Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

Hoa, Le Kha; Vinh, Pham Van; Duc, Nguyen Dinh; Nguyen-Thoi, T.; Son, Le Truong; Thom, Do Van

doi:10.1177/0954406220964522

Cited by 43 publications

(14 citation statements)

References 76 publications

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“…In this case the nonlocal effect of FG nanoplates is investigated. A validation example compared with Sobhy [ 58 ] and Hoa et al [ 59 ] is provided using the following non-dimensional displacement and stresses

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Section: Resultsmentioning

confidence: 99%

Nonlocal Strain Gradient Theory for the Bending of Functionally Graded Porous Nanoplates

Alghanmi

2022

Materials

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Many investigators have become interested in nanostructures due to their outstanding mechanical, chemical, and electrical properties. Two-dimensional nanoplates with higher mechanical properties compared with traditional structural applications are a common structure of nanosystems. Nanoplates have a wide range of uses in various sectors due to their unique properties. This paper focused on the static analysis of functionally graded (FG) nanoplates with porosities. The nonlocal strain gradient theory is combined with four-variable shear deformation theory to model the nanoplate. The proposed model captures both nonlocal and strain gradient impacts on FG nanoplate structures by incorporating the nonlocal and strain gradient factors into the FG plate’s elastic constants. Two different templates of porosity distributions are taken into account. The FG porous nanoplate solutions are compared with previously published ones. The impact of nonlocal and strain gradient parameters, side-to-thickness ratio, aspect ratio, and porosity parameter, are analyzed in detail numerically. This paper presents benchmark solutions for the bending analysis of FG porous nanoplates. Moreover, the current combination of the nonlocal strain gradient theory and the four-variable shear deformation theory can be adapted for various nanostructured materials such as anisotropic, laminated composites, FG carbon nanotube reinforced composites, and so on.

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…”

Section: Resultsmentioning

confidence: 99%

Nonlocal Strain Gradient Theory for the Bending of Functionally Graded Porous Nanoplates

Alghanmi

2022

Materials

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“…After that, plenty of researches are accomplished to analyse the bending, buckling, and vibration response of distinct nano-structures such as nano sized beams, plates, and shells using this theory. [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Researchers have also used the nonlocal theory to study the cracks in the macro-structures. 34 Recently, Van et al 35 presented a size-dependent refined plate theory and studied the bending and vibrations of graphenereinforced composite nano-plates with different types of gradation of graphene platelets.…”

Section: Introductionmentioning

confidence: 99%

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

Chandel

Talha

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper emphasized the size-dependent thermo-elastic vibration characteristics of uncertain functionally graded (FG) porous nano-beams by employing the first-order perturbation theory (FOPT) with the finite element method. An isoparametric quadratic beam element having three nodes is used for the finite element analysis of the nano-beams with variation in degree of uncertainty in material properties, geometric configuration, and thermal environment. The power-law model is employed to obtain the effective material properties of the considered beams. The governing equations are presented according to Eringen’s elasticity theory and Reddy’s beam theory using the minimum potential energy. The computed FOPT results for the vibration statistics are assessed with the help of Monte Carlo simulation (MCS) and a well agreement is found. Further, results are presented by analyzing the effects of degree of source uncertainty, size-dependent parameter, volume fraction indices, porosity distribution, porosity index, thermal environment, and aspect ratios on the fundamental frequency of the FGM nano-beams. The numerical results revealed the significant influence of thermal environment and porosity on the vibration statistics of the nano-beams and provided guidance for the precise and reliable design of nano-devices for the application in thermal environment.

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“…In recent decades, due to the science and technology are developed so rapidly, many intelligent materials appear to serve the complicated requirements in engineering practice such as functionally graded materials (FGMs), piezoelectrics, electroactive polymers, magnetostrictive, and shape memory alloys, in which functionally graded materials are one of the most important and popular structures, which are used and considered widely by scientists worldwide. Traditionally, FGMs are a remarkable type of composite structure, where the material characteristics change gradually and smoothly from one surface to the other ones [1][2][3][4], where they can be dealt with and designed for special duties and applications. A huge number of methods, which are founded by the particulate process, layer process, and melting process are employed to manufacture the FG structures [5].…”

Section: Introductionmentioning

confidence: 99%

The Third‐Order Shear Deformation Theory for Modeling the Static Bending and Dynamic Responses of Piezoelectric Bidirectional Functionally Graded Plates

Dung

Minh

Hùng

et al. 2021

Advances in Materials Science and Engineering

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This work is the first exploration of the static bending and dynamic response analyses of piezoelectric bidirectional functionally graded plates by combining the third-order shear deformation theory of Reddy and the finite element approach, which can numerically model mechanical relations of the structure. The present approach and mechanical model are confirmed through the verification examples. The geometrical and material study is conducted to evaluate the effects of the feedback coefficients, volume fraction parameter, and constraint conditions on the static and dynamic behaviors of piezoelectric bidirectional functionally graded structures, and this work presents a wide variety of static and dynamic behaviors of the plate with many interesting results. There are many meanings that have not been mentioned by any work, especially the working performance of the structure is better than that when the feedback parameter of the piezoelectric component is added, that is, the piezoelectric layer increases the working efficiency. Numerical investigations are the important basis for calculating and designing related materials and structures in technical practice.

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Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

Cited by 43 publications

References 76 publications

Nonlocal Strain Gradient Theory for the Bending of Functionally Graded Porous Nanoplates

Nonlocal Strain Gradient Theory for the Bending of Functionally Graded Porous Nanoplates

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

The Third‐Order Shear Deformation Theory for Modeling the Static Bending and Dynamic Responses of Piezoelectric Bidirectional Functionally Graded Plates

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