Porosity Distribution Pattern Research Articles

Hygrothermomechanical loading-induced vibration study of multilayer piezoelectric nanoplates with functionally graded porous cores resting on a variable viscoelastic substrate

Harnessing vibrations in multifunctional nanostructured plates is pivotal to next-gen microsystems but necessitates understanding scale effects under multifield loading. Investigated in this work are the forced and unforced vibrations of multilayered piezoelectric nanoplates supported on a variable viscoelastic medium and loaded hygrothermo-electromechanically with functionally graded porous (FGP) cores. The viscoelastic foundation is supposed to demonstrate non-linear changes in both stiffness and damping characteristics in the x-coordinate direction. The goal is to improve the accuracy of the results by using the nonlocal strain gradient theory (NSGT) and the third-order shear deformation assumption (TSDA), which include the effects of hardening and softening materials. The FGP core layer considers four states of porosity distribution patterns. These porosity distributions are expected to change in both the in-plane and thickness directions. The governing partial differential equations resulting from Hamilton's principle can be reduced to a system of algebraic equations by applying the Galerkin method. The parametric studies evaluate the effects of several factors, such as the initial electric voltage, viscoelastic medium parameters, moisture rise, temperature changes, porosity distributions, FG index, nonlocal and strain gradient features, and boundary conditions, on the vibration response. The novelty lies in the incorporation of advanced theories, such as the NSGT and TSDT, which capture size-dependent effects and material hardening/softening phenomena. Additionally, the consideration of four distinct porosity distribution patterns in the FGP core layer provides insights into the influence of porosity gradients on the dynamic response. The proposed model can guide the design and optimization of multifunctional nanostructured plates for applications in next-generation microsystems, energy harvesting devices, and smart structures.

Peridynamic differential operator for stress analysis of imperfect functionally graded porous sandwich beams based on refined zigzag theory

This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the uneven type porosity distribution pattern.

On the vibration responses of orthotropic laminated cylindrical panels with non-uniform porosity distributions using higher-order shear deformation theory

The present study investigates free vibration analysis of cylindrical panels made of porous orthotropic layers. Porous material properties are modeled using uniform and two non-uniform porosity distribution patterns through the thickness. The theoretical formulations are expressed based on the higher-order shear deformation theory. The equations of motion of laminated cylindrical panels are established by performing Hamilton’s principle. These fundamental partial differential equations are solved analytically for the laminated cylindrical panels, which are simply supported on all edges. Galerkin’s solution procedure is applied to obtain the natural frequency equation. The natural frequencies are compared to results in the literature to verify the obtained frequency equation. Afterward, novel parametric studies are developed to discuss the influence of porosity parameters, porosity distribution patterns, geometrical parameters, orthotropy, and lamination sequences on the free vibration response of porous laminated cylindrical panels.

Deterioration of volcanic tuffs from rock dwellings in Brhlovce (Slovakia) induced by freeze-thaw cycling studied by non-destructive tests and µCT visualization

The aim of this paper is to evaluate the effect of freeze-thaw-induced weathering of volcanic tuffs from the rock dwellings in the village of Brhlovce (Slovakia) based on a non-destructive and experimental study of tuff pore space properties. Traditional techniques for characterization of the porosity and pore size distribution and new experimental techniques like spontaneous imbibition (pore interconnection) or indicative rock pore structure method (pore size distribution) were compared with pore network models acquired by X-ray computed microtomography before and after freeze-thaw cycling in a custom-built thermodilatometer VLAP04. The results offer insight into how frost weathering altered the pore network of volcanic tuffs. Brhlovce tuffs are highly susceptible to frost damage due to their high porosity, pore interconnectivity, and bimodal pore size distribution pattern, where nanometric-sized micropores predominate over larger micrometric-sized capillary pores. Poromechanical principles were applied to confirm that ice crystallization initiates in well-connected micropores with a corresponding crystallization pressure below 10 MPa. After undergoing 100 freeze-thaw cycles with temperature oscillations ranging from − 10 to 10 °C, there was a significant increase in total porosity, pore interconnectivity, and rock permeability. Additionally, the pore size distribution was altered. These parameters influence the transport of fluids and the moisture regime in rock masses, which can serve as a precursor to physical and chemical weathering processes

