Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

Zhang, Y.P.; Challamel, Noël; Wang, Chen; Zhang, H.

doi:10.1007/s00707-018-2326-9

Cited by 18 publications

(8 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further, by skipping the common operator 1 À kr 2 ð Þ as in [22,41], Eq. (10) leads to the following more compact form of the equilibrium equation in terms of Marcus' moment…”

Section: Problem Definitionmentioning

confidence: 99%

“…In this regard, consider a simply supported rectangular plate, of length a and width b. The boundary conditions for the four edges are given as [41] Observe that this feature is the basis of the controversy in the literature on the appropriate applications of the BCs for nonlocal plates. Specifically, certain problems and paradoxical results have been increasingly discussed in the literature of nonlocal beams and plates, due to the proper definition and treatment of the associated boundary conditions [24,29,30].…”

Section: Formulation Of Boundary Conditionsmentioning

confidence: 99%

“…Finally, the case of nonlocal polygonal Kirchhoff plates has been analyzed in [22], where a solution of the bending problem has been found considering only simply-supported boundary conditions, and resorting to analogies with the solution of the classical (local) Kirchhoff plate. These results have been then exploited in [41] to compare the response of different plates models at the nano scale.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

2021

View full text Add to dashboard Cite

In this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the proposed procedure yields approximate analytical solutions for general shapes and boundary conditions, and even exact solutions for some plate geometries. In addition, several applications are discussed to show the simplicity and applicability of the procedure, and comparison with pertinent data in the literature assesses the accuracy of the proposed approach.

show abstract

“…Further, by skipping the common operator 1 À kr 2 ð Þ as in [22,41], Eq. (10) leads to the following more compact form of the equilibrium equation in terms of Marcus' moment…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Formulation Of Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

2021

View full text Add to dashboard Cite

show abstract

“…As this article is concerned with Eringen’s nonlocal elasticity theory to implement the small-scale effects, the nonlocal stress can be appeared as 14,45–48…”

Section: Constitutive Equations and Solutionmentioning

confidence: 99%

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

Dastjerdi

Malikan

2020

Proceedings of the Institution of Mechanical Engineers, Part N:

View full text Add to dashboard Cite

In this article, we have tried to simulate nonlinear bending analysis of a double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the double-layered graphene sheet has been considered, the effect of van der Waals forces has been taken into account in the analysis. In order to implement the nanoscale impact, the nonlocal elasticity theory has been employed. The solution methodology, which is here based on the semi-analytical polynomial method solving technique presented previously by the authors, has been applied and again its efficiency has been demonstrated due to its highly accurate results. Due to the fact that this research has been done for the first time and there is no validation available, the results of the local single layer sheet are compared with ABAQUS software. The effects of some other parameters on the results have been studied such as the value of eccentricity, van der Waals interaction, and nonlocal parameter.

show abstract

“…Hereinafter, the FRP bar is considered an elastic rod. For a one-dimensional problem in which the longitudinal coordinates are represented by x, Eringen's nonlocal constitutive relation can be expressed as [29][30][31] 1…”

Section: Governing Equations Of the Nonlocal Elastic Modelmentioning

confidence: 99%

Analyzing the Bond Behavior of Fiber-Reinforced Polymer (FRP) Bars Embedded in Engineered Cementitious Composites (ECCs) with the Nonlocal Continuum Rod Model

Ming-fu

Xie

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this study, a nonlocal elastic rod model is applied to analytically evaluate the bond behavior between fiber-reinforced polymer (FRP) bars and engineered cementitious composites (ECCs). The second-order differential equation, which is based on nonlocal elasticity theory, governs the bond behavior of the FRP bars along the bond length. The classical elasticity model is a special case of the nonlocal model. The solution of the second-order differential equation can be obtained by substituting three-stage linear bond stress-slip relationship of the FRP bars. The slip values (solution of the second-order differential equation) within the bond length calculated by the nonlocal continuum rod model are affected by the nonlocal parameter e0a. The results from a case study show that the maximum pullout force decreases when the nonlocal size effect is considered, thereby providing a closer approximation of the experimental data than the existing local model.

show abstract

Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

Cited by 18 publications

References 48 publications

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

Analyzing the Bond Behavior of Fiber-Reinforced Polymer (FRP) Bars Embedded in Engineered Cementitious Composites (ECCs) with the Nonlocal Continuum Rod Model

Contact Info

Product

Resources

About