A comprehensive study on the size-dependent analysis of strain gradient multi-directional functionally graded microplates via finite element model

Karamanlı, Armağan; Aydoğdu, Metin; Vo, Thuc P.

doi:10.1016/j.ast.2021.106550

Cited by 41 publications

(7 citation statements)

References 69 publications

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“…in which ξ is the evaluation coefficient of the porosity volume of the shallow shell. The temperature-dependent characteristics are denoted by S i and may be represented as [30].…”

Section: Description Of the Mfgp Shallow Shellmentioning

confidence: 99%

“…The power distribution law of the MFGP doubly‐curved shallow shells is given by [30]:

S = S_{m} + (S_{c} - S_{m}) {((), \frac{1}{2} goodbreak+ \frac{z}{h})}^{n_{z}} {((), \frac{x}{a})}^{n_{x}} {((), \frac{y}{b})}^{n_{y}} - φ (S_{c} + S_{m}),

where

S

stands for Young's modulus

E

, mass density

ρ

; thermal expansion coefficient

α

; subscripts

m

and

c

indicate metallic and ceramic components, respectively. The Poisson's ratio is considered to be constant and does not depend on the change of the material's mechanical properties;

n_{z}, n_{x},

and

n_{y}

are the power‐law indexes, and

φ

represents the law that controls porosity.…”

Section: Model Of Mfgp Doubly‐curved Shallow Shellsmentioning

confidence: 99%

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An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

Pham,

Tran,

Nguyen

2024

Math Methods in App Sciences

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This paper uses the analytical method with arbitrary boundary conditions to model and analyze the free vibrations of multi‐directionally functionally graded porous (MFGP) doubly‐curved shallow shells resting on the Pasternak foundation in a temperature environment. It is anticipated that all mechanical parameters, except Poisson's ratio, will change in the direction of length, width, and thickness. To comprehensively describe the shell's displacement, strain, and stress fields, a modified first‐order shear deformation theory (FSDT) with an assumption of cosine distribution shear stresses has been developed. The fact that the enhanced FSDT theory does not require the use of shear correction and that the shear stress at the two free faces of the shells is zero are two of the theory's most significant advantages. Using Hamilton's principle and improved FSDT, one may get the governing equation for free vibration analysis of MFGP doubly‐curved shallow shells. The Galerkin approach is proposed to solve the governing equation of MFGP doubly‐curved shallow shells with various boundary conditions. The trustworthiness of the article is evaluated via its publication in the article model's several special cases. From this point on, a collection of findings about the natural frequency of MFGP doubly‐curved shallow shells is identified and shown in the form of tables and graphs. The results provided in this manuscript can be used as a benchmark solution for further studies as far as the vibration behavior of the MFGP doubly‐curved shallow shells is concerned.

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“…in which ξ is the evaluation coefficient of the porosity volume of the shallow shell. The temperature-dependent characteristics are denoted by S i and may be represented as [30].…”

Section: Description Of the Mfgp Shallow Shellmentioning

confidence: 99%

“…The power distribution law of the MFGP doubly‐curved shallow shells is given by [30]:

S = S_{m} + (S_{c} - S_{m}) {((), \frac{1}{2} goodbreak+ \frac{z}{h})}^{n_{z}} {((), \frac{x}{a})}^{n_{x}} {((), \frac{y}{b})}^{n_{y}} - φ (S_{c} + S_{m}),

where

S

stands for Young's modulus

E

, mass density

ρ

; thermal expansion coefficient

α

; subscripts

m

and

c

indicate metallic and ceramic components, respectively. The Poisson's ratio is considered to be constant and does not depend on the change of the material's mechanical properties;

n_{z}, n_{x},

and

n_{y}

are the power‐law indexes, and

φ

represents the law that controls porosity.…”