Nonlinear deformations of size-dependent porous functionally graded plates in a temperature field

In this paper, the Variational Iteration Method (VIM) or Extended Kantorovich Method (EKM) is formulated for the first time for flexible porous functionally graded (PFGM) plates with different boundary conditions and geometric nonlinearity according to the theory of Theodore von Karman. Its accuracy and efficiency are demonstrated. The plate is subjected to a uniform transversal load and temperature field. The displacement field of the plate is approximated based on the classical plate theory (CTP) or Kirchhoff's plate theory. The governing equations are derived using Hamilton's principle. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The material properties vary with thickness and are temperature dependent. Four porosity distribution patterns are considered in this study. Several examples are solved to demonstrate the proposed algorithm. The results obtained are compared with solutions obtained by the Bubnov-Galerkin Method (BGM) in higher approximations, the Finite Difference Method (FDM) of second order accuracy, as well as with results obtained by the Finite Element Method (FEM) of other authors. The results include an analysis of the effect of size dependent parameters, porosity type pattern, porosity index, functionally graded index, temperature field and different types of boundary conditions on the stress–strain state and bending deflection of plates.

The assessment of electric voltage influence on vibrational behavior of intelligent sandwich plates with GO-reinforced metal foam core and piezoelectric actuator face sheets

In this research, it is tried to study the effect of the external electric voltage on the vibrational behavior of a smart sandwich plate made of graphene oxide-strengthened metal foam nanocomposite core and two piezoelectric face sheets for the first time. The sandwich plate is modeled utilizing first-order shear deformation theory. The effective material properties of the core layer are estimated with the aim of the blend of Halpin-Tsai micromechanical model and rule of the mixture while considering different graded graphene oxide distribution patterns. Additionally, various porosity distributions are regarded in the metal matrix of the core layer. The partial differential equations of motion are derived using Hamilton’s principle and the derived governing equations are solved through Navier’s solution. To perform an accurate verification, the obtained results are compared with different literature investigations. Afterward, the influence of various important variants including external electric voltage, aspect ratio of plate, core to face sheet thickness ratio, different porosity distribution patterns, porosity coefficient, nanofillers weight fraction, and various distribution patterns of graphene oxides on the dimensionless frequency of smart sandwich plate in the framework of a group of tables and figures.

Asymmetric two-dimensional poroelastic analysis of heterogeneous smart discs considering hygrothermal loading

The objective of this study is to examine through the finite element method the impacts of employing two-dimensional (2D) properties grading on the behaviors of piezoelectric sensors/actuators due to their significance. These structures are modeled as variable thickness discs and are assumed to be exposed to simultaneous asymmetric loading conditions (thermal, hygral, electrical, and mechanical loads). Results demonstrate that the 2D grading is superior compared to the conventional one-dimensional grading for reducing the von Mises stress. The reduction reached, for instance, 8.3% allowing further increase of loading and/or safety. Also, the change of the displacement is varied between −4.5% and 31% depending on the considered grading pattern, and thus can be controlled to a desired value which helps to improve the sensing and actuating functionality for certain requirements. The study also examines the effects of porosity, and the results are compared to nonporous discs. Reductions of the maximum compressive tangential stress and von Mises stress reached 79.75% and 33.6%, respectively at specific porosity distribution patterns and volume fractions. These findings have significant implications for the manufacturing of smart structures, enabling them to operate in severe working conditions with better sensing and actuating capabilities than previously possible.

Stability of porous orthotropic laminated cylindrical panels subjected to linearly varying edge compression based on shear deformation theory

This study investigates the stability characteristics of porous orthotropic laminated cylindrical panels under the influence of linearly varying edge compression, employing the higher-order shear deformation theory. Four porosity distribution patterns along the laminate thickness are considered to model porous material properties. Theoretical formulations and numerical methods are utilized to evaluate critical buckling loads and mode shapes. The effects of parameters such as porosity, distribution patterns, orthotropy, radius-to-side ratio, aspect ratio, and side-to-thickness ratio on stability characteristics are examined. The research contributes to composite materials and structural stability analysis with potential aerospace, marine, and civil engineering applications.

