Porosity Distribution Pattern Research Articles

Acoustic response behavior of porous 3D graphene foam plate

Sound radiation and sound transmission loss (STL) behavior of porous 3D graphene (3D-GrF) foam plate are presented. Two variable refined plate theory which includes both transverse bending and shear stresses is used to model the plate and Navier’s solution is used to calculate the vibration responses while Rayleigh integral is used to analyze the acoustic response. Variation in free vibration frequencies with the nature of porosity distribution is significant for the 3D-GrF plates having higher porosity co-efficient. The natural frequency of the 3D-GrF plate with more porosity around the center and less porosity at the outer surfaces is high. However, resonant amplitudes of the responses and STL of the plates are controlled by both the nature of the porosity distribution pattern and porosity co-efficient. In general, STL of the plate with less porosity around the center and high porosity at the extreme surfaces is high compared to the other cases.

Effects of porosity and flexoelectricity on static bending and free vibration of AFG piezoelectric nanobeams

Abstract In this paper, based on the strain gradient theory, a size-dependent porous axially functional gradient (AFG) flexoelectric Euler-Bernoulli nanobeam model is developed. A modified power-law formula incorporating porosity volume fraction is presented to describe material properties of porous AFG nanobeam, and two typical porosity distributions patterns are considered. The generalized differential quadrature method is employed to discretize governing equations into a series of linear algebraic equations, so that the static bending deflections and free vibration frequencies are calculated conveniently for various boundary conditions. The credibility of the present mathematical formulation and the associated numerical solution are validated by comparing the results in previous literatures. Parametric studies are performed to illustrate the effects of the flexoelectricity, material length scale parameters, functionally graded index, porosity volume fraction, porosity distribution patterns on the static bending and free vibration behaviors of porous AFG flexoelectric nanobeam. The numerical results may provide support for the application of porous AFG flexoelectric nanobeam in Nano-electro-mechanical system.

Free vibration analysis of thick sandwich cylindrical panels with saturated FG-porous core

In this paper a numerical solution is presented for free vibration analysis of sandwich cylindrical panels made of a saturated functionally graded porous (FG-porous) core and two similar homogenous face sheets. The panel is modeled based on the third order shear deformation theory (TSDT) and stress-strain relations are considered based on the linear poroelasticity theory of Biot. Natural frequencies are calculated for various boundary conditions and a parametric study is presented to study the effects of various parameters on the natural frequencies including geometrical parameters, porosity parameter, porosity distribution pattern, thickness of the porous core and compressibility of porefluid.

Thermo-mechanical vibration of FG curved nanobeam containing porosities and reinforced by graphene platelets

Recently, the graphene platelets (GPLs) are extensively used as reinforcements to enhance the strength of porous materials. However, most studies are focused on the straight GPLs-reinforced structures under macro-scale. In this paper, the thermo-mechanical vibration of a curved functionally graded (FG) porous nanobeam reinforced with GPLs is studied via the curved refined shear deformation beam theory associated with nonlocal strain gradient size scale effect. Four different porosity distribution patterns are employed to account for the graded distribution of porosity, and the GPLs are assumed to be dispersed evenly over the porous nanobeam. The effective mechanical properties of the curved nanobeam with different FG porosity patterns are evaluated by virtue of the Halpin–Tsai micromechanical-based model. The effects of GPL weight fraction, temperature variation, opening angle, porosity distribution pattern and coefficient, as well as size-scale parameters on the vibrational performance of the GPLs-reinforced curved FG porous nanobeam with different boundary conditions are investigated. It is demonstrated that the fundamental frequency enhances with the increase of the GPL weight fraction, while increasing the porosity coefficient does not always decrease the vibrational frequency, which is related to the porosity distribution pattern and boundary condition. Moreover, the thermal environment and size-scale characteristics also have significant influences on the vibration of GPLs-reinforced porous nanobeam.

