• Advances in nano research
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• v.14 no.5
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Advances in nano research
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• v.16 no.1
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• pp.11-26
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• 2024

In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.39-45
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• 2002

In this paper, we study the space of almost continuous functions with the topology of uniform convergence. And we investigate some properties of this space.

• 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.

• Ocean Systems Engineering
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• v.12 no.1
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• pp.63-86
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• 2022

A refined projection-based purely Lagrangian meshfree method is presented towards reliable numerical analysis of fluid flow interactions with saturated/unsaturated porous media of uniform/spatially-varying porosities. The governing equations are reformulated on the basis of two-phase mixture theory with incorporation of volume fraction. These principal equations of mixture are discretized in the context of Incompressible SPH (Smoothed Particle Hydrodynamics) method. Associated with the consideration of governing equations of mixture, a new term arises in the source term of PPE (Poisson Pressure Equation), resulting in modified source term. The linear and nonlinear force terms are included in momentum equation to represent the resistance from porous media. Volume increase of fluid particles are taken into consideration on account of the presence of porous media, and hence multi-resolution ISPH framework is also incorporated. The stability and accuracy of the proposed method are thoroughly examined by reproducing several numerical examples including the interactions between fluid flow and saturated/unsaturated porous media of uniform/spatially-varying porosities. The method shows continuous pressure field, smooth variations of particle volumes and regular distributions of particles at the interface between fluid and porous media.

• Steel and Composite Structures
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• v.42 no.6
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Coupled systems mechanics
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• v.12 no.3
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• pp.199-220
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• 2023

This article presents a new analytical model to study the effect of porosity on the shear correction factors (SCFs) of functionally graded porous beams (FGPB). For this analysis, uneven and logarithmic-uneven porosity functions are adopted to be distributed through the thickness of the FGP beams. Critical to the application of this theory is a determination of the correction factor, which appears as a coefficient in the expression for the transverse shear stress resultant; to compensate for the assumption that the shear strain is uniform through the depth of the cross-section. Using the energy equivalence principle, a general expression is derived from the static SCFs in FGPB. The resulting expression is consistent with the variationally derived results of Reissner's analysis when the latter are reduced from the two-dimensional case (plate) to the one-dimensional one (beam). A convenient algebraic form of the solution is presented and new study cases are given to illustrate the applicability of the present formulation. Numerical results are presented to illustrate the effect of the porosity distribution on the (SCFs) for various FGPBs. Further, the law of changing the mechanical properties of FG beams without porosity and the SCFare numerically validated by comparison with some available results.

• Steel and Composite Structures
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• v.35 no.1
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• pp.111-127
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• 2020

The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. The 2-D differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. 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 plates, it is crucial to consider porosities inside the material structure.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.1-11
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• 2024

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porosity-dependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensatesfor the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the one-dimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changesin FG beams without porosity and the SCF by comparing them with available results.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.763-774
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• 2019

The main aim of this paper is enhancing design of traditional laminated composite plates subjected to static loads. In this regard, this paper suggests embedding a lightweight porous layer in the middle of laminated composite as the core layer of the resulted sandwich plate. The static responses of the suggested structures with uniform, symmetric and non-symmetric porosity distributions are compared to optimize their design. Using the first order shear deformation theories, the static governing equations of the suggested laminated composite plates with a porous layer (LCPPL) rested on two-parameter foundation are obtained. A finite element method is also utilized to solve the governing equations of LCPPLs. Effects of laminated composite and porosity characteristics as well as geometry dimension, edges' boundary conditions and foundation coefficients on the static deflection and stress distribution of the suggested composite plates have been investigated. The results reveal that the use of core between the layers of laminated composites leads to a sharp reduction in the static deflections of LCPPLs. Furthermore, in compare with perfect cores, the use of porous core between the layers of laminated composite plates can offer a considerable reduction in structural weight without a significant difference in their static responses.