Simulation of thermo-hydro-mechanical coupled heat extraction process of geothermal reservoir under varied geological conditions with CO2 as working fluid

The use of supercritical CO2 as a working fluid instead of H2O in an enhanced geothermal system (EGS) for extracting heat from hot dry rock geothermal resources has garnered significant attention. The objective of this study is to investigate how different geological conditions affect the heat extraction behavior of supercritical CO2 and to reveal the efficiency differences between supercritical CO2 and H2O as working fluids in each geological scenario, providing deeper insight into reservoir management. A series of 3D coupled thermo-hydro-mechanical models were established. Besides, the impact of initial temperature, pressure, porosity, permeability, and stress field on the heat extraction of EGS with different working fluids are also analyzed and compared. Results indicate that, at the same circulating volumetric flow rate, CO2-EGS generally exhibits an earlier thermal breakthrough time, lower net energy production, and reduced heat extraction rate compared to H2O-EGS. Taking into account the extended reservoir lifespan and the relatively small pressure difference between injector and producer in CO2-EGS, CO2 is a more suitable working fluid than H2O. Furthermore, the performance of CO2-EGS is primarily affected by the initial temperature, porosity, and permeability distribution pattern, rather than the initial pressure. On the one hand, a reservoir with low initial temperature, porosity and homogeneous permeability were found to be more conducive to enhancing the average net energy production. On the other hand, reservoir vertical permeability anisotropy can have a more profound impact on CO2-EGS efficiency compared to horizontal y permeability anisotropy. Additionally, this study also examined the impact of in situ stress field. It was found that, compared to H2O-EGS, both isotropic and anisotropic in situ stress fields have a weak effect on the performance of CO2-EGS, which can be attributed to the similarity of the channelization degree of the flow field under different stress conditions.

Bending analysis of FGSP nanoplate resting on elastic foundation by using nonlocal quasi-3D theory

In this paper, the bending response of a functionally graded saturated porous (FGSP) nanoplate resting on the Pasternak elastic foundation is analyzed within the framework of quasi-3D higher-order shear deformation theory (quasi-3D HSDT) for the first time. The material properties are presumed to change gradually along the thickness direction following three patterns of porosity distribution: uniform, non-uniform symmetric, and asymmetric. The theory of poroelasticity developed by Biot is utilized in modeling the stress-strain relationships for the saturated condition. Moreover, the nanoscale effects of the structures are considered by Eringen's nonlocal elasticity theory. The governing equations are derived by using the principle of minimum potential energy according to quasi-3D HSDT, which ensures transverse shear stress-free on the upper and lower surfaces of the nanoplate. Based on the obtained closed-form solution, the impacts of the porosity distribution patterns, porosity coefficient, Skempton coefficient, geometrical parameters, elastic foundation, and nonlocal parameters on the bending behavior have been explored. According to the findings, when the pores are saturated by the fluid, the plate stiffness increases. Additionally, increasing the values of the nonlocal parameter for FGSP nanoplates leads to an increase in deflection and stresses. Finally, the present study quantitatively reveals the size-dependent effects of a saturated porous medium.

Axisymmetric thermal vibration analysis of graded porous circular plates based on physical neutral surface and Reddy’s third-order shear theory

In this article, the free vibration of functionally graded porous (FGP) circular plate with various boundary conditions are investigated by means of the differential quadrature method (DQM) based on Reddy’s theory. Performance of the materials varies continuously in the whole thickness and two cosine forms of nonuniform porosity distribution along its thickness are considered. Hamilton’s principle is adopted to derive the governing equation of the system, which effectively considers the effects of thermal stress. It is worth noting that due to the introduction of physics neutral surface, reducing stretching-bending coupling effect, so the complex governing equations have been appropriately simplified. Then, using the DQ method, the natural frequencies of free vibration of FGP circular plates subjected to thermal environments with various boundary conditions were obtained. Convergence and comparative research are performed to prove the convergence, reliability, and accuracy of the DQ method. The effects of various factors such as porosity coefficient, porosity distribution pattern, temperature rise, thickness-diameter ratio, and boundary conditions on the natural frequencies are discussed in detail.

