• Computers and Concrete
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• v.32 no.1
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• pp.75-85
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• 2023

This work utilizes simplified higher-order shear deformation beam theory (HSDBT) to investigate the vibration response for functionally graded carbon nanotube-reinforced composite (CNTRC) beam. Novel to this work, single-walled carbon nanotubes (SWCNTs) are distributed and aligned in a matrix of polymer throughout the beam, resting on a viscoelastic foundation. Four un-similar patterns of reinforcement distribution functions are investigated for the CNTRC beam. Porosity is another consideration taken into account due to its significant effect on functionally graded materials (FGMs) properties. Three types of uneven porosity distributions are studied in this study. The damping coefficient and Winkler's and Pasternak's parameters are considered in investigating the viscosity effect on the foundation. Moreover, the impact of different parameters on the vibration of the CNTRC beam supported by a viscoelastic foundation is discussed. A comparison to other works is made to validate numerical results in addition to analytical discussions. The findings indicate that incorporating a damping coefficient can improve the vibration performance, especially when the spring constant factors are raised. Additionally, it has been noted that the fundamental frequency of a beam increases as the porosity coefficient increases, indicating that porosity may have a significant impact on the vibrational characteristics of beams.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.461-479
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• 2022

A finite element method analysis framework is introduced for the free vibration analyses of functionally graded porous beam structures by employing 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. A comprehensive parametric study is carried out, with a particular focus on the effects of various structural parameters such as the dispersion patterns of GPL reinforcements and porosity, thickness ratio, boundary conditions, nonlocal scale parameter and strain gradient parameters. The results indicate that porosity distribution and GPL pattern have significant effects on the response of the nanocomposite beams.

• Steel and Composite Structures
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• v.36 no.1
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• pp.47-62
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• 2020

In this study, free vibration behavior of trapezoidal sandwich plates with porous core and two graphene platelets (GPLs) reinforced nanocomposite outer layers are presented. The distribution of pores and GPLs are supposed to be functionally graded (FG) along the thickness of core and nanocomposite layers, respectively. The effective Young's modulus of the GPL-reinforced (GPLR) nanocomposite layers is determined using the modified Halpin-Tsai micromechanics model, while the Poisson's ratio and density are computed by the rule of mixtures. The FSDT plate theory is utilized to establish governing partial differential equations and boundary conditions (B.C.s) for trapezoidal plate. The governing equations together with related B.C.s are discretized using a mapping- generalized differential quadrature (GDQ) method in the spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained by GDQ method. Validity of current study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns of two faces through the thickness, porosity coefficient and distribution of porosity on natural frequencies characteristics. New results show the importance of this permeates on vibrational characteristics of porous/GPLR nanocomposite plates. Finally, the influences of B.C.s and dimension as well as the plate geometry such as face to core thickness ratio on the vibration behaviors of the trapezoidal plates are discussed.

• Structural Engineering and Mechanics
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• v.91 no.6
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• pp.551-565
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• 2024

This study presents a methodical investigation into improving structural designs through the analytical examination of the dynamic behavior of functionally graded plates (FGPs) resting on viscoelastic foundations. By employing a four variable first-order shear deformation theory, the study computes non-dimensional frequencies for a variety of porous FGPs with diverse graded patterns and porosity distributions. Different gradient patterns of the plates are considered, and three distinct functions-sigmoid (S-FGM), exponential (E-FGM), and power-law (P-FGM)-are utilized to assess material performance in specific directions. The equations of motion are derived and solved using both Navier's method and Hamilton's principle. Analytical solutions for vibration frequency are provided to validate the proposed methodology against existing literature. Furthermore, a comprehensive parametric analysis is conducted, taking into account various factors such as ceramic material, porosity distribution, gradient index, length-to-thickness ratio, gradient pattern, and damping coefficient. The findings suggest that enhancing the damping coefficient of the viscoelastic foundation can significantly improve the free-vibrational response of functionally graded material plates.

• Journal of the Korean Ceramic Society
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• v.56 no.4
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• pp.350-353
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• 2019

Porous alumina ceramics with addition of 0, 5, 10, 15, and 20 wt% Al(H₂PO₄)₃ were sintered at 1300, 1350, and 1400℃. The effects of the Al(H₂PO₄)₃ addition on crystal phases, water absorption, open porosity, pore size distribution, microstructures, and flexural strength were studied extensively. The experimental results revealed that only characteristic peaks of corundum were indexed in the XRD patterns of the as-prepared porous ceramics. The water absorption and open porosity of the porous Al₂O₃ ceramics increased remarkably with an increase in Al(H₂PO₄)₃ addition. The flexural strength first increased to a maximum value when 5 wt% Al(H₂PO₄)₃ was added and then decreased as additional Al(H₂PO₄)₃ was further added. SEM images showed that the average Al₂O₃ grain size in the porous ceramics changed in an opposite way as the flexural strength. The porous Al₂O₃ ceramics with 10 wt% Al(H₂PO₄)₃ addition exhibited comparable flexural strength to the ceramics without Al(H₂PO₄)₃ addition, although the latter had much higher porosity.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.419-432
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• 2023

