pipes conveying fluid and resting on nonlinear foundation is proposed, and the vibration, natural frequencies and primary resonant of such system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with fractional viscoelastic model is used to govern the construction relation of the nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied on pipe and excitation frequency is close to the first natural frequency. The governing equation for transverse motion of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Journal of the Mineralogical Society of Korea
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• v.23 no.2
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• pp.151-159
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• 2010

The effect of calcite and gypsum on the hydration of Portland cement was investigated using GEM-PSI, a geochemical model. Addition of calcite and gypsum up to 5 wt% of total cement clinker into Portland cement was found to influence the hydrate assemblage of the hydrated cement in different ways. The results of geochemical modelling showed that the fraction of calcium monocarbonate increased by the hydration of cement with the increase of calcite addition. The results of modelling also indicated that gypsum increased the fraction of ettringite in the assemblage of hydrated cement as the amount of gypsum added increases. This study showed that porosity generated by the hydration of cement had a significant relation with the amount of calcite and gypsum added. The porosity of hydrated cement was lower when calcite added up to 3 wt% of cement clinker compared to the hydrated cement with the same amount of gypsum addition. However, when calcite added more than 3% of cement clinker, the porosity of hydrated cement were higher than that of hydrated cement with the same amount of gypsum addition.

• Resources Recycling
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• v.7 no.5
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• pp.13-18
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• 1998

This study was carried out to understand the properties of the E.A.F. steel-making dusts for stabilization processing. The properties are related to mincral composition, shape, particle size, magnetism, density, porosity and leaching characteristic. the dust particles, the size of which ranges from sub-micron to tens-micron, were mainly spherical like balls that were agglomerated each other: the large particles were generally Fe-rich and the small particles were spherical like balls that were agglomerated each other: the large particles were franklinite (ZnFe$_{2}O_{4}$), magnetite (Fe$_{3}O_{4}$) and zincite (ZnO) by XRD analysis. When the dusts were sieved by a wet process, the particle fraction over 200 mesh had 1.5 wt.% with magnetite and quartz. The particles in the size range of 200-500 mesh consisted of magnetite, franklinite. The 82 wt.% of the steel-making dusts were occupied by the particles finer than 500 mesh and contained franklinite and zincite as main mineralogical compositions. When the dusts of around 78% porosity compressed under the load of approximately 1 KPa, the porosity decreased to 68% and to 535 under around 13 KPa. When the E.A.F. dusts were leached according to the Korea standard leaching procedure on the waster, the heavy metals exceeding the leaching criteria were cadmium, lead and mercury.