Nonlocal strain gradient-based isogeometric analysis of graphene platelets-reinforced functionally graded triply periodic minimal surface nanoplates

Recent developments in additive manufacturing (AM) technologies have empowered the design and fabrication of intricate bioinspired engineering structures at the nano/micro scale. However, mathematical modeling and computation of these structures are still challenging. The main target of this study is to address an efficient computational approach for predicting the mechanical behavior of graphene platelets (GPLs)-reinforced functionally graded triply periodic minimal surface (FG-TPMS) nanoplates. The computational model integrates both nonlocal elasticity and strain gradient effects into the NURBS-based isogeometric analysis of these small-scale structures. We establish advanced nanoplate models by combining three sheet-based TPMS architectures with two new porosity distribution patterns and three distribution patterns of GPLs across the thickness direction. Moreover, the present work makes a pioneering attempt to elucidate how the stiffness-hardening and stiffness-softening mechanisms influence FG-TPMS nanoplates reinforced with GPLs. Compared with two common cellular solids, the superiority of TPMS architectures' mechanical performance is demonstrated. Among all, P and IWP TPMS types along with symmetric porosity and GPLs distributions exhibit outstanding behaviors under static bending, free vibration, and dynamic instability. Furthermore, we conducted a performance analysis for the first time, showcasing the superior capabilities of TPMS architectures under dynamic in-plane compressive loads, especially when compared to isotropic plates of equal weight. The findings of this study greatly enhance our understanding of the intricate mechanical responses of GPLs-reinforced TPMS architectures at the small-scale level, contributing to future interdisciplinary applications.

On the selected problems of time-dependent dynamics of composite truncated conical shells-like aerospace structures

In this paper, the nonlinear dynamic responses of ring-stiffened truncated conical sandwich shells-like aerospace structures fabricated by perfectly bonded graphene platelets (GPLs) reinforced composite porous core and face sheets (GPLRC-PC-FS) under asymmetric internal ring-shaped moving load are investigated. The sandwich shells have edge point supports, which are simulated using the translational and rotational artificial springs. In addition to the open cell porosities, closed cells are also considered and analyzed. The spatially discretized nonlinear motion equations are derived based on the first-order shear deformation theory (FSDT) under the von Kármán geometric nonlinearity assumptions using the Ritz method with Chebyshev polynomials as its admissible basis functions. Then, Newmark's time integration scheme along with the Newton–Raphson method is employed to obtain the shell dynamic responses. After demonstrating the robustness and accuracy of the approach, the influence of rings number, their size and arrangement, core porosity distribution and structure, face sheets, GPLs parameters, moving load velocity and boundary conditions on the shell responses are studied. The results show that the shell dynamic behaviors are significantly affected by porosity, but almost are independent of the type of porosity distribution pattern and its structure (open and closed cell porosities). It is shown that the shell deflection can be minimized by suitably choosing the number of rings, their dimensions and arrangement. Moreover, the nonlinear behaviors of the shells have a significant correlation with the number of point supports and by adjusting the support stiffnesses, the nonlinear dynamic responses of the shells can be reduced.