Three-dimensional static and free vibration analysis of graphene platelet–reinforced porous composite cylindrical shell

Because of promoted thermomechanical performance of functionally graded graphene platelet–reinforced composite ultralight porous structural components, this article investigates bending and free vibration behavior of functionally graded graphene platelet–reinforced composite porous cylindrical shell based on the theory of elasticity. Effective elasticity modulus of the composite is estimated with the aid of modified version of Halpin–Tsai micromechanics. Rule of mixtures is used to obtain mass density and Poisson’s ratio of the graphene platelet–reinforced composite shell. An analytical solution is introduced to obtain the natural frequencies and static behavior of simply supported cylindrical shell by applying the state-space technique along the radial coordinate and Fourier series expansion along the circumferential and axial direction. In addition, differential quadrature method is used to explore the response of the cylindrical shell in the other cases of boundary conditions. Validity of the applied approach is examined by comparing the numerical results with those published in the available literature. A comprehensive parametric study is conducted on the effects of different combinations of graphene platelets distribution patterns and porosity distribution patterns, boundary conditions, graphene platelets weight fraction, porosity coefficient, and geometry of the shell (such as mid-radius to thickness ratio and length to mid-radius ratio) on the bending and free vibration behavior of the functionally graded graphene platelet–reinforced composite porous cylindrical shell. The results of this study provide useful practical tips for engineers designing composite structures.

Probabilistic stability analysis of functionally graded graphene reinforced porous beams

This paper presents the first attempt to study the probabilistic stability characteristics of functionally graded (FG) graphene platelets (GPLs) reinforced beams by taking into account the multidimensional probability distributions, such as stochastic porosity and GPL distribution patterns as well as random material properties. For this purpose, a non-inclusive Chebyshev metamodel (CMM), which is implemented on deterministic analysis using discrete singular convolution (DSC) method with excellent computational efficiency and accuracy, is proposed and used to obtain both deterministic and probabilistic results including probability density functions (PDFs), cumulative density functions (CDFs), means and standard deviations of the critical buckling load. The present analysis is rigorously validated through direct comparisons against the results obtained by a direct quasi-Monte Carlo simulation (QMCS) method and those available in open literature. The influences of material properties, porosity distribution, GPL dispersion pattern and boundary condition on probabilistic buckling behaviour of the FG-GPL beam are comprehensively investigated. The global sensitivity analysis is also conducted. The results suggest that the critical buckling load of the FG-GPL beam is most sensitive to porosity distribution, followed by porosity coefficient and GPL weight fraction.

Buckling analyses of FG porous nanocomposite cylindrical shells with graphene platelet reinforcement subjected to uniform external lateral pressure

In this paper, buckling analyses of functionally graded porous nanocomposite cylindrical shells reinforced with graphene platelets (FGPNCS-R-GPLs) under uniform external lateral pressure are performed for the first time. FGPNCS-R-GPLs are built by infiltrating GPLs into the metal matrix containing open-cell internal pores. Hence, different GPLs and porosity distribution patterns called uniform and non-uniform are considered through the thickness of the shell. The modified Halpin-Tsai micromechanics model and the rule of mixtures are employed to estimate the effective modulus of elasticity and to compute density and Poisson’s ratio of the porous nanocomposite shell respectively. The theoretical governing formulations are derived based the first-order shear deformation theory (FSDT), and then they are solved using Rayleigh-Ritz method to obtain the critical buckling pressure. Present formulations are validated by comparing the present numerical results with results obtained by finite element methods. Moreover, the effects of the number layer in the thickness direction, GPLs and porosity distribution patterns, porosity coefficient, GPL weight fraction, GPL shape, circumferential wave number, boundary condition and cylindrical shell dimensions are comprehensively investigated in detail to find the best parameter values to achieve the maximum buckling resistance of FGPNCS-R-GPLs.

Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell

In this article, wave propagation behavior of a size-dependent spinning graphene nanoplatelet-reinforced composite (GNPRC) cylindrical nanoshell with porosity is presented. The effects of small scale are analyzed based on nonlocal strain gradient theory (NSGT), this accurate theory employs exact length scale parameter and nonlocal constant. The governing equations of GNPRC cylindrical nanoshell coupled with piezoelectric actuator (PIAC) are evolved by minimum potential energy principle and solved by the analytical method. For the first time in the current study, wave propagation-porosity behavior of a GNPRC cylindrical nanoshell coupled with PIAC is examined based on NSGT. The results show that, as the angular velocity increases, the difference between the minimum and maximum values of the phase velocity decreases. Another important result of this paper is that, by increasing the radius, extremum values of phase velocity occur in the lower values of the wave number. Finally, the influences of porosity, angular velocity, wave number and different graphene platelet distribution patterns on the phase velocity are investigated using the mentioned continuum mechanics theory. The outputs of the present work can be used in structural health monitoring and ultrasonic inspection techniques.

