Transient Thermal Stresses in FG Porous Rotating Truncated Cones Reinforced by Graphene Platelets

Babaei, Masoud; Kiarasi, Faraz; Asemi, Kamran; Dimitri, Rossana; Tornabene, Francesco

doi:10.3390/app12083932

Cited by 21 publications

(5 citation statements)

References 62 publications

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“…Although we herein have developed the RDITGCNFE format for the unsaturated soil flow problem and simulated the moisture content of two types of soil parameters in Table 1, the method in this paper can simulate the moisture content of other types of soil parameters in Table 1 and can generalize to more complicated unsteady nonlinear PDEs, even actual engineering and industry problems, such as the axisymmetric rotating truncated cone made of functionally graded porous materials reinforced by graphene platelets under a thermal loading in [41]. Hence, the RDITGCNFE format has very capacious applied space.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

A New Reduced-Dimension Iteration Two-Grid Crank–Nicolson Finite-Element Method for Unsaturated Soil Water Flow Problem

Hou,

Teng,

Luo

et al. 2024

Mathematics

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The main objective of this paper is to reduce the dimensionality of unknown coefficient vectors of finite-element (FE) solutions in two-grid (CN) FE (TGCNFE) format for the nonlinear unsaturated soil water flow problem by using a proper orthogonal decomposition (POD) and to design a new reduced-dimension iteration TGCNFE (RDITGCNFE). For this objective, a new time semi-discrete CN (TSDCN) scheme for the nonlinear unsaturated soil water flow problem is first designed and the existence, stability, and error estimates of TSDCN solutions are demonstrated. Subsequently, a new TGCNFE format for the nonlinear unsaturated soil water flow problem is designed and the existence, unconditional stability, and error estimates of TGCNFE solutions are demonstrated. Next, a new RDITGCNFE format with the same FE basis functions as the TGCNFE format is built by the POD method and the existence, unconditional stability, and error estimates of RDITGCNFE solutions are discussed. Ultimately, the rightness of theory results and the superiority of the RDITGCNFE format are verified by two sets of numerical tests. It is worth noting that the RDITGCNFE format differs completely from all previous reduced-dimension methods, including the authors’ previous works. Therefore, the study of this paper can not only provide a new theoretical method for the dimensionality reduction of numerical models for nonlinear problems but also provide an algorithm implementation technology for the numerical simulation of practical engineering problems.

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Section: Conclusion and Discussionmentioning

confidence: 99%

A New Reduced-Dimension Iteration Two-Grid Crank–Nicolson Finite-Element Method for Unsaturated Soil Water Flow Problem

Hou,

Teng,

Luo

et al. 2024

Mathematics

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“…Based on the rule of mixtures, the mass density and Poisson’s ratio of nanocomposite materials are defined as [ 61 , 62 , 63 ]

whereas

refers to the associated shear modulus. The volumetric content of GPLs,

, is assumed to vary throughout the spherical cap’s thickness, having five different dispersion patterns (see Figure 2 ):

where

and

denote the upper limits of

; and subscript i = 1, 2 or 3 refers to various porosity distributions within each pattern.…”

Section: Theoretical Problemmentioning

confidence: 99%

Numerical Study on the Buckling Behavior of FG Porous Spherical Caps Reinforced by Graphene Platelets

et al. 2023

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The buckling response of functionally graded (FG) porous spherical caps reinforced by graphene platelets (GPLs) is assessed here, including both symmetric and uniform porosity patterns in the metal matrix, together with five different GPL distributions. The Halpin–Tsai model is here applied, together with an extended rule of mixture to determine the elastic properties and mass density of the selected shells, respectively. The equilibrium equations of the pre-buckling state are here determined according to a linear three-dimensional (3D) elasticity basics and principle of virtual work, whose solution is determined from classical finite elements. The buckling load is, thus, obtained based on the nonlinear Green strain field and generalized geometric stiffness concept. A large parametric investigation studies the sensitivity of the natural frequencies of FG porous spherical caps reinforced by GPLs to different parameters, namely, the porosity coefficients and distributions, together with different polar angles and stiffness coefficients of the elastic foundation, but also different GPL patterns and weight fractions of graphene nanofillers. Results denote that the maximum and minimum buckling loads are reached for GPL-X and GPL-O distributions, respectively. Additionally, the difference between the maximum and minimum critical buckling loads for different porosity distributions is approximately equal to 90%, which belong to symmetric distributions. It is also found that a high weight fraction of GPLs and a high porosity coefficient yield the highest and lowest effects of the structure on the buckling loads of the structure for an amount of 100% and 12.5%, respectively.

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“…where v GPL and v m are the Poisson's ratio of the nanofillers and matrix, respectively. The shear modulus, G, of the shell part is expressed as below [66][67][68][69][70]:…”

Section: Definition Of the Geometry And Materials Properties Of The S...mentioning

confidence: 99%

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Zhou,

Zhang,

Nyasha Chirukam

et al. 2023

Mathematics

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In this paper, the free vibration response of a stiffened functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer cylindrical shell panel is studied for the first time. The shell is stiffened by both stringers and rings. Additionally, the effect of reinforcing the shell panel, ring and stinger with GPLs is independently studied. Halpin–Tsai relations are employed to evaluate the mechanical properties of the shell panel, rings and stringers. The first-order shear deformation shell theory, accompanied by the Lekhnitsky smeared stiffener model, using the numerical finite element method and Hamilton principle, is employed to develop the governing motion equations of the shell panel. Four different types of GPL patterns, including FG-A, FG-X, FG-O and UD, are assumed across the thickness of the shell panel, rings and stringers. The effects of different factors, including various weight fractions and patterns of GPLs nanofillers, the geometry of the shell panel and stiffeners and two displacement boundary conditions, on the natural frequencies of the shell panel, have been studied.

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Transient Thermal Stresses in FG Porous Rotating Truncated Cones Reinforced by Graphene Platelets

Cited by 21 publications

References 62 publications

A New Reduced-Dimension Iteration Two-Grid Crank–Nicolson Finite-Element Method for Unsaturated Soil Water Flow Problem

A New Reduced-Dimension Iteration Two-Grid Crank–Nicolson Finite-Element Method for Unsaturated Soil Water Flow Problem

Numerical Study on the Buckling Behavior of FG Porous Spherical Caps Reinforced by Graphene Platelets

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

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