Vibration analysis of porous orthotropic cylindrical panels resting on elastic foundations based on shear deformation theory

Cylindrical panels are one of the most essential structural members of engineering structures, with mechanical, civil, aeronautical, and marine engineering applications. They are subjected to a wide range of vibrational loads. This article presents a novel higher-order porosity distribution and a free vibration analysis for porous orthotropic cylindrical panels resting on elastic foundations under higher-order shear deformation theory. It is assumed that cylindrical panels are composed of porous materials with uniformly and non-uniformly distributed pores. The porous panels' material properties are distributed in the thickness direction using specific functions. The equations of motion are derived using Hamilton's principle based on trigonometrical shear deformation theory and solved by performing the Galerkin solution procedure with simply supported edge conditions. The accuracy of the obtained natural frequency equation is confirmed by comparing the results to those of previously published in literature. Under comprehensive parametric studies, the influence of porosity coefficient, porosity distribution patterns, radius-to-curve length ratio, orthotropy, and stiffness of elastic foundation parameters on the free vibration response of porous orthotropic cylindrical panels are discussed in detail.

Out-of-plane moving load response and vibrational behavior of sandwich curved beams with GPLRC face sheets and porous core

As a first endeavor, the out-of-plane free vibrational behaviors and moving load responses of sandwich curved beams with graphene platelets reinforced composite face sheets and porous core (GPLRC-FS-PC) are carried out. The governing equations are derived based on the first-order shear deformation theory (FSDT) using Hamilton’s principle, which are discretized by employing the differential quadrature method (DQM) and Newmark’s method in the spatial and time domains, respectively. To simulate the moving load using the DQM, the Heaviside function approach is utilized. The effective elastic properties of face sheets are estimated using Halpin-Tsai micromechanical model. The approach is validated by presenting convergence studies and accuracy verification followed by parametric studies. The numerical results indicate that by adding little amount of graphene platelets (GPLs) into the face sheets and core layer, the fundamental natural frequency and the displacement amplitudes under moving load significantly increases and decreases, respectively, regardless of the beam boundary conditions. It is revealed that the GPLs distribution patterns in face sheets and the core porosity distribution patterns affect the critical load velocities of the GPLRC-FS-PC sandwich curved beams. Also, it is shown that the frequency parameters strongly depend on the face sheet to core thickness ratio.

Continuous Wavelet Transformation to Quantify small-scale Cycles of Petrophysical Properties; a New Approach Applied in a Potential Disposal Repository of Nuclear Waste, SW Hungary

Continuous Wavelet Transformation (CWT) was applied to study the small-scale repetitive oscillations of porosity distribution patterns in a 5 m silty-claystone core sample of the Boda Claystone Formation. We handled the fluctuations in voxel porosity averages over unequal depth distributions as signals over uneven time intervals. The strength of wavelet analysis lies in the ability to study the fluctuation of a signal in detail, i.e., the wavelet transforms permit automatic localization of the cyclic attributes' sequences both in time (the depth domain) and according to their frequency (the frequency domain). Thereupon, three main frequency branches (cycles) were discerned: small scale (5, 6.67, and 11 cm), intermediate scale (20, 30 cm), and large scale (66.67 cm). Depending on the CWT coefficients magnitude plot, we were able to detect the developments of porosity oscillation according to the depth variable. Thus, small-scale cycles were seen throughout the core sample., the intermediate-scale cycles were strong in the upper parts of the core sample and dwindled toward greater depths, and the large cycle was predominant in the lower part of the core sample. The cross-correlation of the wavelet coefficients of porosity and rock-forming components allows a detailed study of the inter-dependence of such parameters as their relationship changes over time. The distinct peaks at zero lag indicates that the measured wavelet coefficient series were contemporaneously correlated; their strong positive correlations suggest that both examined series respond similarly and simultaneously to other exogenous factors. The results emphasize that cyclical porosity fluctuations at all scales would concern three main factors; sediment deposition, diagenetic processes, and structural deformation (i.e., convolute laminations).