Mixed solutions of mathematical and numerical methods for reactive mass transport problems of two different porosity regions in fluid-saturated porous media

Reactive mass transport is a common phenomenon associated with groundwater pollution in the field of groundwater hydrology. For a reactive mass transport problem involving two different porosity regions, in which the porosity of the fluid-saturated porous medium has a constant distribution in the left region and an exponential distribution in the right region, theoretical solutions for both dimensional and dimensionless acid concentrations have been derived mathematically in the left region by using the interface condition substitution strategy. The fundamental idea behind this strategy is that the boundary condition at the entrance of the left region and the mathematical governing equation of the right region at the interface location between the left and right regions can be used to determine two independent constants involved in the theoretical solutions for the dimensional and dimensionless acid concentrations in the left region of the reactive mass transport system. Since both the acid concentration and its first derivative are known at the left boundary (i.e. the interface location) of the right region, it is possible to derive analytical expressions for the numerical solution (e.g. the finite element solution) in the right region by using the point-by-point marching strategy. The related theoretical results have demonstrated that the porosity distribution pattern in the right region of the system can have a significant influence on the dimensionless acid concentration distribution in the whole system, so that it affects not only the chemical dissolution front instability, but also the reactive mass transport process in an underground water system.

Nanoporous Silica of Some Egyptian Diatom Frustules as a Promising Natural Material

Background:Diatoms are a large unique group of unicellular microalgae with a significant ornamented cell wall made of hydrated silica, which is called "frustule". Their ornamented siliceous shells are usually composed of multi-layer structures with multi-scale porosity, which can be used as a promising source to obtain hierarchical macro and mesoporous silica microparticles. The present study is one step forward through a long road seeking for green nanofabrication techniques of such porous materials that will be economically more efficient with large design flexibility.Materials and Methods:For seeking different porosity scales, architectures, and distribution patterns, a total of 237 diatom species and varieties belonging to 68 genera were identified from 59 samples, which were collected from different Egyptian habitats and environments. Of these eight species were selected to study their frustules' ultra-structures in details, including; Aulacoseira granulata (Ehrenberg) Simonsen, Actinocyclus octonarius Ehrenberg, Cyclotella meneghiniana Kützing, Pleurosira laevis (Ehrenberg) Compére, Synedra ulna (Nitzsch) Ehrenberg, Achnanthes brevipes Agardh, Nitzschia amphibia Grunow and Nitzschia palea (Kützing) W. Smith. Nitzschia palea (Kützing) W. Smith was also isolated and cultivated.Results:The ultrastructure and porosity of all studied species had been revealed. The porosity scale was ranged from 5 to 500 nm in diameter.Conclusion:The obtained results showed the potential of diatom frustules in nanotechnology as a source of natural silica microparticles with macro and mesoporous structures could be of a large interest for applications including ultra, micro and nanofiltration, drug delivery systems, optoelectronics, or other novel nanotechnology applications.

Dynamic characteristics of functionally graded porous beams with interval material properties

This paper presents a new computational approach named hybrid Chebyshev surrogate model with discrete singular convolution (CSM-DSC) method to study the nondeterministic dynamic characteristics of functionally graded (FG) porous beams with material uncertainties. In the proposed approach, interval analysis can be directly applied in hybrid CSM-DSC computational framework, then the upper and low bounds of the dynamic responses of FG porous beams with various boundary conditions can be readily obtained. Based on Hamilton’s principle and Timoshenko beam theory, the governing equation is established and solved by DSC method. By utilizing the higher-dimensional Chebyshev surrogate (HDCS) model, the approximate performance function involving uncertainty in three critical material properties, such as Young’s modulus, mass density and porosity coefficient, is developed numerically. In order to verify the validity and accuracy of the proposed method, deterministic analysis and nondeterministic analysis are implemented to compare the present results against the published ones, and those obtained by the finite element method (FEM) and quasi-Monte Carlo simulation (QMCS) method. A comprehensive parametric study is then conducted to examine the influences of material parameter uncertainties, porosity distribution patterns, porosity coefficient, boundary conditions, and aspect ratio on the bounds of frequencies. The results show that the uncertainty of Young’s modulus has the most significant effect on beam’s dynamic responses, followed by that of mass density whereas the influence of the uncertain of porosity coefficient is much less pronounced.

Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

In this article, we present for the first time a research analysis for the size-dependent effects on thermal buckling and post-buckling behaviors of functionally graded material micro-plates with porosities (imperfect FGM) using isogeometric analysis. A seventh-order shear deformation plate theory associated with the modified couple stress theory (MCST) is particularly imposed to capture the size-dependent phenomenon within imperfect FGM micro-plates. The material properties of imperfect FGM micro-plates with three different distributions of porosities including even, uneven and logarithmic-uneven varying across the plate thickness are derived from the modified rule-of-mixture assumption. The nonlinear governing equation for size-dependent imperfect FGM micro-plate under uniform, linear and nonlinear temperature rise is derived using the Von-Kármán assumption and Hamilton’s principle. Through numerical example, the effect of temperature rise, boundary conditions, power index, porosity volume fraction, porosity distribution pattern and material length scale parameter on thermal buckling and post-buckling behaviors of FGP micro-plates are investigated.

Fluid Permeability of Graded Porosity Scaffolds Architectured with Minimal Surfaces.

The natural local porosity variation in the native tissue can be replicated by graded porosity scaffolds. Scaffolds with radial porosity distribution can be a solution to improve both mechanical and biological functions of the biomimetic scaffolds. In the present study, fluid permeability as a quantitative indicator of biological performance is studied numerically and experimentally for different pore shapes and porosity distribution patterns in the scaffolds designed on the basis of triply periodic minimal surfaces (TPMSs). Among the uniform porosity scaffolds, those designed on the basis of P* (P surface) and Y** (G surface) showed the highest permeability. In the radially graded porosity scaffolds with linear porosity distribution, permeability was found to be about twice more sensitive to the peripheral porosity than the porosity at the center. The results suggest that the permeability-gradient parameter relationships can follow different trends depending on the pore shape as opposed to the conventional uniform porosity scaffolds. This implies the need for the design maps that were developed to choose appropriate scaffold pore design parameters. Finally, experimental permeability measurement was performed via a constant head permeability test, and the effect of test parameters (i.e., fluid height) was discussed.

Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution

The present article deals with thermal buckling of functionally graded plates with porosity and resting on elastic foundation. The basic formulation is based on quasi 3D theory. The present theory contains only four unknowns and also accommodates the thickness stretching effect. Porosity-dependent material coefficients of the plate are compositionally graded throughout the thickness according to a modified micromechanical model. Different patterns of porosity distributions are considered. The thermal loads are assumed to be uniform, linear and non-linear temperature rises through the thickness direction. The plate is assumed to be simply supported on all edges. Various numerical examples are given to check the accuracy and reliability of the present solution, in which both the present results and those reported in the literature are provided. In addition, several numerous new results for thick FG plates with porosity are also presented.

An analytical solution for bending and free vibration responses of functionally graded beams with porosities Effect of the micromechanical models

In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present higher-order shear deformation model, the equations of motion are derived from Hamilton\'s principle. Navier type solution method was used to obtain displacement, stresses and frequencies, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams.

Exact solutions for postbuckling of a graded porous beam

An exact, closed-form solution for the postbuckling responses of graded porous beams subjected to axially loading is obtained. It was assumed that the properties of the graded porous materials vary continuously through thickness of the beams, the equations governing the axial and transverse deformations are derived based on the classical beam theory and the physical neutral surface concept. The two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations. The nonlinear equation is directly solved without any use of approximation and a closed-form solution for postbuckled deformation is obtained as a function of the applied load. The exact solutions explicitly describe the nonlinear equilibrium paths of the buckled beam and thus are able to provide insight into deformation problems. Based on the exact solutions obtained herein, the effects of various factors such as porosity distribution pattern, porosity coefficient and boundary conditions on postbuckling behavior of graded porous beams have been investigated.

