• Korean Journal of Ecology and Environment
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• v.37 no.3 s.108
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• pp.297-303
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• 2004

Two dimensional cellular automaton (CA) models were developed to investigate growth of biofilms in aquatic ecosystems. Simple local rules on CA were applied to governing growth of bacterial populations in relation to different nutrient concentrations. Initial bacterial distribution played an important role in determining population size and morphology of biofilm at low concentrations of nutrition. With clumped distribution, population size increased slowly compared with uniform and random distributions, while the porosity tented to be higher with uniform distribution compared with other initial distributions.

• Journal of Korean Society of Water and Wastewater
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• v.9 no.2
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• pp.84-96
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• 1995

The dewatering characteristics of the sewage sludge was investigated through the experimental observations and model simulations. The activated sludge and the anaerobically digested sludge were examined for the dewaterability evaluation within the pressure range of $0{\sim}10^6N/m^2$. Modified Buchner funnel test and compression test by the consolidometer were conducted to evaluate average specific resistance, porosity, and moisture percentage of filter cake. Shirato's technique of compression-permeability test was followed for the pressure range lower than about $10^2N/m^2$. The flocculation effects on sludge dewatering was also examined for ferric chloride and polymeric flocculant. The application of hydrated lime which can be used for flue-gas desulfurization showed improved moisture percentage, and was thought to have positive feasibility in combined system of sludge dewatering and incineration. Determined characteristic constants were applied to Tiller's cake filtration model to simulate liquid pressure distribution and porosity distribution in cake. Model simulations showed a sharp drop of the porosity close to the cake-medium interface for the highly compressible material such as the activated sludge and the anaerobically digested sludge.

• Steel and Composite Structures
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• v.21 no.1
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• pp.123-136
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• 2016

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, 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.

• Advances in materials Research
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• v.8 no.3
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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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• v.35 no.2
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• pp.295-306
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• 2020

This paper deals with free vibration analysis of non-uniform column resting on elastic foundations and subjected to follower force at its free end. The internal pores and graphene platelets (GPLs) are distributed in the matrix according to different patterns. The model is proposed with material parameters varying in the thickness of column to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite column, it is crucial to consider porosities inside the material structure.

• Advances in nano research
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• v.7 no.1
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• pp.25-38
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• 2019

This research is aimed at studying the asymmetric thermal buckling of porous functionally graded (FG) annular nanoplates resting on an elastic substrate which are made of two different sets of porous distribution, based on nonlocal elasticity theory. Porosity-dependent properties of inhomogeneous nanoplates are supposed to vary through the thickness direction and are defined via a modified power law function in which the porosities with even and uneven type are approximated. In this model, three types of thermal loading, i.e., uniform temperature rise, linear temperature distribution and heat conduction across the thickness direction are considered. Based on Hamilton's principle and the adjacent equilibrium criterion, the stability equations of nanoporous annular plates on elastic substrate are obtained. Afterwards, an analytical solution procedure is established to achieve the critical buckling temperatures of annular nanoplates with porosities under different loading conditions. Detailed numerical studies are performed to demonstrate the influences of the porosity volume fraction, various thermal loading, material gradation, nonlocal parameter for higher modes, elastic substrate coefficients and geometrical dimensions on the critical buckling temperatures of a nanoporous annular plate. Also, it is discussed that because of present of thermal moment at the boundary conditions, porous nanoplate with simply supported boundary condition doesn't buckle.

• Advances in nano research
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• v.12 no.5
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• pp.441-455
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• 2022

This study explores the linear and nonlinear solutions of sigmoid functionally graded material (S-FGM) nanoplate with porous effects. A size-dependent numerical solution is established using the strain gradient theory and isogeometric finite element formulation. The nonlinear nonlocal strain gradient is developed based on the Reissner-Mindlin plate theory and the Von-Karman strain assumption. The sigmoid function is utilized to modify the classical functionally graded material to ensure the constituent volume distribution. Two different patterns of porosity distribution are investigated, viz. pattern A and pattern B, in which the porosities are symmetric and asymmetric varied across the plate's thickness, respectively. The nonlinear finite element governing equations are established for bending analysis of S-FGM nanoplates, and the Newton-Raphson iteration technique is derived from the nonlinear responses. The isogeometric finite element method is the most suitable numerical method because it can satisfy a higher-order derivative requirement of the nonlocal strain gradient theory. Several numerical results are presented to investigate the influences of porosity distributions, power indexes, aspect ratios, nonlocal and strain gradient parameters on the porous S-FGM nanoplate's linear and nonlinear bending responses.

• Steel and Composite Structures
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• v.43 no.1
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• pp.31-54
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• 2022

This paper is concerned with the buckling behavior of functionally graded graphene reinforced porous nanocomposite beams based on the finite element method (FEM) using two variables trigonometric shear deformation theory. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The finite element approach is developed using a nonlocal strain gradient theory. The governing equations derived here are solved introducing a 3-nodes beam element, and then the critical buckling load is calculated with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the accuracy of the present model, a comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern of GPL reinforcements on the Buckling behavior of the nanocomposite beam. The effects of various structural parameters such as the dispersion patterns for the graphene and porosity, thickness ratio, boundary conditions, and nonlocal and strain gradient parameters are brought out. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams, and the results allows to identify the most effective way to achieve improved buckling behavior of the porous nanocomposite beam.

• Steel and Composite Structures
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• v.43 no.1
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• pp.1-17
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• 2022

The free and forced nonlinear dynamic behaviors of Porous Functionally Graded Material (PFGM) plates are examined by means of a High-Order Implicit Algorithm (HOIA). The formulation is developed using the Third-order Shear Deformation Theory (TSDT). Unlike previous works, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite, and the distribution of the porosity is assumed to be gradually variable through the thickness of the PFGM plates. Using the Hamilton principle, we establish the governing equations of motion. The Finite Element Method (FEM) is used to compute approximations of the resulting equations; FEM is adopted using a four-node quadrilateral finite element with seven Degrees Of Freedom (DOF) per node. Nonlinear equations are solved by a HOIA. The accuracy and the performance of the proposed approach are verified by presenting comparisons with literature results for vibration natural frequencies and dynamic response of PFGM plates under external loading. The influences of porosity volume fraction, porosity distribution, slenderness ratio and other parameters on the vibrations of PFGM plate are explored. The results demonstrate the significant impact of different physical and geometrical parameters on the vibration behavior of the PFGM plate.

• Computers and Concrete
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• v.32 no.1
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• pp.87-97
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• 2023

The bending of a porous FG plate is discussed in this study using a novel higher quasi-3D hyperbolic shear deformation theory with four unknowns. The proposed theory takes into consideration the normal and transverse shear deformation effect and ensures the parabolic distribution of the transverse stresses through the thickness direction with zero-traction at the top and the bottom surfaces of the structure. Innovative porous functionally graded materials (FGM) have through-thickness porosity as a unique attribute that gradually varies with their qualities. An analytical solution of the static response of the perfect and imperfect FG plate was derived based on the virtual work principle and solved using Navier's procedure. The validity and the efficiency of the current model is confirmed by comparing the results with those obtained by others solutions. The comparisons showed that the present model is very efficient and simple in terms of computation time and exactness. The impact of the porosity parameter, aspect ratio, and thickness ratio on the bending of porous FG plate is shown through a discussion of several numerical results.