• Coupled systems mechanics
• /
• v.11 no.5
• /
• pp.389-409
• /
• 2022

During the manufacture of FGM plates, defects such as porosities can appear. Those can change the entire behavior of these plates. This paper aims to investigate the free vibration characteristics of porous functionally graded (FG) plates resting on elastic foundations. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power-law formulation, and the Poisson ratio is held constant. Different types of porosity distribution rates are considered. To examine the accuracy of the present formulation, several comparison studies are investigated. Effects of variation of porosity distribution rate, foundation parameter, power-law index and thickness ratio on the fundamental frequency of plates have been investigated.

• Restorative Dentistry and Endodontics
• /
• v.46 no.4
• /
• pp.57.1-57.9
• /
• 2021

Objectives: This study aimed to compare and evaluate the porosity and pore size distribution of high-viscosity glass ionomer cements (HVGICs) and conventional glass ionomer cements (GICs) using micro-computed tomography (micro-CT). Materials and Methods: Forty cylindrical specimens (n = 10) were produced in standardized molds using HVGICs and conventional GICs (Ketac Molar Easymix, Vitro Molar, MaxxionR, and Riva Self-Cure). The specimens were prepared according to ISO 9917-1 standards, scanned in a high-energy micro-CT device, and reconstructed using specific parameters. After reconstruction, segmentation procedures, and image analysis, total porosity and pore size distribution were obtained for specimens in each group. After checking the normality of the data distribution, the Kruskal-Wallis test followed by the Student-Newman-Keuls test was used to detect differences in porosity among the experimental groups with a 5% significance level. Results: Ketac Molar Easymix showed statistically significantly lower total porosity (0.15%) than MaxxionR (0.62%), Riva (0.42%), and Vitro Molar (0.57%). The pore size in all experimental cements was within the small-size range (< 0.01 mm³), but Vitro Molar showed statistically significantly more pores/defects with a larger size (> 0.01 mm³). Conclusions: Major differences in porosity and pore size were identified among the evaluated GICs. Among these, the Ketac Molar Easymix HVGIC showed the lowest porosity and void size.

• Structural Engineering and Mechanics
• /
• v.71 no.1
• /
• pp.89-98
• /
• 2019

In this study, the mechanical bending behaviors of functionally graded porous nanobeams are investigated. Four types of porosity which are, the classical power porosity function, the symmetric with mid-plane cosine function, bottom surface distribution and top surface distribution are proposed in analysis of nanobeam for the first time. A comparison between four types of porosity are illustrated. The effect of nano-scale is described by the differential nonlocal continuum theory of Eringen by adding the length scale into the constitutive equations as a material parameter comprising information about nanoscopic forces and its interactions. The graded material is designated by a power function through the thickness of nanobeam. The beam is simply-supported and is assumed to be thin, and hence, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Numerical results show effects of porosity type, material graduation, and nanoscale parameters on the static deflection of nanobeam.

• Geomechanics and Engineering
• /
• v.30 no.2
• /
• pp.153-167
• /
• 2022

This study proposes a method to analyze the distribution of coal porosity disturbances after the excavation of ultra-large-diameter water jet boreholes using a coal wetting and softening model. The high-pressure jet is regarded as a short-term high-pressure water injection process. The water injection range is the coal softening range. The time when the reference point of the borehole wall is shocked by the high-pressure water column is equivalent to the time of high-pressure water injection of the coal wall. The influence of roadway excavation with support and borehole diameter on the ultra-large-diameter jet drilling excavation is also studied. The coal core around the borehole is used to measure the gas permeability for determining the porosity disturbance distribution of the coal in the sampling plane to verify the correctness of the simulation results. Results show that the excavation borehole is beneficial to the expansion of the roadway excavation disturbance, and the expansion distance of the roadway excavation disturbance has a quadratic relationship with the borehole diameter. Wetting and softening of the coal around the borehole wall will promote the uniform distribution of the overall porosity disturbance and reduce the amplitude of disturbance fluctuations.