Section: Model Of Mfgp Doubly‐curved Shallow Shellsmentioning

confidence: 99%

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

Pham,

Tran,

Nguyen

2024

Math Methods in App Sciences

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“…Ghobadi et al [49] performed a size-dependent thermo-electro-mechanical free oscillation analysis of graded flexoelectric nanoplates using a perturbation technique. Karamanli et al [50] utilized the modified strain gradient continuum elasticity for size-dependent linear mechanical analysis of microplates having multi-directional heterogeneity. Hou et al [51], Yang et al [52], Wang et al [53], Tang et al [54], Sahmani et al [55], and Ma et al [56] constructed plate models having non-uniform thickness on the basis of different unconventional elasticity theories for nonlinear mechanical responses of functionally graded composite sector and elliptical nanoplates.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal couple stress-based quasi-3D nonlinear dynamics of agglomerated CNT-reinforced micro/nano-plates before and after bifurcation phenomenon

2023

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In present research exploration, the nonlinear dynamic stability characteristics of axially compressed nanocomposite plates at micro/nano-scale reinforced with randomly oriented carbon nanotubes (CNTs) are investigated within the both prebuckling and postbuckling regimes. To accomplish this examination, the nonlocal couple stress (NCS) continuum elasticity is incorporated to a quasi-3D plate theory which separates the plate deformation to the bending and shear parts considering simultaneously the transverse shear and normal displacements. In addition, a two-parameter homogenization scheme is utilized to obtain the effective characters of the randomly oriented CNT-reinforced nanocomposites. The NCS-based nonlinear differential equations of motion are discretized using the Kronecker tensor product together with the shifted Chebyshev-Gauss-Lobatto gridding pattern. Thereafter, the Galerkin technique together with the pseudo arc-length continuation method are employed to achieve the NCS-based frequency-load and nonlinear frequency ratio-deflection curves before and after of the bifurcation point. It is deduced that for a randomly oriented CNT-reinforced heterogeneous micro/nano-plate in which the most CNTs are located inside clusters, increasing the value of cluster volume fraction leads to increase a bit the significance of the softening and stiffing characters related to the nonlocal and couple stress tensors before the bifurcation phenomenon, but it causes to decrease them after the critical bifurcation point. Opposite patterns before and after the bifurcation phenomenon are predicted for the agglomeration in which the most CNTs are located outside clusters.

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“…The functional gradient plate structures composed by a variety of materials combine the excellent performance of a variety of component materials, so the functional gradient plates are important in the fields of aerospace, transportation engineering, construction and other fields. The interference of the plate structures is taken from external conditions in the process of work, and many mechanical behaviors such as bending and vibration, so many scholars have made a lot of research on the mechanical behaviors of the plates and have achieved rich research results [10][11][12][13][14][15][16]. Mao [17] investigated the modal perfor-mance of a sandwich composite plate and provided a new design idea for dynamic behaviors of sandwich plates.…”

Section: Introductionmentioning

confidence: 99%

Static Bending and Vibration Analysis of a Rectangular Functionally Gradient Piezoelectric Plate on an Elastic Foundation

Wei

Yao

2022

Applied Sciences

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In this paper, a functionally graded piezoelectric plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, and its static bending and fundamental frequencies are analyzed. First, based on Kirchhoff plate theory and the Hamilton principle, the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method (DQM). Finally, the effects of physical parameters such as length-to-height ratio, length-to-width ratio, material graded index, foundation stiffness coefficient, temperature change value and external voltage value on static bending deflection, and fundamental frequency value of the functionally graded piezoelectric plate with four sides simply supported are discussed. The calculated results are in good agreement with those in the literature. The data results show that the increase in the elastic foundation stiffness coefficient will increase the equivalent stiffness of the plate. In the process of work, due to the equivalent pressure value generated by the influence of the external voltage, it will lead to unstable phenomena.

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A comprehensive study on the size-dependent analysis of strain gradient multi-directional functionally graded microplates via finite element model

Cited by 41 publications

References 69 publications

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

Nonlocal couple stress-based quasi-3D nonlinear dynamics of agglomerated CNT-reinforced micro/nano-plates before and after bifurcation phenomenon

Static Bending and Vibration Analysis of a Rectangular Functionally Gradient Piezoelectric Plate on an Elastic Foundation

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