This paper studies the effects of porosity distributions on buckling and post-buckling behaviors of a functionally graded saturated porous (FGSP) circular plate. The plate is under the uniformly distributed radial loading and simply supported and clamped boundary conditions. Pores are saturated with compressible fluid (e.g., gases) that cannot escape from the porous solid. Elastic modulus is assumed to vary continuously through the thickness according to three different functions corresponding to three different cases of porosity distributions, including monotonous, symmetric, and asymmetric cases. Governing equations are derived utilizing the classical plate theory and Sanders nonlinear strain-displacement relations, and they are solved numerically via shooting method. Results are verified with the known results in the literature. The obtained results for the monotonous and symmetric cases with the asymmetric case presented in the literature are shown in comparative figures. Effects of the poroelastic material parameters, boundary conditions, and thickness change on the post-buckling behavior of the plate are discussed in details. The results reveal that buckling and post-buckling behaviors of the plate in the monotonous and symmetric cases differ from the asymmetric case, especially in small deflections, that asymmetric distribution of elastic moduli can be the cause.

• Structural Engineering and Mechanics
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• v.73 no.2
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• pp.191-207
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• 2020

This study aims at investigating the size-dependent free vibration of porous nanoplates when exposed to hygrothermal environment and rested on Kerr foundation. Based on the modified power-law model, material properties of porous functionally graded (FG) nanoplates are supposed to change continuously along the thickness direction. The generalized nonlocal strain gradient elasticity theory incorporating three scale factors (i.e. lower- and higher-order nonlocal parameters, strain gradient length scale parameter), is employed to expand the assumption of second shear deformation theory (SSDT) for considering the small size effect on plates. The governing equations are obtained based on Hamilton's principle and then the equations are solved using an analytical method. The elastic Kerr foundation, as a highly effected foundation type, is adopted to capture the foundation effects. Three different patterns of porosity (namely, even, uneven and logarithmic-uneven porosities) are also considered to fill some gaps of porosity impact. A comparative study is given by using various structural models to show the effect of material composition, porosity distribution, temperature and moisture differences, size dependency and elastic Kerr foundation on the size-dependent free vibration of porous nanoplates. Results show a significant change in higher-order frequencies due to small scale parameters, which could be due to the size effect mechanisms. Furthermore, Porosities inside of the material properties often present a stiffness softening effect on the vibration frequency of FG nanoplates.

• Computers and Concrete
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• v.34 no.2
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• pp.179-193
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• 2024

The bending and buckling effect for carbon nanotube-reinforced composite (CNTRC) beams can be evaluated by developing the theory of third shear deformation (TSDT). This study examines beams supported by viscoelastic foundations, where single-walled carbon nanotubes (SWCNTs) are dispersed and oriented within a polymer matrix. Four patterns of reinforcement are used for the CNTRC beams. The rule of mixtures is assessed for the material properties of CNTRC beams. The effective functionally graded materials (FGM) properties are studied by considering three different uneven distribution types of porosity. The damping coefficient is considered to investigate the viscosity effect on the foundation in addition to Winkler's and Pasternak's parameters. The accuracy of the current theory is inspected with multiple comparison works. Moreover, the effects of different beam parameters on the CNTRC beam bending and buckling over a viscoelastic foundation are discussed. The results demonstrated that the O-beam is the weakest type of CNTRC beam to resist buckling and flexure loads, whereas the X-beam is the strongest. Moreover, it is indicated that the presence of porosity in the beams decreases the stiffness and increases deflection. In comparison, the deflection was reduced in the presence of a viscoelastic foundation.

• Journal of the Korea Institute of Building Construction
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• v.24 no.5
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• pp.541-552
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• 2024

This study introduces a new analytical model known as the Cellular Automaton Method(CAM) designed to predict the degree of deterioration in concrete, taking into account its complex pore structure. The CAM model assesses the impacts of moisture migration, driven by capillary action and pressure differentials at the gas-liquid interface, which are influenced by the distribution of pores. It also evaluates how porosity and diffusion coefficients affect the penetration of chloride ions. The model's application revealed distinct moisture movement patterns in concrete structures, distinguishing between those with porosity levels below and above 40 percent. Additionally, it facilitated a comparison and analysis of chloride ion diffusion phenomena, based on diffusion coefficients in areas penetrated by moisture, against results obtained from the Finite Element Method(FEM). The comparison showed a maximum deviation of only 0.989 percent between the predicted outcomes of the FEM and CAM, demonstrating substantial agreement and validating CAM's efficacy in simulating the diffusion processes of chloride ions within concrete under actual salt damage conditions. Thus, CAM proves to be a reliable tool for modeling and anticipating deterioration in concrete structures exposed to saline environments.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.291-309
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• 2023

This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C⁰ and C¹ continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.