Free Vibration and Dynamic Analysis on Free-Constrained Layer of Graphene Based on Composite Conical Shell via Jacobi–Ritz Method

Excessive vibration has always been a serious problem for conical shell structures, while the application of the graphene-based free-constrained layer (GFCL) based on carbon fiber-reinforced composite (CFRC) structure is a novel way to improve structural performance. An analytical model for vibration and dynamic characteristics of the GFCL-CFRC conical shell resting on the Winkler–Pasternak elastic foundation with arbitrary boundary conditions is constructed, and four types of GFCL porosity distribution and GFCL dispersion pattern are considered in this model. The multi-segment technique and virtual spring technique are utilized to simulate arbitrary boundary conditions. Then, the first-order shear deformation theory (FSDT) and Hamilton’s principle are employed to obtain the motion equation of the GFCL-CFRC conical shell, and the motion equation of the GFCL-CFRC conical shell is solved by the Ritz method. In conclusion, the dispersion mode of GFCL, thickness ratio of GFCL, and fiber angle have influence on the dynamic performance. With a reasonable design, the dynamic performance of the GFCL-CFRC conical shell can be further improved.

A size-dependent quasi-3D model for bending and buckling of porous functionally graded curved nanobeam

In this work, we provide an analysis of the bending and buckling properties of functionally graded (FG) nanobeams with trigonometric function-dependent porosity distribution. Herein, a high-order curved nanobeam model considering both shear deformations and thickness stretching effect is established. Two-phase local/nonlocal stress-driven gradient theory is utilized to capture small-scale effects. Hamilton's principle is adopted to obtain the governing equation and boundary conditions, and the analytical solutions, such as exact formulas for lateral displacement and critical buckling load are obtained by employing Navier's method for simply supported boundary conditions. Furthermore, the effects of local volume fraction, nonlocal parameter, material length scale parameter, shear deformation, material distribution, and porosity distribution pattern in stress-driven models are analyzed in detail. The parametric studies indicate that the thickness stretching effect has a different influence on bending and buckling. In addition, the thickness stretching effect and the opening angle show different coupling mechanisms during bending and buckling. On the other hand, the higher-order buckling mode leads to a more significant scale effect and thickness tensile effect, but reduces the influence of the opening angle. Finally, we find that due to the coupling effect between the pore distribution pattern and the orientation bias of the FG nanobeam, the variation of the material gradient index leads to a different order of the dimensionless critical buckling loads predicted by the three pore distributions.

Microstructure design and mechanical properties of 3D printed graded lattice sandwich structures with tailored porosity

A novel sandwich structure with graded lattice core was proposed, which achieves gradient design by means of tailored porosity. An analytical model was developed to determine the compression response of graded lattice cores of sandwich structures. To validate the analytical model, two types of graded lattice sandwich structures were fabricated via additive manufacturing and compression tests were performed. The analytical predictions were in good agreement with the experimental results. It was found that the effective Young's modulus of graded lattice sandwich structures is independent of porosity distribution pattern, but dependent on both porosity parameter and power law index. Meanwhile, as the porosity parameter increases, both yield stress and critical buckling stress decrease. The structure with SCI porosity distribution pattern exhibits superior load-bearing capabilities in graded lattice sandwich structures, indicating that desirable mechanical properties can be achieved through controlled structural porosity.

Statistical analysis and Neural Network Modeling of functionally graded porous nanobeams vibration in an elastic medium by considering the surface effects

The natural frequency of a clamped–clamped functionally graded porous (FGP) nanobeam is predicted in this study. Material distribution is considered based on monotonous, symmetric, and non-symmetric patterns in the thickness direction. This paper deals with governing equations of nanobeams based on third-order shear deformation beam theory in conjunction with nonlocal strain gradient theory (NSGT) and surface effects. Artificial neural network (ANN) is utilized to predict the effect of eight parameters including temperature gradient, residual surface stress, porosity distribution pattern, porosity parameter, nonlocal and material length scale parameters, and elastic and shear coefficients of Pasternak foundation on the fundamental frequency of FGP nanobeam. Different training methods are selected to simulate input and output dependency. Results show that the dependency of the natural frequency is inverse to the temperature gradient and nonlocal parameter in the sense that increasing these factors will decrease the natural frequency. Also, increasing the material length scale parameter grows the effect of the nonlocal parameter. Residual surface stress, material length scale, and Pasternak foundation parameters have a direct effect on the output and among them; the material length scale parameter has a more noticeable effect. Finally, it was found that by increasing the porosity parameter value, the diversity of natural frequency levels up drastically