Buckling analysis of two-directionally porous beam

In this paper, buckling analysis of two-directionally porous beam is conducted. Based on the available results of Young's modulus and mass density via Gaussian random field theory, a new two-directionally porous beam model is developed. With the help of Euler–Bernoulli beam theory and minimum total potential energy principle, the equilibrium equations for nonlinear and linear buckling are derived. The numerical solutions of critical buckling loads for different porosity distribution patterns can be obtained by generalized differential quadrature method. The final numerical results exhibit that more porosities near the middle surface or the two edges of beam can lead to a larger critical buckling load when the same total volume fraction of porosity is in different porosity distribution patterns. The effect of porosity distribution in thickness direction is more dominated on the critical buckling load than that of the axial porosity distribution. Moreover, the critical buckling load becomes more sensitive to aspect ratio of beam and total volume fraction of the porosity when increasing mode number. The critical buckling load of two-directionally porous beam depends not only on bending coefficient (like the one-directionally porous beam), but also on first and second derivatives of the bending coefficient.

Mechanical and microstructural properties of cordierite-bonded porous SiC ceramics processed by infiltration technique using various pore formers

Cordierite-bonded porous SiC ceramics were prepared by air sintering of cordierite sol infiltrated porous powder compacts of SiC with graphite and polymer microbeads as pore-forming agents. The effect of sintering temperature, type of pore former and its morphology on microstructure, mechanical strength, phase composition, porosity and pore size distribution pattern of porous SiC ceramics were investigated. Depending on type and size of pore former, the average pore diameter, porosities and flexural strength of the final ceramics sintered at 1400 °C varied in the range of ~ 7.6 to 10.1 µm, 34–49 vol% and 34–15 MPa, respectively. The strength–porosity relationship was explained by the minimum solid area (MSA) model. After mechanical stress was applied to the porous SiC ceramics, microstructures of fracture surface appeared without affecting dense struts of thickness ~ 2 to 10 µm showing restriction in crack propagation through interfacial zone of SiC particles. The effect of corrosion on oxide bond phases was investigated in strong acid and basic salt medium at 90 °C. The residual mechanical strength, SEM micrographs and EDX analyses were conducted on the corroded samples and explained the corrosion mechanisms.

A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation

A novel quasi-3D hyperbolic theory is presented for the free vibration analysis of functionally graded (FG) porous plates resting on elastic foundations by dividing transverse displacement into bending, shear, and thickness stretching parts. The elastic foundation can be chosen as Winkler, Pasternak or Kerr foundation. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. A Galerkin method is developed for the solution of the eigenvalue problem of the presented quasi-3D hyperbolic plate model. The presented quasi-3D hyperbolic theory is simple and easy to implement since it uses only five-unknown variables to determine fourfold coupled (axial-shear-bending-stretching) vibration responses. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, stiffness of foundation parameters, mode numbers, and geometry on the natural frequencies of imperfect FG plates.

Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets

This paper studies free vibration and elastic buckling of functionally graded porous nanocomposite beams where the internal pores and graphene platelets (GPLs) are layer-wise distributed in the matrix either uniformly or non-uniformly according to three different patterns. A multilayer beam model is proposed with material parameters varying across layers to achieve graded distributions in both porosity and nanofillers. Mechanical properties of closed-cell cellular solids under Gaussian Random Field scheme are used to determine the variation of Poisson's ratio and the relationship between porosity coefficients and mass density. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. Theoretical formulations are based on Timoshenko beam theory and Ritz method is employed to obtain the dimensionless fundamental natural frequency and critical buckling load of porous nanocomposite beams. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, geometry and size of GPL reinforcements on the free vibration and buckling behaviors of the nanocomposite beam with different metal matrixes and porosity coefficients. The results indicate that the effective stiffness of the porous nanocomposite beam can be best improved when both porosity distribution and GPL dispersion pattern are non-uniform but symmetric.