Static and stability analysis of nonlocal functionally graded nanobeams
TL;DR: In this paper, the size-dependent static-buckling behavior of functionally graded (FG) nanobeams is investigated on the basis of the nonlocal continuum model, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators.
About: This article is published in Composite Structures.The article was published on 2013-02-01. It has received 236 citations till now. The article focuses on the topics: Timoshenko beam theory & Finite element method.
Citations
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TL;DR: In this article, a size-dependent Timoshenko beam model, which accounts for through-thickness power-law variation of a two-constituent functionally graded (FG) material, is derived in the framework of the nonlocal strain gradient theory.
349 citations
TL;DR: In this article, the effects of the gradient index, length scale parameter and length-to-thickness ratio on the vibration of functionally graded material (FGM) nanobeams were examined.
282 citations
TL;DR: In this paper, a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures is presented, mainly focusing on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory.
275 citations
TL;DR: In this paper, a review aimed at directing the light to research work concerned with bending, buckling, vibrations, and wave propagation of nanobeams modeled according to the nonlocal elasticity theory of Eringen.
272 citations
TL;DR: In this article, the effects of the through-thickness power-law variation of a two-constituent functionally graded (FG) material and size-dependent parameters on nonlinear bending deflection and free vibration frequencies are investigated.
254 citations
References
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TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.
Abstract: Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.
3,929 citations
"Static and stability analysis of no..." refers background in this paper
...Unlike the constitutive equation in classical elasticity, Eringen’s nonlocal elasticity theory [2] states that the stress at a point x in a body depends not only on the strain at point x but also on those at all other points of the body....
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...One widely promising size-dependent continuum theory is the nonlocal elasticity theory pioneered by Eringen [2]....
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Book•
01 Jan 1984
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
3,043 citations
Additional excerpts
...(4) and obtain, Reddy [40] Z L...
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TL;DR: In this article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.
1,519 citations
"Static and stability analysis of no..." refers background or methods or result in this paper
...Reddy [5] reformulated local beam theory by using the nonlocal differential constitutive relations of Eringen to study bending, vibration, and buckling behaviors of nanobeams....
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...L/h l Reddy [5] Aydogdu [7] Present...
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...L/h l Analytical Reddy [5] Aydogdu [7] Present...
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...The results are closer to those of Aydogdu [7] than those presented by Reddy [5]....
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...As can be noted, the obtained results are identical for analytical solution and a good agreement with those of Reddy [5] and Aydogdu [7] [Error = % 0....
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Book•
01 Jan 2016
TL;DR: The Theory and Analysis of Elastic Plates and Shells, Second Edition as mentioned in this paper presents a complete survey of the behavior of these structural elements in aerospace, automotive, and civil engineering structures.
Abstract: Because plates and shells are common structural elements in aerospace, automotive, and civil engineering structures, engineers must understand the behavior of such structures through the study of theory and analysis. Compiling this information into a single volume, Theory and Analysis of Elastic Plates and Shells, Second Edition presents a complete
1,253 citations
"Static and stability analysis of no..." refers methods in this paper
...The kinematic relations according to Euler– Bernoulli beam theory are given by, Reddy [37]...
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TL;DR: In this paper, the dynamic thermoelastic response of functionally graded cylinders and plates is studied, and a finite element model of the formulation is developed, where the heat conduction and the thermo-elastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading.
Abstract: The dynamic thermoelastic response of functionally graded cylinders and plates is studied. Thermomechanical coupling is included in the formulation, and a finite element model of the formulation is developed. The heat conduction and the thermoelastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading. In addition, a thermoelastic boundary value problem using the first-order shear deformation plate theory (FSDT) that accounts for the transverse shear strains and the rotations, coupled with a three-dimensional heat conduction equation, is formulated for a functionally graded plate. Both problems are studied by varying the volume fraction of a ceramic and a metal using a power law distribution.
1,196 citations
"Static and stability analysis of no..." refers background in this paper
...Reddy [18] and Praveen [19] studied the thermo-mechanical behavior of FG plates....
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