• Steel and Composite Structures
• /
• v.33 no.6
• /
• pp.865-875
• /
• 2019

The current article proposed to develop a geometrical model for the analysis and modelling of the uniaxial functionally graded structure using the higher-order displacement kinematics with and without the presence of porosity including the distribution. Additionally, the formulation is capable of modelling three different kinds of grading patterns i.e., Power-law, sigmoid and exponential distribution of the individual constituents through the thickness direction. Also, the model includes the distribution of porosity (even and uneven kind) through the panel thickness. The structural governing equation of the porous graded structure is obtained (Hamilton's principle) and solved mathematically by means of the isoparametric finite element technique. Initially, the linear frequency parameters are obtained for different geometrical configuration via own computer code. The comparison and the corresponding convergence studies are performed for the unidirectional FG structure for the validation purpose. Finally, the impact of different influencing parameters like aspect ratio (O), thickness ratio (S), curvature ratio (R/h), porosity index (λ), type of porosity (even or uneven), power-law exponent (n), boundary condition on the free vibration characteristics are obtained for the FG panel and discussed in details.

• Steel and Composite Structures
• /
• v.36 no.3
• /
• pp.293-305
• /
• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

• Nuclear Engineering and Technology
• /
• v.35 no.1
• /
• pp.55-63
• /
• 2003

Threshold porosity above which fission gas release channels would be formed in the rim egion of high burnup UO$_2$ fuel was estimated by the Monte Carlo method and Hoshen-Kopelman algorithm. With the assumption that both rim pore and rim grain can be represented by cube, pore distribution in the rim was simulated 3-dimensionally by the Monte Carlo method according to porosity and pore size distribution. Then, using the Hoshen-Kopelman algorithm, the fraction of open rim pores interlinked to the outer surface of a fuel pellet was derived as a function of rim porosity. The simulation showed that porosity of 24-25% is the threshold above which the number of rim pores forming release channels increases very rapidly. On the other hand, channels would not be formed if the porosity is less than about 23.5%. This is consistent with the observation that, for porosity less than 23.5%, almost no fission gas is released in the rim. However, once the rim porosity reaches beyond 25%, extensive open paths would be developed and considerable fission gas release would start in the rim.

• Steel and Composite Structures
• /
• v.42 no.5
• /
• pp.711-722
• /
• 2022

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

• Steel and Composite Structures
• /
• v.45 no.5
• /
• pp.697-713
• /
• 2022

In the context of the finite elements method, the dynamic behavior of porous functionally graded double wishbone vehicle suspension structural system incorporating joints flexibility constraints under road bump excitation is studied and analyzed. The functionally graded material properties distribution through the thickness direction is simulated by the power law including the porosity effect. To explore the porosity effects, both classical and adopted porosity models are considered based on even porosity distribution pattern. The dynamic equations of motion are derived based on the Hamiltonian principle. Closed forms of the inertia and material stiffness components are derived. Based on the plane frame isoparametric Timoshenko beam element, the dynamic finite elements equations are developed incorporating joint flexibilities constraints. The Newmark's implicit direct integration methodology is utilized to obtain the transient vibration time response under road bump excitation. The presented procedure is validated by comparing the computational model results with the available numerical solutions and an excellent agreement is observed. Obtained results show that the decrease of porosity percentage and material graduation tends to decrease the deflection as well as the resulting stresses of the control arms thus improving the dynamic performance and increasing the service lifetime of the control arms.

• Clean Technology
• /
• v.29 no.4
• /
• pp.249-254
• /
• 2023

In this study, porosity estimation was conducted by the physical properties of zeolite. Because of the difficulty of directly measuring the porosity of particulate matter, the porosity was calculated by applying the measured physical properties of zeolite to the calculation formula presented in various literature. For this purpose, the average particle size, particle size distribution, specific surface area, and pore characteristics of three types of zeolite - zeolite beta, zeolite Y, and ZSM-5 - were measured. In addition, the true density using gas and liquid phases, and two types apparent density (tap and untapped density) were measured. We calculated the porosity using these results, compare and analyzed the results, and evaluated main factors that determine the porosity.